Safe Haskell	Safe-Inferred
Language	GHC2021

I

Contents

Interval
Known
Testing
Danger

Description

I am a Haskell module designed to be imported as follows:

import I (I)
import I qualified

I exist so that you don't have to manually check that a value is within an interval. For example:

I Int (N 5) (P 5): An Int known to be in the interval [-5, +5].
I Natural 100 'Nothing: A Natural known to be in the interval [100, +infinity).
I Rational ('Just '( 'False, 0 / 1)) ('Just '( 'True, 1 / 2)): A Rational known to be in the interval (0, +0.5].

Synopsis

data I (x :: Type) (l :: L x) (r :: R x)
type family T (x :: Type) :: k
type family MinT (x :: Type) :: T x
type family MaxT (x :: Type) :: T x
type family L (x :: Type) :: k
type family MinL (x :: Type) :: L x
type family R (x :: Type) :: k
type family MaxR (x :: Type) :: R x
class IntervalCtx x l r => Interval (x :: Type) (l :: L x) (r :: R x) where
- type IntervalCtx x l r :: Constraint
- type MinI x l r :: T x
- type MaxI x l r :: T x
- inhabitant :: I x l r
- from :: x -> Maybe (I x l r)
- plus' :: I x l r -> I x l r -> Maybe (I x l r)
- mult' :: I x l r -> I x l r -> Maybe (I x l r)
- minus' :: I x l r -> I x l r -> Maybe (I x l r)
- negate' :: I x l r -> Maybe (I x l r)
- recip' :: I x l r -> Maybe (I x l r)
- div' :: I x l r -> I x l r -> Maybe (I x l r)
unwrap :: forall x l r. I x l r -> x
wrap :: Interval x (MinL x) (MaxR x) => x -> I x (MinL x) (MaxR x)
unsafe :: forall x l r. (HasCallStack, Interval x l r) => x -> I x l r
class Interval x l r => Clamp (x :: Type) (l :: L x) (r :: R x) where
- clamp :: x -> I x l r
class (Interval x ld rd, Interval x lu ru) => Up (x :: Type) (ld :: L x) (rd :: R x) (lu :: L x) (ru :: R x) where
- up :: I x ld rd -> I x lu ru
down :: forall x lu ru ld rd. Interval x ld rd => I x lu ru -> Maybe (I x ld rd)
class Interval x l r => Discrete (x :: Type) (l :: L x) (r :: R x) where
- pred' :: I x l r -> Maybe (I x l r)
- succ' :: I x l r -> Maybe (I x l r)
class Discrete x l r => Succ (x :: Type) (l :: L x) (r :: R x) where
- succ :: I x l r -> I x l r
class Discrete x l r => Pred (x :: Type) (l :: L x) (r :: R x) where
- pred :: I x l r -> I x l r
class Interval x l r => One (x :: Type) (l :: L x) (r :: R x) where
- one :: I x l r
class Interval x l r => Zero (x :: Type) (l :: L x) (r :: R x) where
- zero :: I x l r
class Zero x l r => Negate (x :: Type) (l :: L x) (r :: R x) where
- negate :: I x l r -> I x l r
class Interval x l r => Plus (x :: Type) (l :: L x) (r :: R x) where
- plus :: I x l r -> I x l r -> I x l r
class Interval x l r => Mult (x :: Type) (l :: L x) (r :: R x) where
- mult :: I x l r -> I x l r -> I x l r
class Zero x l r => Minus (x :: Type) (l :: L x) (r :: R x) where
- minus :: I x l r -> I x l r -> I x l r
class Interval x l r => Div (x :: Type) (l :: L x) (r :: R x) where
- div :: I x l r -> I x l r -> I x l r
class (Interval x l r, KnownCtx x l r t) => Known (x :: Type) (l :: L x) (r :: R x) (t :: T x) where
- type KnownCtx x l r t :: Constraint
- known' :: Proxy t -> I x l r
known :: forall {x} t l r. Known x l r t => I x l r
class Interval x l r => With (x :: Type) (l :: L x) (r :: R x) where
- with :: I x l r -> (forall (t :: T x). Known x l r t => Proxy t -> b) -> b
min :: forall x l r. Known x l r (MinI x l r) => I x l r
max :: forall x l r. Known x l r (MaxI x l r) => I x l r
single :: forall x l r. (MinI x l r ~ MaxI x l r, Known x l r (MinI x l r)) => I x l r
class Interval x l r => Shove (x :: Type) (l :: L x) (r :: R x) where
- shove :: x -> I x l r
unsafest :: forall x l r. x -> I x l r

type MaxR CChar Source #
Instance details Defined in I.Autogen.CChar type MaxR CChar = MaxT CChar
type MaxR CInt Source #
Instance details Defined in I.Autogen.CInt type MaxR CInt = MaxT CInt
type MaxR CIntMax Source #
Instance details Defined in I.Autogen.CIntMax type MaxR CIntMax = MaxT CIntMax
type MaxR CIntPtr Source #
Instance details Defined in I.Autogen.CIntPtr type MaxR CIntPtr = MaxT CIntPtr
type MaxR CLLong Source #
Instance details Defined in I.Autogen.CLLong type MaxR CLLong = MaxT CLLong
type MaxR CLong Source #
Instance details Defined in I.Autogen.CLong type MaxR CLong = MaxT CLong
type MaxR CPtrdiff Source #
Instance details Defined in I.Autogen.CPtrdiff type MaxR CPtrdiff = MaxT CPtrdiff
type MaxR CSChar Source #
Instance details Defined in I.Autogen.CSChar type MaxR CSChar = MaxT CSChar
type MaxR CShort Source #
Instance details Defined in I.Autogen.CShort type MaxR CShort = MaxT CShort
type MaxR CSize Source #
Instance details Defined in I.Autogen.CSize type MaxR CSize = MaxT CSize
type MaxR CUChar Source #
Instance details Defined in I.Autogen.CUChar type MaxR CUChar = MaxT CUChar
type MaxR CUInt Source #
Instance details Defined in I.Autogen.CUInt type MaxR CUInt = MaxT CUInt
type MaxR CUIntMax Source #
Instance details Defined in I.Autogen.CUIntMax type MaxR CUIntMax = MaxT CUIntMax
type MaxR CUIntPtr Source #
Instance details Defined in I.Autogen.CUIntPtr type MaxR CUIntPtr = MaxT CUIntPtr
type MaxR CULLong Source #
Instance details Defined in I.Autogen.CULLong type MaxR CULLong = MaxT CULLong
type MaxR CULong Source #
Instance details Defined in I.Autogen.CULong type MaxR CULong = MaxT CULong
type MaxR CUShort Source #
Instance details Defined in I.Autogen.CUShort type MaxR CUShort = MaxT CUShort
type MaxR CWchar Source #
Instance details Defined in I.Autogen.CWchar type MaxR CWchar = MaxT CWchar
type MaxR Int16 Source #
Instance details Defined in I.Autogen.Int16 type MaxR Int16 = MaxT Int16
type MaxR Int32 Source #
Instance details Defined in I.Autogen.Int32 type MaxR Int32 = MaxT Int32
type MaxR Int64 Source #
Instance details Defined in I.Autogen.Int64 type MaxR Int64 = MaxT Int64
type MaxR Int8 Source #
Instance details Defined in I.Int8 type MaxR Int8 = MaxT Int8
type MaxR Rational Source #
Instance details Defined in I.Rational type MaxR Rational = 'Nothing :: Maybe (Bool, Rational)
type MaxR Word16 Source #
Instance details Defined in I.Autogen.Word16 type MaxR Word16 = MaxT Word16
type MaxR Word32 Source #
Instance details Defined in I.Autogen.Word32 type MaxR Word32 = MaxT Word32
type MaxR Word64 Source #
Instance details Defined in I.Autogen.Word64 type MaxR Word64 = MaxT Word64
type MaxR Word8 Source #
Instance details Defined in I.Word8 type MaxR Word8 = MaxT Word8
type MaxR Integer Source #
Instance details Defined in I.Integer type MaxR Integer = 'Nothing :: Maybe Integer
type MaxR Natural Source #
Instance details Defined in I.Natural type MaxR Natural = 'Nothing :: Maybe Natural
type MaxR Int Source #
Instance details Defined in I.Autogen.Int type MaxR Int = MaxT Int
type MaxR Word Source #
Instance details Defined in I.Autogen.Word type MaxR Word = MaxT Word

class IntervalCtx x l r => Interval (x :: Type) (l :: L x) (r :: R x) where Source #

For I x l r to be a valid interval type, Interval x l r needs to be satisfied. All Intervals are non-empty.

NB: When defining Interval instances, instead of mentioning any necessary constraints in the instance context, mention them them in IntervalCtx. By doing so, when an instance of Interval x l r is satisfied, IntervalCtx x l r is satisfied as well. If you don't do this, with won't behave as you would expect.

Minimal complete definition

inhabitant, from

Associated Types

type IntervalCtx x l r :: Constraint Source #

Constraints to be satisfied for I x l r to be a valid non-empty interval type.

type IntervalCtx x l r = ()

type MinI x l r :: T x Source #

Minimum value of type x contained in the interval I x l r, if any. If I x l r is unbounded on the left end, then it's ok to leave MinI x l r undefined. If defined, it should mean the same as l.

type MinI x l r = TypeError (('Text "MinI not defined in instance \8216" ':<>: 'ShowType (Interval x l r)) ':<>: 'Text "\8217")

type MaxI x l r :: T x Source #

Maximum value of type x contained in the interval I x l r, if any. If I x l r is unbounded on the right end, then it's ok to leave MaxI x l r undefined. If defined, it should mean the same as r.

type MaxI x l r = TypeError (('Text "MaxI not defined in instance \8216" ':<>: 'ShowType (Interval x l r)) ':<>: 'Text "\8217")

Methods

inhabitant :: I x l r Source #

Proof that there is at least one element in the I x l r interval.

No guarantees are made about the value of inhabitant other than the fact that it is known to inhabit the interval. The only exception to this are intervals that contain a single inhabitant, in which case inhabitant will produce it. See single.

from :: x -> Maybe (I x l r) Source #

Wrap the x value in the interval I x l r, if it fits.

Consider using wrap if the interval includes all values of type x.
Consider using known if you have type-level knowledge about the value of x.
Consider using unsafe if you know that the x is within the interval.

Identity law

forall (x :: Type).
  such that isJust (from x).
    fmap unwrap (from x)  ==  Just x

plus' :: I x l r -> I x l r -> Maybe (I x l r) Source #

plus' a b adds a and b.

Nothing if the result would be out of the interval. See plus, too.

mult' :: I x l r -> I x l r -> Maybe (I x l r) Source #

mult' a b multiplies a times b.

Nothing if the result would be out of the interval. See mult, too.

minus' :: I x l r -> I x l r -> Maybe (I x l r) Source #

minus' a b substracts b from a.

Nothing if the result would be out of the interval. See minus, too.

negate' :: I x l r -> Maybe (I x l r) Source #

negate' a is the additive inverse of a.

Nothing if the result would be out of the interval. See negate, too.

recip' :: I x l r -> Maybe (I x l r) Source #

recip' a is the multiplicative inverse of a.

Nothing if the result would be out of the interval.

div' :: I x l r -> I x l r -> Maybe (I x l r) Source #

div' a b divides a by b.

Nothing if the result would be out of the interval. See div too.

Instances

Instances details

IntervalCtx CChar l r => Interval CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Associated Types type IntervalCtx CChar l r Source # type MinI CChar l r :: T x :: Type Source # type MaxI CChar l r :: T x :: Type Source # Methods inhabitant :: I CChar l r Source # from :: CChar -> Maybe (I CChar l r) Source # plus' :: I CChar l r -> I CChar l r -> Maybe (I CChar l r) Source # mult' :: I CChar l r -> I CChar l r -> Maybe (I CChar l r) Source # minus' :: I CChar l r -> I CChar l r -> Maybe (I CChar l r) Source # negate' :: I CChar l r -> Maybe (I CChar l r) Source # recip' :: I CChar l r -> Maybe (I CChar l r) Source # div' :: I CChar l r -> I CChar l r -> Maybe (I CChar l r) Source #
IntervalCtx CInt l r => Interval CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Associated Types type IntervalCtx CInt l r Source # type MinI CInt l r :: T x :: Type Source # type MaxI CInt l r :: T x :: Type Source # Methods inhabitant :: I CInt l r Source # from :: CInt -> Maybe (I CInt l r) Source # plus' :: I CInt l r -> I CInt l r -> Maybe (I CInt l r) Source # mult' :: I CInt l r -> I CInt l r -> Maybe (I CInt l r) Source # minus' :: I CInt l r -> I CInt l r -> Maybe (I CInt l r) Source # negate' :: I CInt l r -> Maybe (I CInt l r) Source # recip' :: I CInt l r -> Maybe (I CInt l r) Source # div' :: I CInt l r -> I CInt l r -> Maybe (I CInt l r) Source #
IntervalCtx CIntMax l r => Interval CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Associated Types type IntervalCtx CIntMax l r Source # type MinI CIntMax l r :: T x :: Type Source # type MaxI CIntMax l r :: T x :: Type Source # Methods inhabitant :: I CIntMax l r Source # from :: CIntMax -> Maybe (I CIntMax l r) Source # plus' :: I CIntMax l r -> I CIntMax l r -> Maybe (I CIntMax l r) Source # mult' :: I CIntMax l r -> I CIntMax l r -> Maybe (I CIntMax l r) Source # minus' :: I CIntMax l r -> I CIntMax l r -> Maybe (I CIntMax l r) Source # negate' :: I CIntMax l r -> Maybe (I CIntMax l r) Source # recip' :: I CIntMax l r -> Maybe (I CIntMax l r) Source # div' :: I CIntMax l r -> I CIntMax l r -> Maybe (I CIntMax l r) Source #
IntervalCtx CIntPtr l r => Interval CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Associated Types type IntervalCtx CIntPtr l r Source # type MinI CIntPtr l r :: T x :: Type Source # type MaxI CIntPtr l r :: T x :: Type Source # Methods inhabitant :: I CIntPtr l r Source # from :: CIntPtr -> Maybe (I CIntPtr l r) Source # plus' :: I CIntPtr l r -> I CIntPtr l r -> Maybe (I CIntPtr l r) Source # mult' :: I CIntPtr l r -> I CIntPtr l r -> Maybe (I CIntPtr l r) Source # minus' :: I CIntPtr l r -> I CIntPtr l r -> Maybe (I CIntPtr l r) Source # negate' :: I CIntPtr l r -> Maybe (I CIntPtr l r) Source # recip' :: I CIntPtr l r -> Maybe (I CIntPtr l r) Source # div' :: I CIntPtr l r -> I CIntPtr l r -> Maybe (I CIntPtr l r) Source #
IntervalCtx CLLong l r => Interval CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Associated Types type IntervalCtx CLLong l r Source # type MinI CLLong l r :: T x :: Type Source # type MaxI CLLong l r :: T x :: Type Source # Methods inhabitant :: I CLLong l r Source # from :: CLLong -> Maybe (I CLLong l r) Source # plus' :: I CLLong l r -> I CLLong l r -> Maybe (I CLLong l r) Source # mult' :: I CLLong l r -> I CLLong l r -> Maybe (I CLLong l r) Source # minus' :: I CLLong l r -> I CLLong l r -> Maybe (I CLLong l r) Source # negate' :: I CLLong l r -> Maybe (I CLLong l r) Source # recip' :: I CLLong l r -> Maybe (I CLLong l r) Source # div' :: I CLLong l r -> I CLLong l r -> Maybe (I CLLong l r) Source #
IntervalCtx CLong l r => Interval CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Associated Types type IntervalCtx CLong l r Source # type MinI CLong l r :: T x :: Type Source # type MaxI CLong l r :: T x :: Type Source # Methods inhabitant :: I CLong l r Source # from :: CLong -> Maybe (I CLong l r) Source # plus' :: I CLong l r -> I CLong l r -> Maybe (I CLong l r) Source # mult' :: I CLong l r -> I CLong l r -> Maybe (I CLong l r) Source # minus' :: I CLong l r -> I CLong l r -> Maybe (I CLong l r) Source # negate' :: I CLong l r -> Maybe (I CLong l r) Source # recip' :: I CLong l r -> Maybe (I CLong l r) Source # div' :: I CLong l r -> I CLong l r -> Maybe (I CLong l r) Source #
IntervalCtx CPtrdiff l r => Interval CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Associated Types type IntervalCtx CPtrdiff l r Source # type MinI CPtrdiff l r :: T x :: Type Source # type MaxI CPtrdiff l r :: T x :: Type Source # Methods inhabitant :: I CPtrdiff l r Source # from :: CPtrdiff -> Maybe (I CPtrdiff l r) Source # plus' :: I CPtrdiff l r -> I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source # mult' :: I CPtrdiff l r -> I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source # minus' :: I CPtrdiff l r -> I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source # negate' :: I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source # recip' :: I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source # div' :: I CPtrdiff l r -> I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source #
IntervalCtx CSChar l r => Interval CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Associated Types type IntervalCtx CSChar l r Source # type MinI CSChar l r :: T x :: Type Source # type MaxI CSChar l r :: T x :: Type Source # Methods inhabitant :: I CSChar l r Source # from :: CSChar -> Maybe (I CSChar l r) Source # plus' :: I CSChar l r -> I CSChar l r -> Maybe (I CSChar l r) Source # mult' :: I CSChar l r -> I CSChar l r -> Maybe (I CSChar l r) Source # minus' :: I CSChar l r -> I CSChar l r -> Maybe (I CSChar l r) Source # negate' :: I CSChar l r -> Maybe (I CSChar l r) Source # recip' :: I CSChar l r -> Maybe (I CSChar l r) Source # div' :: I CSChar l r -> I CSChar l r -> Maybe (I CSChar l r) Source #
IntervalCtx CShort l r => Interval CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Associated Types type IntervalCtx CShort l r Source # type MinI CShort l r :: T x :: Type Source # type MaxI CShort l r :: T x :: Type Source # Methods inhabitant :: I CShort l r Source # from :: CShort -> Maybe (I CShort l r) Source # plus' :: I CShort l r -> I CShort l r -> Maybe (I CShort l r) Source # mult' :: I CShort l r -> I CShort l r -> Maybe (I CShort l r) Source # minus' :: I CShort l r -> I CShort l r -> Maybe (I CShort l r) Source # negate' :: I CShort l r -> Maybe (I CShort l r) Source # recip' :: I CShort l r -> Maybe (I CShort l r) Source # div' :: I CShort l r -> I CShort l r -> Maybe (I CShort l r) Source #
IntervalCtx CSize l r => Interval CSize (l :: L CSize :: Type) (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Associated Types type IntervalCtx CSize l r Source # type MinI CSize l r :: T x :: Type Source # type MaxI CSize l r :: T x :: Type Source # Methods inhabitant :: I CSize l r Source # from :: CSize -> Maybe (I CSize l r) Source # plus' :: I CSize l r -> I CSize l r -> Maybe (I CSize l r) Source # mult' :: I CSize l r -> I CSize l r -> Maybe (I CSize l r) Source # minus' :: I CSize l r -> I CSize l r -> Maybe (I CSize l r) Source # negate' :: I CSize l r -> Maybe (I CSize l r) Source # recip' :: I CSize l r -> Maybe (I CSize l r) Source # div' :: I CSize l r -> I CSize l r -> Maybe (I CSize l r) Source #
IntervalCtx CUChar l r => Interval CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Associated Types type IntervalCtx CUChar l r Source # type MinI CUChar l r :: T x :: Type Source # type MaxI CUChar l r :: T x :: Type Source # Methods inhabitant :: I CUChar l r Source # from :: CUChar -> Maybe (I CUChar l r) Source # plus' :: I CUChar l r -> I CUChar l r -> Maybe (I CUChar l r) Source # mult' :: I CUChar l r -> I CUChar l r -> Maybe (I CUChar l r) Source # minus' :: I CUChar l r -> I CUChar l r -> Maybe (I CUChar l r) Source # negate' :: I CUChar l r -> Maybe (I CUChar l r) Source # recip' :: I CUChar l r -> Maybe (I CUChar l r) Source # div' :: I CUChar l r -> I CUChar l r -> Maybe (I CUChar l r) Source #
IntervalCtx CUInt l r => Interval CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Associated Types type IntervalCtx CUInt l r Source # type MinI CUInt l r :: T x :: Type Source # type MaxI CUInt l r :: T x :: Type Source # Methods inhabitant :: I CUInt l r Source # from :: CUInt -> Maybe (I CUInt l r) Source # plus' :: I CUInt l r -> I CUInt l r -> Maybe (I CUInt l r) Source # mult' :: I CUInt l r -> I CUInt l r -> Maybe (I CUInt l r) Source # minus' :: I CUInt l r -> I CUInt l r -> Maybe (I CUInt l r) Source # negate' :: I CUInt l r -> Maybe (I CUInt l r) Source # recip' :: I CUInt l r -> Maybe (I CUInt l r) Source # div' :: I CUInt l r -> I CUInt l r -> Maybe (I CUInt l r) Source #
IntervalCtx CUIntMax l r => Interval CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Associated Types type IntervalCtx CUIntMax l r Source # type MinI CUIntMax l r :: T x :: Type Source # type MaxI CUIntMax l r :: T x :: Type Source # Methods inhabitant :: I CUIntMax l r Source # from :: CUIntMax -> Maybe (I CUIntMax l r) Source # plus' :: I CUIntMax l r -> I CUIntMax l r -> Maybe (I CUIntMax l r) Source # mult' :: I CUIntMax l r -> I CUIntMax l r -> Maybe (I CUIntMax l r) Source # minus' :: I CUIntMax l r -> I CUIntMax l r -> Maybe (I CUIntMax l r) Source # negate' :: I CUIntMax l r -> Maybe (I CUIntMax l r) Source # recip' :: I CUIntMax l r -> Maybe (I CUIntMax l r) Source # div' :: I CUIntMax l r -> I CUIntMax l r -> Maybe (I CUIntMax l r) Source #
IntervalCtx CUIntPtr l r => Interval CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Associated Types type IntervalCtx CUIntPtr l r Source # type MinI CUIntPtr l r :: T x :: Type Source # type MaxI CUIntPtr l r :: T x :: Type Source # Methods inhabitant :: I CUIntPtr l r Source # from :: CUIntPtr -> Maybe (I CUIntPtr l r) Source # plus' :: I CUIntPtr l r -> I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source # mult' :: I CUIntPtr l r -> I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source # minus' :: I CUIntPtr l r -> I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source # negate' :: I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source # recip' :: I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source # div' :: I CUIntPtr l r -> I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source #
IntervalCtx CULLong l r => Interval CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Associated Types type IntervalCtx CULLong l r Source # type MinI CULLong l r :: T x :: Type Source # type MaxI CULLong l r :: T x :: Type Source # Methods inhabitant :: I CULLong l r Source # from :: CULLong -> Maybe (I CULLong l r) Source # plus' :: I CULLong l r -> I CULLong l r -> Maybe (I CULLong l r) Source # mult' :: I CULLong l r -> I CULLong l r -> Maybe (I CULLong l r) Source # minus' :: I CULLong l r -> I CULLong l r -> Maybe (I CULLong l r) Source # negate' :: I CULLong l r -> Maybe (I CULLong l r) Source # recip' :: I CULLong l r -> Maybe (I CULLong l r) Source # div' :: I CULLong l r -> I CULLong l r -> Maybe (I CULLong l r) Source #
IntervalCtx CULong l r => Interval CULong (l :: L CULong :: Type) (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Associated Types type IntervalCtx CULong l r Source # type MinI CULong l r :: T x :: Type Source # type MaxI CULong l r :: T x :: Type Source # Methods inhabitant :: I CULong l r Source # from :: CULong -> Maybe (I CULong l r) Source # plus' :: I CULong l r -> I CULong l r -> Maybe (I CULong l r) Source # mult' :: I CULong l r -> I CULong l r -> Maybe (I CULong l r) Source # minus' :: I CULong l r -> I CULong l r -> Maybe (I CULong l r) Source # negate' :: I CULong l r -> Maybe (I CULong l r) Source # recip' :: I CULong l r -> Maybe (I CULong l r) Source # div' :: I CULong l r -> I CULong l r -> Maybe (I CULong l r) Source #
IntervalCtx CUShort l r => Interval CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Associated Types type IntervalCtx CUShort l r Source # type MinI CUShort l r :: T x :: Type Source # type MaxI CUShort l r :: T x :: Type Source # Methods inhabitant :: I CUShort l r Source # from :: CUShort -> Maybe (I CUShort l r) Source # plus' :: I CUShort l r -> I CUShort l r -> Maybe (I CUShort l r) Source # mult' :: I CUShort l r -> I CUShort l r -> Maybe (I CUShort l r) Source # minus' :: I CUShort l r -> I CUShort l r -> Maybe (I CUShort l r) Source # negate' :: I CUShort l r -> Maybe (I CUShort l r) Source # recip' :: I CUShort l r -> Maybe (I CUShort l r) Source # div' :: I CUShort l r -> I CUShort l r -> Maybe (I CUShort l r) Source #
IntervalCtx CWchar l r => Interval CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Associated Types type IntervalCtx CWchar l r Source # type MinI CWchar l r :: T x :: Type Source # type MaxI CWchar l r :: T x :: Type Source # Methods inhabitant :: I CWchar l r Source # from :: CWchar -> Maybe (I CWchar l r) Source # plus' :: I CWchar l r -> I CWchar l r -> Maybe (I CWchar l r) Source # mult' :: I CWchar l r -> I CWchar l r -> Maybe (I CWchar l r) Source # minus' :: I CWchar l r -> I CWchar l r -> Maybe (I CWchar l r) Source # negate' :: I CWchar l r -> Maybe (I CWchar l r) Source # recip' :: I CWchar l r -> Maybe (I CWchar l r) Source # div' :: I CWchar l r -> I CWchar l r -> Maybe (I CWchar l r) Source #
IntervalCtx Int16 l r => Interval Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Associated Types type IntervalCtx Int16 l r Source # type MinI Int16 l r :: T x :: Type Source # type MaxI Int16 l r :: T x :: Type Source # Methods inhabitant :: I Int16 l r Source # from :: Int16 -> Maybe (I Int16 l r) Source # plus' :: I Int16 l r -> I Int16 l r -> Maybe (I Int16 l r) Source # mult' :: I Int16 l r -> I Int16 l r -> Maybe (I Int16 l r) Source # minus' :: I Int16 l r -> I Int16 l r -> Maybe (I Int16 l r) Source # negate' :: I Int16 l r -> Maybe (I Int16 l r) Source # recip' :: I Int16 l r -> Maybe (I Int16 l r) Source # div' :: I Int16 l r -> I Int16 l r -> Maybe (I Int16 l r) Source #
IntervalCtx Int32 l r => Interval Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Associated Types type IntervalCtx Int32 l r Source # type MinI Int32 l r :: T x :: Type Source # type MaxI Int32 l r :: T x :: Type Source # Methods inhabitant :: I Int32 l r Source # from :: Int32 -> Maybe (I Int32 l r) Source # plus' :: I Int32 l r -> I Int32 l r -> Maybe (I Int32 l r) Source # mult' :: I Int32 l r -> I Int32 l r -> Maybe (I Int32 l r) Source # minus' :: I Int32 l r -> I Int32 l r -> Maybe (I Int32 l r) Source # negate' :: I Int32 l r -> Maybe (I Int32 l r) Source # recip' :: I Int32 l r -> Maybe (I Int32 l r) Source # div' :: I Int32 l r -> I Int32 l r -> Maybe (I Int32 l r) Source #
IntervalCtx Int64 l r => Interval Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Associated Types type IntervalCtx Int64 l r Source # type MinI Int64 l r :: T x :: Type Source # type MaxI Int64 l r :: T x :: Type Source # Methods inhabitant :: I Int64 l r Source # from :: Int64 -> Maybe (I Int64 l r) Source # plus' :: I Int64 l r -> I Int64 l r -> Maybe (I Int64 l r) Source # mult' :: I Int64 l r -> I Int64 l r -> Maybe (I Int64 l r) Source # minus' :: I Int64 l r -> I Int64 l r -> Maybe (I Int64 l r) Source # negate' :: I Int64 l r -> Maybe (I Int64 l r) Source # recip' :: I Int64 l r -> Maybe (I Int64 l r) Source # div' :: I Int64 l r -> I Int64 l r -> Maybe (I Int64 l r) Source #
IntervalCtx Int8 l r => Interval Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Associated Types type IntervalCtx Int8 l r Source # type MinI Int8 l r :: T x :: Type Source # type MaxI Int8 l r :: T x :: Type Source # Methods inhabitant :: I Int8 l r Source # from :: Int8 -> Maybe (I Int8 l r) Source # plus' :: I Int8 l r -> I Int8 l r -> Maybe (I Int8 l r) Source # mult' :: I Int8 l r -> I Int8 l r -> Maybe (I Int8 l r) Source # minus' :: I Int8 l r -> I Int8 l r -> Maybe (I Int8 l r) Source # negate' :: I Int8 l r -> Maybe (I Int8 l r) Source # recip' :: I Int8 l r -> Maybe (I Int8 l r) Source # div' :: I Int8 l r -> I Int8 l r -> Maybe (I Int8 l r) Source #
IntervalCtx Word16 l r => Interval Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Associated Types type IntervalCtx Word16 l r Source # type MinI Word16 l r :: T x :: Type Source # type MaxI Word16 l r :: T x :: Type Source # Methods inhabitant :: I Word16 l r Source # from :: Word16 -> Maybe (I Word16 l r) Source # plus' :: I Word16 l r -> I Word16 l r -> Maybe (I Word16 l r) Source # mult' :: I Word16 l r -> I Word16 l r -> Maybe (I Word16 l r) Source # minus' :: I Word16 l r -> I Word16 l r -> Maybe (I Word16 l r) Source # negate' :: I Word16 l r -> Maybe (I Word16 l r) Source # recip' :: I Word16 l r -> Maybe (I Word16 l r) Source # div' :: I Word16 l r -> I Word16 l r -> Maybe (I Word16 l r) Source #
IntervalCtx Word32 l r => Interval Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Associated Types type IntervalCtx Word32 l r Source # type MinI Word32 l r :: T x :: Type Source # type MaxI Word32 l r :: T x :: Type Source # Methods inhabitant :: I Word32 l r Source # from :: Word32 -> Maybe (I Word32 l r) Source # plus' :: I Word32 l r -> I Word32 l r -> Maybe (I Word32 l r) Source # mult' :: I Word32 l r -> I Word32 l r -> Maybe (I Word32 l r) Source # minus' :: I Word32 l r -> I Word32 l r -> Maybe (I Word32 l r) Source # negate' :: I Word32 l r -> Maybe (I Word32 l r) Source # recip' :: I Word32 l r -> Maybe (I Word32 l r) Source # div' :: I Word32 l r -> I Word32 l r -> Maybe (I Word32 l r) Source #
IntervalCtx Word64 l r => Interval Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Associated Types type IntervalCtx Word64 l r Source # type MinI Word64 l r :: T x :: Type Source # type MaxI Word64 l r :: T x :: Type Source # Methods inhabitant :: I Word64 l r Source # from :: Word64 -> Maybe (I Word64 l r) Source # plus' :: I Word64 l r -> I Word64 l r -> Maybe (I Word64 l r) Source # mult' :: I Word64 l r -> I Word64 l r -> Maybe (I Word64 l r) Source # minus' :: I Word64 l r -> I Word64 l r -> Maybe (I Word64 l r) Source # negate' :: I Word64 l r -> Maybe (I Word64 l r) Source # recip' :: I Word64 l r -> Maybe (I Word64 l r) Source # div' :: I Word64 l r -> I Word64 l r -> Maybe (I Word64 l r) Source #
IntervalCtx Word8 l r => Interval Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Associated Types type IntervalCtx Word8 l r Source # type MinI Word8 l r :: T x :: Type Source # type MaxI Word8 l r :: T x :: Type Source # Methods inhabitant :: I Word8 l r Source # from :: Word8 -> Maybe (I Word8 l r) Source # plus' :: I Word8 l r -> I Word8 l r -> Maybe (I Word8 l r) Source # mult' :: I Word8 l r -> I Word8 l r -> Maybe (I Word8 l r) Source # minus' :: I Word8 l r -> I Word8 l r -> Maybe (I Word8 l r) Source # negate' :: I Word8 l r -> Maybe (I Word8 l r) Source # recip' :: I Word8 l r -> Maybe (I Word8 l r) Source # div' :: I Word8 l r -> I Word8 l r -> Maybe (I Word8 l r) Source #
IntervalCtx Int l r => Interval Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Associated Types type IntervalCtx Int l r Source # type MinI Int l r :: T x :: Type Source # type MaxI Int l r :: T x :: Type Source # Methods inhabitant :: I Int l r Source # from :: Int -> Maybe (I Int l r) Source # plus' :: I Int l r -> I Int l r -> Maybe (I Int l r) Source # mult' :: I Int l r -> I Int l r -> Maybe (I Int l r) Source # minus' :: I Int l r -> I Int l r -> Maybe (I Int l r) Source # negate' :: I Int l r -> Maybe (I Int l r) Source # recip' :: I Int l r -> Maybe (I Int l r) Source # div' :: I Int l r -> I Int l r -> Maybe (I Int l r) Source #
IntervalCtx Word l r => Interval Word (l :: L Word :: Type) (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Associated Types type IntervalCtx Word l r Source # type MinI Word l r :: T x :: Type Source # type MaxI Word l r :: T x :: Type Source # Methods inhabitant :: I Word l r Source # from :: Word -> Maybe (I Word l r) Source # plus' :: I Word l r -> I Word l r -> Maybe (I Word l r) Source # mult' :: I Word l r -> I Word l r -> Maybe (I Word l r) Source # minus' :: I Word l r -> I Word l r -> Maybe (I Word l r) Source # negate' :: I Word l r -> Maybe (I Word l r) Source # recip' :: I Word l r -> Maybe (I Word l r) Source # div' :: I Word l r -> I Word l r -> Maybe (I Word l r) Source #
IntervalCtx Natural l ('Nothing :: Maybe Natural) => Interval Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Associated Types type IntervalCtx Natural l 'Nothing Source # type MinI Natural l 'Nothing :: T x :: Type Source # type MaxI Natural l 'Nothing :: T x :: Type Source # Methods inhabitant :: I Natural l 'Nothing Source # from :: Natural -> Maybe (I Natural l 'Nothing) Source # plus' :: I Natural l 'Nothing -> I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source # mult' :: I Natural l 'Nothing -> I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source # minus' :: I Natural l 'Nothing -> I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source # negate' :: I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source # recip' :: I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source # div' :: I Natural l 'Nothing -> I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source #
IntervalCtx Natural l ('Just r) => Interval Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Associated Types type IntervalCtx Natural l ('Just r) Source # type MinI Natural l ('Just r) :: T x :: Type Source # type MaxI Natural l ('Just r) :: T x :: Type Source # Methods inhabitant :: I Natural l ('Just r) Source # from :: Natural -> Maybe (I Natural l ('Just r)) Source # plus' :: I Natural l ('Just r) -> I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source # mult' :: I Natural l ('Just r) -> I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source # minus' :: I Natural l ('Just r) -> I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source # negate' :: I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source # recip' :: I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source # div' :: I Natural l ('Just r) -> I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational 'Nothing 'Nothing Source # type MinI Rational 'Nothing 'Nothing :: T x :: Type Source # type MaxI Rational 'Nothing 'Nothing :: T x :: Type Source # Methods inhabitant :: I Rational0 'Nothing 'Nothing Source # from :: Rational0 -> Maybe (I Rational0 'Nothing 'Nothing) Source # plus' :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> Maybe (I Rational0 'Nothing 'Nothing) Source # mult' :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> Maybe (I Rational0 'Nothing 'Nothing) Source # minus' :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> Maybe (I Rational0 'Nothing 'Nothing) Source # negate' :: I Rational0 'Nothing 'Nothing -> Maybe (I Rational0 'Nothing 'Nothing) Source # recip' :: I Rational0 'Nothing 'Nothing -> Maybe (I Rational0 'Nothing 'Nothing) Source # div' :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> Maybe (I Rational0 'Nothing 'Nothing) Source #
Interval Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Associated Types type IntervalCtx Integer 'Nothing 'Nothing Source # type MinI Integer 'Nothing 'Nothing :: T x :: Type Source # type MaxI Integer 'Nothing 'Nothing :: T x :: Type Source # Methods inhabitant :: I Integer0 'Nothing 'Nothing Source # from :: Integer0 -> Maybe (I Integer0 'Nothing 'Nothing) Source # plus' :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source # mult' :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source # minus' :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source # negate' :: I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source # recip' :: I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source # div' :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source #
IntervalCtx Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)) => Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational 'Nothing ('Just '('False, r)) Source # type MinI Rational 'Nothing ('Just '('False, r)) :: T x :: Type Source # type MaxI Rational 'Nothing ('Just '('False, r)) :: T x :: Type Source # Methods inhabitant :: I Rational0 'Nothing ('Just '('False, r)) Source # from :: Rational0 -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source # plus' :: I Rational0 'Nothing ('Just '('False, r)) -> I Rational0 'Nothing ('Just '('False, r)) -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source # mult' :: I Rational0 'Nothing ('Just '('False, r)) -> I Rational0 'Nothing ('Just '('False, r)) -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source # minus' :: I Rational0 'Nothing ('Just '('False, r)) -> I Rational0 'Nothing ('Just '('False, r)) -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source # negate' :: I Rational0 'Nothing ('Just '('False, r)) -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source # recip' :: I Rational0 'Nothing ('Just '('False, r)) -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source # div' :: I Rational0 'Nothing ('Just '('False, r)) -> I Rational0 'Nothing ('Just '('False, r)) -> Maybe (I Rational0 'Nothing ('Just '('False, r))) Source #
IntervalCtx Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)) => Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational 'Nothing ('Just '('True, r)) Source # type MinI Rational 'Nothing ('Just '('True, r)) :: T x :: Type Source # type MaxI Rational 'Nothing ('Just '('True, r)) :: T x :: Type Source # Methods inhabitant :: I Rational0 'Nothing ('Just '('True, r)) Source # from :: Rational0 -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source # plus' :: I Rational0 'Nothing ('Just '('True, r)) -> I Rational0 'Nothing ('Just '('True, r)) -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source # mult' :: I Rational0 'Nothing ('Just '('True, r)) -> I Rational0 'Nothing ('Just '('True, r)) -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source # minus' :: I Rational0 'Nothing ('Just '('True, r)) -> I Rational0 'Nothing ('Just '('True, r)) -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source # negate' :: I Rational0 'Nothing ('Just '('True, r)) -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source # recip' :: I Rational0 'Nothing ('Just '('True, r)) -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source # div' :: I Rational0 'Nothing ('Just '('True, r)) -> I Rational0 'Nothing ('Just '('True, r)) -> Maybe (I Rational0 'Nothing ('Just '('True, r))) Source #
IntervalCtx Integer ('Nothing :: Maybe Integer) ('Just r) => Interval Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Associated Types type IntervalCtx Integer 'Nothing ('Just r) Source # type MinI Integer 'Nothing ('Just r) :: T x :: Type Source # type MaxI Integer 'Nothing ('Just r) :: T x :: Type Source # Methods inhabitant :: I Integer0 'Nothing ('Just r) Source # from :: Integer0 -> Maybe (I Integer0 'Nothing ('Just r)) Source # plus' :: I Integer0 'Nothing ('Just r) -> I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source # mult' :: I Integer0 'Nothing ('Just r) -> I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source # minus' :: I Integer0 'Nothing ('Just r) -> I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source # negate' :: I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source # recip' :: I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source # div' :: I Integer0 'Nothing ('Just r) -> I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source #
IntervalCtx Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)) => Interval Rational ('Just '('False, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational ('Just '('False, l)) 'Nothing Source # type MinI Rational ('Just '('False, l)) 'Nothing :: T x :: Type Source # type MaxI Rational ('Just '('False, l)) 'Nothing :: T x :: Type Source # Methods inhabitant :: I Rational0 ('Just '('False, l)) 'Nothing Source # from :: Rational0 -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source # plus' :: I Rational0 ('Just '('False, l)) 'Nothing -> I Rational0 ('Just '('False, l)) 'Nothing -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source # mult' :: I Rational0 ('Just '('False, l)) 'Nothing -> I Rational0 ('Just '('False, l)) 'Nothing -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source # minus' :: I Rational0 ('Just '('False, l)) 'Nothing -> I Rational0 ('Just '('False, l)) 'Nothing -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source # negate' :: I Rational0 ('Just '('False, l)) 'Nothing -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source # recip' :: I Rational0 ('Just '('False, l)) 'Nothing -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source # div' :: I Rational0 ('Just '('False, l)) 'Nothing -> I Rational0 ('Just '('False, l)) 'Nothing -> Maybe (I Rational0 ('Just '('False, l)) 'Nothing) Source #
IntervalCtx Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)) => Interval Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational ('Just '('True, l)) 'Nothing Source # type MinI Rational ('Just '('True, l)) 'Nothing :: T x :: Type Source # type MaxI Rational ('Just '('True, l)) 'Nothing :: T x :: Type Source # Methods inhabitant :: I Rational0 ('Just '('True, l)) 'Nothing Source # from :: Rational0 -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source # plus' :: I Rational0 ('Just '('True, l)) 'Nothing -> I Rational0 ('Just '('True, l)) 'Nothing -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source # mult' :: I Rational0 ('Just '('True, l)) 'Nothing -> I Rational0 ('Just '('True, l)) 'Nothing -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source # minus' :: I Rational0 ('Just '('True, l)) 'Nothing -> I Rational0 ('Just '('True, l)) 'Nothing -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source # negate' :: I Rational0 ('Just '('True, l)) 'Nothing -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source # recip' :: I Rational0 ('Just '('True, l)) 'Nothing -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source # div' :: I Rational0 ('Just '('True, l)) 'Nothing -> I Rational0 ('Just '('True, l)) 'Nothing -> Maybe (I Rational0 ('Just '('True, l)) 'Nothing) Source #
IntervalCtx Integer ('Just l) ('Nothing :: Maybe Integer) => Interval Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Associated Types type IntervalCtx Integer ('Just l) 'Nothing Source # type MinI Integer ('Just l) 'Nothing :: T x :: Type Source # type MaxI Integer ('Just l) 'Nothing :: T x :: Type Source # Methods inhabitant :: I Integer0 ('Just l) 'Nothing Source # from :: Integer0 -> Maybe (I Integer0 ('Just l) 'Nothing) Source # plus' :: I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source # mult' :: I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source # minus' :: I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source # negate' :: I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source # recip' :: I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source # div' :: I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source #
IntervalCtx Rational ('Just '('False, l)) ('Just '('False, r)) => Interval Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational ('Just '('False, l)) ('Just '('False, r)) Source # type MinI Rational ('Just '('False, l)) ('Just '('False, r)) :: T x :: Type Source # type MaxI Rational ('Just '('False, l)) ('Just '('False, r)) :: T x :: Type Source # Methods inhabitant :: I Rational ('Just '('False, l)) ('Just '('False, r)) Source # from :: Rational -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source # plus' :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> I Rational ('Just '('False, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source # mult' :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> I Rational ('Just '('False, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source # minus' :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> I Rational ('Just '('False, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source # negate' :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source # recip' :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source # div' :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> I Rational ('Just '('False, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('False, r))) Source #
IntervalCtx Rational ('Just '('False, l)) ('Just '('True, r)) => Interval Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational ('Just '('False, l)) ('Just '('True, r)) Source # type MinI Rational ('Just '('False, l)) ('Just '('True, r)) :: T x :: Type Source # type MaxI Rational ('Just '('False, l)) ('Just '('True, r)) :: T x :: Type Source # Methods inhabitant :: I Rational ('Just '('False, l)) ('Just '('True, r)) Source # from :: Rational -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source # plus' :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> I Rational ('Just '('False, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source # mult' :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> I Rational ('Just '('False, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source # minus' :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> I Rational ('Just '('False, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source # negate' :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source # recip' :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source # div' :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> I Rational ('Just '('False, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('False, l)) ('Just '('True, r))) Source #
IntervalCtx Rational ('Just '('True, l)) ('Just '('False, r)) => Interval Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational ('Just '('True, l)) ('Just '('False, r)) Source # type MinI Rational ('Just '('True, l)) ('Just '('False, r)) :: T x :: Type Source # type MaxI Rational ('Just '('True, l)) ('Just '('False, r)) :: T x :: Type Source # Methods inhabitant :: I Rational ('Just '('True, l)) ('Just '('False, r)) Source # from :: Rational -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source # plus' :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> I Rational ('Just '('True, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source # mult' :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> I Rational ('Just '('True, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source # minus' :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> I Rational ('Just '('True, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source # negate' :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source # recip' :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source # div' :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> I Rational ('Just '('True, l)) ('Just '('False, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('False, r))) Source #
IntervalCtx Rational ('Just '('True, l)) ('Just '('True, r)) => Interval Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type IntervalCtx Rational ('Just '('True, l)) ('Just '('True, r)) Source # type MinI Rational ('Just '('True, l)) ('Just '('True, r)) :: T x :: Type Source # type MaxI Rational ('Just '('True, l)) ('Just '('True, r)) :: T x :: Type Source # Methods inhabitant :: I Rational ('Just '('True, l)) ('Just '('True, r)) Source # from :: Rational -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source # plus' :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> I Rational ('Just '('True, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source # mult' :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> I Rational ('Just '('True, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source # minus' :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> I Rational ('Just '('True, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source # negate' :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source # recip' :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source # div' :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> I Rational ('Just '('True, l)) ('Just '('True, r)) -> Maybe (I Rational ('Just '('True, l)) ('Just '('True, r))) Source #
IntervalCtx Integer ('Just l) ('Just r) => Interval Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Associated Types type IntervalCtx Integer ('Just l) ('Just r) Source # type MinI Integer ('Just l) ('Just r) :: T x :: Type Source # type MaxI Integer ('Just l) ('Just r) :: T x :: Type Source # Methods inhabitant :: I Integer ('Just l) ('Just r) Source # from :: Integer -> Maybe (I Integer ('Just l) ('Just r)) Source # plus' :: I Integer ('Just l) ('Just r) -> I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source # mult' :: I Integer ('Just l) ('Just r) -> I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source # minus' :: I Integer ('Just l) ('Just r) -> I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source # negate' :: I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source # recip' :: I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source # div' :: I Integer ('Just l) ('Just r) -> I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source #

unwrap :: forall x l r. I x l r -> x Source #

Obtain the x that is wrapped in the I x l r.

Identity law

wrap . unwrap == id
unwrap . wrap == id

wrap :: Interval x (MinL x) (MaxR x) => x -> I x (MinL x) (MaxR x) Source #

Wrap the given x in the interval I x (MinL x) (MaxR x).

This function always succeeds because the interval known to fit all the values of type x.

Identity law

wrap . unwrap == id
unwrap . wrap == id

If the interval is not as big as x:

Consider using from.
Consider using known if you have type-level knowledge about the value of x.
Consider using unsafe if you know that the x is within the interval.

unsafe :: forall x l r. (HasCallStack, Interval x l r) => x -> I x l r Source #

unsafe allows you to wrap an x in an I x l r, failing with error if the x is outside the interval.

WARNING: This function calls from, which means that you can't use it to implement from. You will have to use unsafest in that case. Your code will loop indefinitely otherwise.

class Interval x l r => Clamp (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals that support clamping.

Minimal complete definition

Nothing

Methods

clamp :: x -> I x l r Source #

Wrap x in I x l r, making sure that x is within the interval ends by clamping it to MinI x l r if less than l, or to MaxI x l r if more than r, if necessary.

default clamp :: (Known x l r (MinI x l r), Known x l r (MaxI x l r), Ord x) => x -> I x l r Source #

Instances

Instances details

Interval CChar l r => Clamp CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods clamp :: CChar -> I CChar l r Source #
Interval CInt l r => Clamp CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods clamp :: CInt -> I CInt l r Source #
Interval CIntMax l r => Clamp CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods clamp :: CIntMax -> I CIntMax l r Source #
Interval CIntPtr l r => Clamp CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods clamp :: CIntPtr -> I CIntPtr l r Source #
Interval CLLong l r => Clamp CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods clamp :: CLLong -> I CLLong l r Source #
Interval CLong l r => Clamp CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods clamp :: CLong -> I CLong l r Source #
Interval CPtrdiff l r => Clamp CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods clamp :: CPtrdiff -> I CPtrdiff l r Source #
Interval CSChar l r => Clamp CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods clamp :: CSChar -> I CSChar l r Source #
Interval CShort l r => Clamp CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods clamp :: CShort -> I CShort l r Source #
Interval CSize l r => Clamp CSize (l :: L CSize :: Type) (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods clamp :: CSize -> I CSize l r Source #
Interval CUChar l r => Clamp CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods clamp :: CUChar -> I CUChar l r Source #
Interval CUInt l r => Clamp CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods clamp :: CUInt -> I CUInt l r Source #
Interval CUIntMax l r => Clamp CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods clamp :: CUIntMax -> I CUIntMax l r Source #
Interval CUIntPtr l r => Clamp CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods clamp :: CUIntPtr -> I CUIntPtr l r Source #
Interval CULLong l r => Clamp CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods clamp :: CULLong -> I CULLong l r Source #
Interval CULong l r => Clamp CULong (l :: L CULong :: Type) (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods clamp :: CULong -> I CULong l r Source #
Interval CUShort l r => Clamp CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods clamp :: CUShort -> I CUShort l r Source #
Interval CWchar l r => Clamp CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods clamp :: CWchar -> I CWchar l r Source #
Interval Int16 l r => Clamp Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods clamp :: Int16 -> I Int16 l r Source #
Interval Int32 l r => Clamp Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods clamp :: Int32 -> I Int32 l r Source #
Interval Int64 l r => Clamp Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods clamp :: Int64 -> I Int64 l r Source #
Interval Int8 l r => Clamp Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods clamp :: Int8 -> I Int8 l r Source #
Interval Word16 l r => Clamp Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods clamp :: Word16 -> I Word16 l r Source #
Interval Word32 l r => Clamp Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods clamp :: Word32 -> I Word32 l r Source #
Interval Word64 l r => Clamp Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods clamp :: Word64 -> I Word64 l r Source #
Interval Word8 l r => Clamp Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods clamp :: Word8 -> I Word8 l r Source #
Interval Int l r => Clamp Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods clamp :: Int -> I Int l r Source #
Interval Word l r => Clamp Word (l :: L Word :: Type) (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods clamp :: Word -> I Word l r Source #
Interval Natural l ('Nothing :: Maybe Natural) => Clamp Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods clamp :: Natural -> I Natural l 'Nothing Source #
Interval Natural l ('Just r) => Clamp Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods clamp :: Natural -> I Natural l ('Just r) Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) => Clamp Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods clamp :: Rational0 -> I Rational0 'Nothing 'Nothing Source #
Interval Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) => Clamp Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods clamp :: Integer0 -> I Integer0 'Nothing 'Nothing Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)) => Clamp Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods clamp :: Rational0 -> I Rational0 'Nothing ('Just '('True, r)) Source #
Interval Integer ('Nothing :: Maybe Integer) ('Just r) => Clamp Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods clamp :: Integer0 -> I Integer0 'Nothing ('Just r) Source #
Interval Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)) => Clamp Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods clamp :: Rational0 -> I Rational0 ('Just '('True, l)) 'Nothing Source #
Interval Integer ('Just l) ('Nothing :: Maybe Integer) => Clamp Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods clamp :: Integer0 -> I Integer0 ('Just l) 'Nothing Source #
Interval Rational ('Just '('True, l)) ('Just '('True, r)) => Clamp Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods clamp :: Rational -> I Rational ('Just '('True, l)) ('Just '('True, r)) Source #
Interval Integer ('Just l) ('Just r) => Clamp Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods clamp :: Integer -> I Integer ('Just l) ('Just r) Source #

class (Interval x ld rd, Interval x lu ru) => Up (x :: Type) (ld :: L x) (rd :: R x) (lu :: L x) (ru :: R x) where Source #

Intervals that can be upcasted to a larger Interval type.

Minimal complete definition

Nothing

Methods

up :: I x ld rd -> I x lu ru Source #

Proof that I x ld rd can be upcasted into I x lu ru.

Identity law

forall (a :: I x ld rd).
  (Up x ld rd lu ru) =>
    unwrap a == unwrap (up a :: I x lu ru)

default up :: HasCallStack => I x ld rd -> I x lu ru Source #

Instances

Instances details

(Interval CChar ld rd, Interval CChar lu ru, lu <= ld, rd <= ru) => Up CChar (ld :: L CChar :: Type) (rd :: R CChar :: Type) (lu :: L CChar :: Type) (ru :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods up :: I CChar ld rd -> I CChar lu ru Source #
(Interval CInt ld rd, Interval CInt lu ru, lu <= ld, rd <= ru) => Up CInt (ld :: L CInt :: Type) (rd :: R CInt :: Type) (lu :: L CInt :: Type) (ru :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods up :: I CInt ld rd -> I CInt lu ru Source #
(Interval CIntMax ld rd, Interval CIntMax lu ru, lu <= ld, rd <= ru) => Up CIntMax (ld :: L CIntMax :: Type) (rd :: R CIntMax :: Type) (lu :: L CIntMax :: Type) (ru :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods up :: I CIntMax ld rd -> I CIntMax lu ru Source #
(Interval CIntPtr ld rd, Interval CIntPtr lu ru, lu <= ld, rd <= ru) => Up CIntPtr (ld :: L CIntPtr :: Type) (rd :: R CIntPtr :: Type) (lu :: L CIntPtr :: Type) (ru :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods up :: I CIntPtr ld rd -> I CIntPtr lu ru Source #
(Interval CLLong ld rd, Interval CLLong lu ru, lu <= ld, rd <= ru) => Up CLLong (ld :: L CLLong :: Type) (rd :: R CLLong :: Type) (lu :: L CLLong :: Type) (ru :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods up :: I CLLong ld rd -> I CLLong lu ru Source #
(Interval CLong ld rd, Interval CLong lu ru, lu <= ld, rd <= ru) => Up CLong (ld :: L CLong :: Type) (rd :: R CLong :: Type) (lu :: L CLong :: Type) (ru :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods up :: I CLong ld rd -> I CLong lu ru Source #
(Interval CPtrdiff ld rd, Interval CPtrdiff lu ru, lu <= ld, rd <= ru) => Up CPtrdiff (ld :: L CPtrdiff :: Type) (rd :: R CPtrdiff :: Type) (lu :: L CPtrdiff :: Type) (ru :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods up :: I CPtrdiff ld rd -> I CPtrdiff lu ru Source #
(Interval CSChar ld rd, Interval CSChar lu ru, lu <= ld, rd <= ru) => Up CSChar (ld :: L CSChar :: Type) (rd :: R CSChar :: Type) (lu :: L CSChar :: Type) (ru :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods up :: I CSChar ld rd -> I CSChar lu ru Source #
(Interval CShort ld rd, Interval CShort lu ru, lu <= ld, rd <= ru) => Up CShort (ld :: L CShort :: Type) (rd :: R CShort :: Type) (lu :: L CShort :: Type) (ru :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods up :: I CShort ld rd -> I CShort lu ru Source #
(Interval CSize ld rd, Interval CSize lu ru, lu <= ld, rd <= ru) => Up CSize (ld :: L CSize :: Type) (rd :: R CSize :: Type) (lu :: L CSize :: Type) (ru :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods up :: I CSize ld rd -> I CSize lu ru Source #
(Interval CUChar ld rd, Interval CUChar lu ru, lu <= ld, rd <= ru) => Up CUChar (ld :: L CUChar :: Type) (rd :: R CUChar :: Type) (lu :: L CUChar :: Type) (ru :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods up :: I CUChar ld rd -> I CUChar lu ru Source #
(Interval CUInt ld rd, Interval CUInt lu ru, lu <= ld, rd <= ru) => Up CUInt (ld :: L CUInt :: Type) (rd :: R CUInt :: Type) (lu :: L CUInt :: Type) (ru :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods up :: I CUInt ld rd -> I CUInt lu ru Source #
(Interval CUIntMax ld rd, Interval CUIntMax lu ru, lu <= ld, rd <= ru) => Up CUIntMax (ld :: L CUIntMax :: Type) (rd :: R CUIntMax :: Type) (lu :: L CUIntMax :: Type) (ru :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods up :: I CUIntMax ld rd -> I CUIntMax lu ru Source #
(Interval CUIntPtr ld rd, Interval CUIntPtr lu ru, lu <= ld, rd <= ru) => Up CUIntPtr (ld :: L CUIntPtr :: Type) (rd :: R CUIntPtr :: Type) (lu :: L CUIntPtr :: Type) (ru :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods up :: I CUIntPtr ld rd -> I CUIntPtr lu ru Source #
(Interval CULLong ld rd, Interval CULLong lu ru, lu <= ld, rd <= ru) => Up CULLong (ld :: L CULLong :: Type) (rd :: R CULLong :: Type) (lu :: L CULLong :: Type) (ru :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods up :: I CULLong ld rd -> I CULLong lu ru Source #
(Interval CULong ld rd, Interval CULong lu ru, lu <= ld, rd <= ru) => Up CULong (ld :: L CULong :: Type) (rd :: R CULong :: Type) (lu :: L CULong :: Type) (ru :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods up :: I CULong ld rd -> I CULong lu ru Source #
(Interval CUShort ld rd, Interval CUShort lu ru, lu <= ld, rd <= ru) => Up CUShort (ld :: L CUShort :: Type) (rd :: R CUShort :: Type) (lu :: L CUShort :: Type) (ru :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods up :: I CUShort ld rd -> I CUShort lu ru Source #
(Interval CWchar ld rd, Interval CWchar lu ru, lu <= ld, rd <= ru) => Up CWchar (ld :: L CWchar :: Type) (rd :: R CWchar :: Type) (lu :: L CWchar :: Type) (ru :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods up :: I CWchar ld rd -> I CWchar lu ru Source #
(Interval Int16 ld rd, Interval Int16 lu ru, lu <= ld, rd <= ru) => Up Int16 (ld :: L Int16 :: Type) (rd :: R Int16 :: Type) (lu :: L Int16 :: Type) (ru :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods up :: I Int16 ld rd -> I Int16 lu ru Source #
(Interval Int32 ld rd, Interval Int32 lu ru, lu <= ld, rd <= ru) => Up Int32 (ld :: L Int32 :: Type) (rd :: R Int32 :: Type) (lu :: L Int32 :: Type) (ru :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods up :: I Int32 ld rd -> I Int32 lu ru Source #
(Interval Int64 ld rd, Interval Int64 lu ru, lu <= ld, rd <= ru) => Up Int64 (ld :: L Int64 :: Type) (rd :: R Int64 :: Type) (lu :: L Int64 :: Type) (ru :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods up :: I Int64 ld rd -> I Int64 lu ru Source #
(Interval Int8 ld rd, Interval Int8 lu ru, lu <= ld, rd <= ru) => Up Int8 (ld :: L Int8 :: Type) (rd :: R Int8 :: Type) (lu :: L Int8 :: Type) (ru :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods up :: I Int8 ld rd -> I Int8 lu ru Source #
(Interval Word16 ld rd, Interval Word16 lu ru, lu <= ld, rd <= ru) => Up Word16 (ld :: L Word16 :: Type) (rd :: R Word16 :: Type) (lu :: L Word16 :: Type) (ru :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods up :: I Word16 ld rd -> I Word16 lu ru Source #
(Interval Word32 ld rd, Interval Word32 lu ru, lu <= ld, rd <= ru) => Up Word32 (ld :: L Word32 :: Type) (rd :: R Word32 :: Type) (lu :: L Word32 :: Type) (ru :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods up :: I Word32 ld rd -> I Word32 lu ru Source #
(Interval Word64 ld rd, Interval Word64 lu ru, lu <= ld, rd <= ru) => Up Word64 (ld :: L Word64 :: Type) (rd :: R Word64 :: Type) (lu :: L Word64 :: Type) (ru :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods up :: I Word64 ld rd -> I Word64 lu ru Source #
(Interval Word8 ld rd, Interval Word8 lu ru, lu <= ld, rd <= ru) => Up Word8 (ld :: L Word8 :: Type) (rd :: R Word8 :: Type) (lu :: L Word8 :: Type) (ru :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods up :: I Word8 ld rd -> I Word8 lu ru Source #
(Interval Int ld rd, Interval Int lu ru, lu <= ld, rd <= ru) => Up Int (ld :: L Int :: Type) (rd :: R Int :: Type) (lu :: L Int :: Type) (ru :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods up :: I Int ld rd -> I Int lu ru Source #
(Interval Word ld rd, Interval Word lu ru, lu <= ld, rd <= ru) => Up Word (ld :: L Word :: Type) (rd :: R Word :: Type) (lu :: L Word :: Type) (ru :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods up :: I Word ld rd -> I Word lu ru Source #
Interval x l r => Up x (l :: L x :: Type) (r :: R x :: Type) (l :: L x :: Type) (r :: R x :: Type) Source #	Identity. This instance is INCOHERENT, but that's OK because all implementations of `up` should give the same result, and this instance is as fast as possible. So, it doesn't matter whether this instance or another one is picked.
Instance details Defined in I.Internal Methods up :: I x l r -> I x l r Source #
(lu <= ld, Interval Natural ld yrd, Interval Natural lu ('Nothing :: Maybe Natural)) => Up Natural (ld :: L Natural :: Type) (yrd :: R Natural :: Type) (lu :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods up :: I Natural ld yrd -> I Natural lu 'Nothing Source #
(Interval Rational yld yrd, Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational))) => Up Rational (yld :: L Rational :: Type) (yrd :: R Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods up :: I Rational0 yld yrd -> I Rational0 'Nothing 'Nothing Source #
(Interval Integer yld yrd, Interval Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer)) => Up Integer (yld :: L Integer :: Type) (yrd :: R Integer :: Type) ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods up :: I Integer0 yld yrd -> I Integer0 'Nothing 'Nothing Source #
(lu <= ld, rd <= ru, Interval Natural ld ('Just rd), Interval Natural lu ('Just ru)) => Up Natural (ld :: L Natural :: Type) ('Just rd :: R Natural :: Type) (lu :: L Natural :: Type) ('Just ru :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods up :: I Natural ld ('Just rd) -> I Natural lu ('Just ru) Source #
(Interval Rational yld ('Just '('False, rd)), Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, ru)), ru <= rd) => Up Rational (yld :: L Rational :: Type) ('Just '('False, rd) :: R Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, ru) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods up :: I Rational0 yld ('Just '('False, rd)) -> I Rational0 'Nothing ('Just '('False, ru)) Source #
(Interval Rational yld ('Just '(ird, rd)), Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, ru)), ru <= rd) => Up Rational (yld :: L Rational :: Type) ('Just '(ird, rd) :: R Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, ru) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods up :: I Rational0 yld ('Just '(ird, rd)) -> I Rational0 'Nothing ('Just '('True, ru)) Source #
(rd <= ru, Interval Integer yld ('Just rd), Interval Integer ('Nothing :: Maybe Integer) ('Just ru)) => Up Integer (yld :: L Integer :: Type) ('Just rd :: R Integer :: Type) ('Nothing :: Maybe Integer) ('Just ru :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods up :: I Integer0 yld ('Just rd) -> I Integer0 'Nothing ('Just ru) Source #
(Interval Rational ('Just '('False, ld)) yrd, Interval Rational ('Just '('False, lu)) ('Nothing :: Maybe (Bool, Rational)), lu <= ld) => Up Rational ('Just '('False, ld) :: L Rational :: Type) (yrd :: R Rational :: Type) ('Just '('False, lu) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods up :: I Rational0 ('Just '('False, ld)) yrd -> I Rational0 ('Just '('False, lu)) 'Nothing Source #
(Interval Rational ('Just '(ild, ld)) yrd, Interval Rational ('Just '('True, lu)) ('Nothing :: Maybe (Bool, Rational)), lu <= ld) => Up Rational ('Just '(ild, ld) :: L Rational :: Type) (yrd :: R Rational :: Type) ('Just '('True, lu) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods up :: I Rational0 ('Just '(ild, ld)) yrd -> I Rational0 ('Just '('True, lu)) 'Nothing Source #
(lu <= ld, Interval Integer ('Just ld) yrd, Interval Integer ('Just lu) ('Nothing :: Maybe Integer)) => Up Integer ('Just ld :: L Integer :: Type) (yrd :: R Integer :: Type) ('Just lu :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods up :: I Integer0 ('Just ld) yrd -> I Integer0 ('Just lu) 'Nothing Source #
(Interval Rational ('Just '('False, ld)) ('Just '('False, rd)), Interval Rational ('Just '('False, lu)) ('Just '('False, ru)), lu <= ld, rd <= ru) => Up Rational ('Just '('False, ld) :: L Rational :: Type) ('Just '('False, rd) :: R Rational :: Type) ('Just '('False, lu) :: L Rational :: Type) ('Just '('False, ru) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods up :: I Rational ('Just '('False, ld)) ('Just '('False, rd)) -> I Rational ('Just '('False, lu)) ('Just '('False, ru)) Source #
(Interval Rational ('Just '('False, ld)) ('Just '(ird, rd)), Interval Rational ('Just '('False, lu)) ('Just '('True, ru)), lu <= ld, rd <= ru) => Up Rational ('Just '('False, ld) :: L Rational :: Type) ('Just '(ird, rd) :: R Rational :: Type) ('Just '('False, lu) :: L Rational :: Type) ('Just '('True, ru) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods up :: I Rational ('Just '('False, ld)) ('Just '(ird, rd)) -> I Rational ('Just '('False, lu)) ('Just '('True, ru)) Source #
(Interval Rational ('Just '(ild, ld)) ('Just '('False, rd)), Interval Rational ('Just '('True, lu)) ('Just '('False, ru)), lu <= ld, rd <= ru) => Up Rational ('Just '(ild, ld) :: L Rational :: Type) ('Just '('False, rd) :: R Rational :: Type) ('Just '('True, lu) :: L Rational :: Type) ('Just '('False, ru) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods up :: I Rational ('Just '(ild, ld)) ('Just '('False, rd)) -> I Rational ('Just '('True, lu)) ('Just '('False, ru)) Source #
(Interval Rational ('Just '(ild, ld)) ('Just '(ird, rd)), Interval Rational ('Just '('True, lu)) ('Just '('True, ru)), lu <= ld, rd <= ru) => Up Rational ('Just '(ild, ld) :: L Rational :: Type) ('Just '(ird, rd) :: R Rational :: Type) ('Just '('True, lu) :: L Rational :: Type) ('Just '('True, ru) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods up :: I Rational ('Just '(ild, ld)) ('Just '(ird, rd)) -> I Rational ('Just '('True, lu)) ('Just '('True, ru)) Source #
(lu <= ld, rd <= ru, Interval Integer ('Just ld) ('Just rd), Interval Integer ('Just lu) ('Just ru)) => Up Integer ('Just ld :: L Integer :: Type) ('Just rd :: R Integer :: Type) ('Just lu :: L Integer :: Type) ('Just ru :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods up :: I Integer ('Just ld) ('Just rd) -> I Integer ('Just lu) ('Just ru) Source #

down :: forall x lu ru ld rd. Interval x ld rd => I x lu ru -> Maybe (I x ld rd) Source #

Downcast I x lu ru into I x ld rd if wrapped x value fits in I x ld rd.

class Interval x l r => Discrete (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals that contain discrete elements.

Methods

pred' :: I x l r -> Maybe (I x l r) Source #

Predecessor. That is, the previous discrete value in the interval.

Nothing if the result would be out of the interval. See pred too.

succ' :: I x l r -> Maybe (I x l r) Source #

Successor. That is, the next discrete value in the interval.

Nothing if the result would be out of the interval. See succ too.

Instances

Instances details

(Interval CChar l r, l /= r) => Discrete CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods pred' :: I CChar l r -> Maybe (I CChar l r) Source # succ' :: I CChar l r -> Maybe (I CChar l r) Source #
(Interval CInt l r, l /= r) => Discrete CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods pred' :: I CInt l r -> Maybe (I CInt l r) Source # succ' :: I CInt l r -> Maybe (I CInt l r) Source #
(Interval CIntMax l r, l /= r) => Discrete CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods pred' :: I CIntMax l r -> Maybe (I CIntMax l r) Source # succ' :: I CIntMax l r -> Maybe (I CIntMax l r) Source #
(Interval CIntPtr l r, l /= r) => Discrete CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods pred' :: I CIntPtr l r -> Maybe (I CIntPtr l r) Source # succ' :: I CIntPtr l r -> Maybe (I CIntPtr l r) Source #
(Interval CLLong l r, l /= r) => Discrete CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods pred' :: I CLLong l r -> Maybe (I CLLong l r) Source # succ' :: I CLLong l r -> Maybe (I CLLong l r) Source #
(Interval CLong l r, l /= r) => Discrete CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods pred' :: I CLong l r -> Maybe (I CLong l r) Source # succ' :: I CLong l r -> Maybe (I CLong l r) Source #
(Interval CPtrdiff l r, l /= r) => Discrete CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods pred' :: I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source # succ' :: I CPtrdiff l r -> Maybe (I CPtrdiff l r) Source #
(Interval CSChar l r, l /= r) => Discrete CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods pred' :: I CSChar l r -> Maybe (I CSChar l r) Source # succ' :: I CSChar l r -> Maybe (I CSChar l r) Source #
(Interval CShort l r, l /= r) => Discrete CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods pred' :: I CShort l r -> Maybe (I CShort l r) Source # succ' :: I CShort l r -> Maybe (I CShort l r) Source #
(Interval CSize l r, l /= r) => Discrete CSize (l :: L CSize :: Type) (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods pred' :: I CSize l r -> Maybe (I CSize l r) Source # succ' :: I CSize l r -> Maybe (I CSize l r) Source #
(Interval CUChar l r, l /= r) => Discrete CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods pred' :: I CUChar l r -> Maybe (I CUChar l r) Source # succ' :: I CUChar l r -> Maybe (I CUChar l r) Source #
(Interval CUInt l r, l /= r) => Discrete CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods pred' :: I CUInt l r -> Maybe (I CUInt l r) Source # succ' :: I CUInt l r -> Maybe (I CUInt l r) Source #
(Interval CUIntMax l r, l /= r) => Discrete CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods pred' :: I CUIntMax l r -> Maybe (I CUIntMax l r) Source # succ' :: I CUIntMax l r -> Maybe (I CUIntMax l r) Source #
(Interval CUIntPtr l r, l /= r) => Discrete CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods pred' :: I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source # succ' :: I CUIntPtr l r -> Maybe (I CUIntPtr l r) Source #
(Interval CULLong l r, l /= r) => Discrete CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods pred' :: I CULLong l r -> Maybe (I CULLong l r) Source # succ' :: I CULLong l r -> Maybe (I CULLong l r) Source #
(Interval CULong l r, l /= r) => Discrete CULong (l :: L CULong :: Type) (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods pred' :: I CULong l r -> Maybe (I CULong l r) Source # succ' :: I CULong l r -> Maybe (I CULong l r) Source #
(Interval CUShort l r, l /= r) => Discrete CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods pred' :: I CUShort l r -> Maybe (I CUShort l r) Source # succ' :: I CUShort l r -> Maybe (I CUShort l r) Source #
(Interval CWchar l r, l /= r) => Discrete CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods pred' :: I CWchar l r -> Maybe (I CWchar l r) Source # succ' :: I CWchar l r -> Maybe (I CWchar l r) Source #
(Interval Int16 l r, l /= r) => Discrete Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods pred' :: I Int16 l r -> Maybe (I Int16 l r) Source # succ' :: I Int16 l r -> Maybe (I Int16 l r) Source #
(Interval Int32 l r, l /= r) => Discrete Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods pred' :: I Int32 l r -> Maybe (I Int32 l r) Source # succ' :: I Int32 l r -> Maybe (I Int32 l r) Source #
(Interval Int64 l r, l /= r) => Discrete Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods pred' :: I Int64 l r -> Maybe (I Int64 l r) Source # succ' :: I Int64 l r -> Maybe (I Int64 l r) Source #
(Interval Int8 l r, l /= r) => Discrete Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods pred' :: I Int8 l r -> Maybe (I Int8 l r) Source # succ' :: I Int8 l r -> Maybe (I Int8 l r) Source #
(Interval Word16 l r, l /= r) => Discrete Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods pred' :: I Word16 l r -> Maybe (I Word16 l r) Source # succ' :: I Word16 l r -> Maybe (I Word16 l r) Source #
(Interval Word32 l r, l /= r) => Discrete Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods pred' :: I Word32 l r -> Maybe (I Word32 l r) Source # succ' :: I Word32 l r -> Maybe (I Word32 l r) Source #
(Interval Word64 l r, l /= r) => Discrete Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods pred' :: I Word64 l r -> Maybe (I Word64 l r) Source # succ' :: I Word64 l r -> Maybe (I Word64 l r) Source #
(Interval Word8 l r, l /= r) => Discrete Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods pred' :: I Word8 l r -> Maybe (I Word8 l r) Source # succ' :: I Word8 l r -> Maybe (I Word8 l r) Source #
(Interval Int l r, l /= r) => Discrete Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods pred' :: I Int l r -> Maybe (I Int l r) Source # succ' :: I Int l r -> Maybe (I Int l r) Source #
(Interval Word l r, l /= r) => Discrete Word (l :: L Word :: Type) (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods pred' :: I Word l r -> Maybe (I Word l r) Source # succ' :: I Word l r -> Maybe (I Word l r) Source #
Interval Natural l ('Nothing :: Maybe Natural) => Discrete Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods pred' :: I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source # succ' :: I Natural l 'Nothing -> Maybe (I Natural l 'Nothing) Source #
(Interval Natural l ('Just r), l /= r) => Discrete Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods pred' :: I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source # succ' :: I Natural l ('Just r) -> Maybe (I Natural l ('Just r)) Source #
Discrete Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods pred' :: I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source # succ' :: I Integer0 'Nothing 'Nothing -> Maybe (I Integer0 'Nothing 'Nothing) Source #
Interval Integer ('Nothing :: Maybe Integer) ('Just r) => Discrete Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods pred' :: I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source # succ' :: I Integer0 'Nothing ('Just r) -> Maybe (I Integer0 'Nothing ('Just r)) Source #
Interval Integer ('Just l) ('Nothing :: Maybe Integer) => Discrete Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods pred' :: I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source # succ' :: I Integer0 ('Just l) 'Nothing -> Maybe (I Integer0 ('Just l) 'Nothing) Source #
(Interval Integer ('Just l) ('Just r), l /= r) => Discrete Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods pred' :: I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source # succ' :: I Integer ('Just l) ('Just r) -> Maybe (I Integer ('Just l) ('Just r)) Source #

class Discrete x l r => Succ (x :: Type) (l :: L x) (r :: R x) where Source #

Discrete Intervals where obtaining the successor is knonwn to be a closed operation.

Methods

succ :: I x l r -> I x l r Source #

succ a is the next discrete value in the interval, the successor.

Correspondence with succ'

forall (a :: I x l r).
  (Succ x l r) =>
    succ' a  ==  Just (succ a)

Instances

Instances details

Discrete Integer l ('Nothing :: Maybe Integer) => Succ Integer (l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods succ :: I Integer0 l 'Nothing -> I Integer0 l 'Nothing Source #
Discrete Natural l ('Nothing :: Maybe Natural) => Succ Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods succ :: I Natural l 'Nothing -> I Natural l 'Nothing Source #

class Discrete x l r => Pred (x :: Type) (l :: L x) (r :: R x) where Source #

Discrete Intervals where obtaining the predecessor is knonwn to be a closed operation.

Methods

pred :: I x l r -> I x l r Source #

pred a is the previous discrete value in the interval, the predecessor.

Correspondence with pred'

forall (a :: I x l r).
  (Pred x l r) =>
    pred' a  ==  Just (pred a)

Instances

Instances details

Discrete Integer ('Nothing :: Maybe Integer) r => Pred Integer ('Nothing :: Maybe Integer) (r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods pred :: I Integer0 'Nothing r -> I Integer0 'Nothing r Source #

class Interval x l r => One (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals known to be inhabited by the number one.

Methods

one :: I x l r Source #

One.

Instances

Instances details

(Interval CChar l r, l <= P 1, P 1 <= r) => One CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods one :: I CChar l r Source #
(Interval CInt l r, l <= P 1, P 1 <= r) => One CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods one :: I CInt l r Source #
(Interval CIntMax l r, l <= P 1, P 1 <= r) => One CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods one :: I CIntMax l r Source #
(Interval CIntPtr l r, l <= P 1, P 1 <= r) => One CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods one :: I CIntPtr l r Source #
(Interval CLLong l r, l <= P 1, P 1 <= r) => One CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods one :: I CLLong l r Source #
(Interval CLong l r, l <= P 1, P 1 <= r) => One CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods one :: I CLong l r Source #
(Interval CPtrdiff l r, l <= P 1, P 1 <= r) => One CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods one :: I CPtrdiff l r Source #
(Interval CSChar l r, l <= P 1, P 1 <= r) => One CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods one :: I CSChar l r Source #
(Interval CShort l r, l <= P 1, P 1 <= r) => One CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods one :: I CShort l r Source #
(Interval CSize l r, l <= 1, 1 <= r) => One CSize (l :: L CSize :: Type) (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods one :: I CSize l r Source #
(Interval CUChar l r, l <= 1, 1 <= r) => One CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods one :: I CUChar l r Source #
(Interval CUInt l r, l <= 1, 1 <= r) => One CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods one :: I CUInt l r Source #
(Interval CUIntMax l r, l <= 1, 1 <= r) => One CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods one :: I CUIntMax l r Source #
(Interval CUIntPtr l r, l <= 1, 1 <= r) => One CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods one :: I CUIntPtr l r Source #
(Interval CULLong l r, l <= 1, 1 <= r) => One CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods one :: I CULLong l r Source #
(Interval CULong l r, l <= 1, 1 <= r) => One CULong (l :: L CULong :: Type) (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods one :: I CULong l r Source #
(Interval CUShort l r, l <= 1, 1 <= r) => One CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods one :: I CUShort l r Source #
(Interval CWchar l r, l <= P 1, P 1 <= r) => One CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods one :: I CWchar l r Source #
(Interval Int16 l r, l <= P 1, P 1 <= r) => One Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods one :: I Int16 l r Source #
(Interval Int32 l r, l <= P 1, P 1 <= r) => One Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods one :: I Int32 l r Source #
(Interval Int64 l r, l <= P 1, P 1 <= r) => One Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods one :: I Int64 l r Source #
(Interval Int8 l r, l <= P 1, P 1 <= r) => One Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods one :: I Int8 l r Source #
(Interval Word16 l r, l <= 1, 1 <= r) => One Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods one :: I Word16 l r Source #
(Interval Word32 l r, l <= 1, 1 <= r) => One Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods one :: I Word32 l r Source #
(Interval Word64 l r, l <= 1, 1 <= r) => One Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods one :: I Word64 l r Source #
(Interval Word8 l r, l <= 1, 1 <= r) => One Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods one :: I Word8 l r Source #
(Interval Int l r, l <= P 1, P 1 <= r) => One Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods one :: I Int l r Source #
(Interval Word l r, l <= 1, 1 <= r) => One Word (l :: L Word :: Type) (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods one :: I Word l r Source #
(Interval Natural l ('Nothing :: Maybe Natural), l <= 1) => One Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods one :: I Natural l 'Nothing Source #
(Interval Natural l ('Just r), l <= 1, 1 <= r) => One Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods one :: I Natural l ('Just r) Source #
One Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods one :: I Rational0 'Nothing 'Nothing Source #
One Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods one :: I Integer0 'Nothing 'Nothing Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)), (1 / 1) < r) => One Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods one :: I Rational0 'Nothing ('Just '('False, r)) Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)), (1 / 1) <= r) => One Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods one :: I Rational0 'Nothing ('Just '('True, r)) Source #
(Interval Integer ('Nothing :: Maybe Integer) ('Just r), P 1 <= r) => One Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods one :: I Integer0 'Nothing ('Just r) Source #
(Interval Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)), l < (1 / 1)) => One Rational ('Just '('False, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods one :: I Rational0 ('Just '('False, l)) 'Nothing Source #
(Interval Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)), l <= (1 / 1)) => One Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods one :: I Rational0 ('Just '('True, l)) 'Nothing Source #
(Interval Integer ('Just l) ('Nothing :: Maybe Integer), l <= P 1) => One Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods one :: I Integer0 ('Just l) 'Nothing Source #
(l < (1 / 1), (1 / 1) < r, Interval Rational ('Just '('False, l)) ('Just '('False, r))) => One Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods one :: I Rational ('Just '('False, l)) ('Just '('False, r)) Source #
(l < (1 / 1), (1 / 1) <= r, Interval Rational ('Just '('False, l)) ('Just '('True, r))) => One Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods one :: I Rational ('Just '('False, l)) ('Just '('True, r)) Source #
(l <= (1 / 1), (1 / 1) < r, Interval Rational ('Just '('True, l)) ('Just '('False, r))) => One Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods one :: I Rational ('Just '('True, l)) ('Just '('False, r)) Source #
(l <= (1 / 1), (1 / 1) <= r, Interval Rational ('Just '('True, l)) ('Just '('True, r))) => One Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods one :: I Rational ('Just '('True, l)) ('Just '('True, r)) Source #
(Interval Integer ('Just l) ('Just r), l <= P 1, P 1 <= r) => One Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods one :: I Integer ('Just l) ('Just r) Source #

class Interval x l r => Zero (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals known to be inhabited by the number zero.

Methods

zero :: I x l r Source #

Zero.

Instances

Instances details

(Interval CChar l r, l <= P 0, P 0 <= r) => Zero CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods zero :: I CChar l r Source #
(Interval CInt l r, l <= P 0, P 0 <= r) => Zero CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods zero :: I CInt l r Source #
(Interval CIntMax l r, l <= P 0, P 0 <= r) => Zero CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods zero :: I CIntMax l r Source #
(Interval CIntPtr l r, l <= P 0, P 0 <= r) => Zero CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods zero :: I CIntPtr l r Source #
(Interval CLLong l r, l <= P 0, P 0 <= r) => Zero CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods zero :: I CLLong l r Source #
(Interval CLong l r, l <= P 0, P 0 <= r) => Zero CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods zero :: I CLong l r Source #
(Interval CPtrdiff l r, l <= P 0, P 0 <= r) => Zero CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods zero :: I CPtrdiff l r Source #
(Interval CSChar l r, l <= P 0, P 0 <= r) => Zero CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods zero :: I CSChar l r Source #
(Interval CShort l r, l <= P 0, P 0 <= r) => Zero CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods zero :: I CShort l r Source #
Interval CSize 0 r => Zero CSize 0 (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods zero :: I CSize 0 r Source #
Interval CUChar 0 r => Zero CUChar 0 (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods zero :: I CUChar 0 r Source #
Interval CUInt 0 r => Zero CUInt 0 (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods zero :: I CUInt 0 r Source #
Interval CUIntMax 0 r => Zero CUIntMax 0 (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods zero :: I CUIntMax 0 r Source #
Interval CUIntPtr 0 r => Zero CUIntPtr 0 (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods zero :: I CUIntPtr 0 r Source #
Interval CULLong 0 r => Zero CULLong 0 (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods zero :: I CULLong 0 r Source #
Interval CULong 0 r => Zero CULong 0 (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods zero :: I CULong 0 r Source #
Interval CUShort 0 r => Zero CUShort 0 (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods zero :: I CUShort 0 r Source #
(Interval CWchar l r, l <= P 0, P 0 <= r) => Zero CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods zero :: I CWchar l r Source #
(Interval Int16 l r, l <= P 0, P 0 <= r) => Zero Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods zero :: I Int16 l r Source #
(Interval Int32 l r, l <= P 0, P 0 <= r) => Zero Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods zero :: I Int32 l r Source #
(Interval Int64 l r, l <= P 0, P 0 <= r) => Zero Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods zero :: I Int64 l r Source #
(Interval Int8 l r, l <= P 0, P 0 <= r) => Zero Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods zero :: I Int8 l r Source #
Interval Word16 0 r => Zero Word16 0 (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods zero :: I Word16 0 r Source #
Interval Word32 0 r => Zero Word32 0 (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods zero :: I Word32 0 r Source #
Interval Word64 0 r => Zero Word64 0 (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods zero :: I Word64 0 r Source #
Interval Word8 0 r => Zero Word8 0 (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods zero :: I Word8 0 r Source #
Interval Natural 0 r => Zero Natural 0 (r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods zero :: I Natural 0 r Source #
(Interval Int l r, l <= P 0, P 0 <= r) => Zero Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods zero :: I Int l r Source #
Interval Word 0 r => Zero Word 0 (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods zero :: I Word 0 r Source #
Zero Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods zero :: I Rational0 'Nothing 'Nothing Source #
Zero Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods zero :: I Integer0 'Nothing 'Nothing Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)), (0 / 1) < r) => Zero Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods zero :: I Rational0 'Nothing ('Just '('False, r)) Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)), (0 / 1) <= r) => Zero Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods zero :: I Rational0 'Nothing ('Just '('True, r)) Source #
(Interval Integer ('Nothing :: Maybe Integer) ('Just r), P 0 <= r) => Zero Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods zero :: I Integer0 'Nothing ('Just r) Source #
(Interval Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)), l < (0 / 1)) => Zero Rational ('Just '('False, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods zero :: I Rational0 ('Just '('False, l)) 'Nothing Source #
(Interval Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)), l <= (0 / 1)) => Zero Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods zero :: I Rational0 ('Just '('True, l)) 'Nothing Source #
(Interval Integer ('Just l) ('Nothing :: Maybe Integer), l <= P 0) => Zero Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods zero :: I Integer0 ('Just l) 'Nothing Source #
(l < (0 / 1), (0 / 1) < r, Interval Rational ('Just '('False, l)) ('Just '('False, r))) => Zero Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods zero :: I Rational ('Just '('False, l)) ('Just '('False, r)) Source #
(l < (0 / 1), (0 / 1) <= r, Interval Rational ('Just '('False, l)) ('Just '('True, r))) => Zero Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods zero :: I Rational ('Just '('False, l)) ('Just '('True, r)) Source #
(l <= (0 / 1), (0 / 1) < r, Interval Rational ('Just '('True, l)) ('Just '('False, r))) => Zero Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods zero :: I Rational ('Just '('True, l)) ('Just '('False, r)) Source #
(l <= (0 / 1), (0 / 1) <= r, Interval Rational ('Just '('True, l)) ('Just '('True, r))) => Zero Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods zero :: I Rational ('Just '('True, l)) ('Just '('True, r)) Source #
(Interval Integer ('Just l) ('Just r), l <= P 0, P 0 <= r) => Zero Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods zero :: I Integer ('Just l) ('Just r) Source #

class Zero x l r => Negate (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals where negation is known to be a closed operation.

Methods

negate :: I x l r -> I x l r Source #

Additive inverse, if it fits in the interval.

Identity law

forall (a :: I x l r).
  (Negate x l r) =>
    a == negate (negate a)

Correspondence with negate'

forall (a :: I x l r) (b :: I x l r).
  (Minus x l r) =>
    negate' a b  ==  Just (negate a b)

Instances

Instances details

(Zero CChar l r, l == Negate r) => Negate CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods negate :: I CChar l r -> I CChar l r Source #
(Zero CInt l r, l == Negate r) => Negate CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods negate :: I CInt l r -> I CInt l r Source #
(Zero CIntMax l r, l == Negate r) => Negate CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods negate :: I CIntMax l r -> I CIntMax l r Source #
(Zero CIntPtr l r, l == Negate r) => Negate CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods negate :: I CIntPtr l r -> I CIntPtr l r Source #
(Zero CLLong l r, l == Negate r) => Negate CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods negate :: I CLLong l r -> I CLLong l r Source #
(Zero CLong l r, l == Negate r) => Negate CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods negate :: I CLong l r -> I CLong l r Source #
(Zero CPtrdiff l r, l == Negate r) => Negate CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods negate :: I CPtrdiff l r -> I CPtrdiff l r Source #
(Zero CSChar l r, l == Negate r) => Negate CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods negate :: I CSChar l r -> I CSChar l r Source #
(Zero CShort l r, l == Negate r) => Negate CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods negate :: I CShort l r -> I CShort l r Source #
(Zero CWchar l r, l == Negate r) => Negate CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods negate :: I CWchar l r -> I CWchar l r Source #
(Zero Int16 l r, l == Negate r) => Negate Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods negate :: I Int16 l r -> I Int16 l r Source #
(Zero Int32 l r, l == Negate r) => Negate Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods negate :: I Int32 l r -> I Int32 l r Source #
(Zero Int64 l r, l == Negate r) => Negate Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods negate :: I Int64 l r -> I Int64 l r Source #
(Zero Int8 l r, l == Negate r) => Negate Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods negate :: I Int8 l r -> I Int8 l r Source #
(Zero Int l r, l == Negate r) => Negate Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods negate :: I Int l r -> I Int l r Source #
Negate Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods negate :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing Source #
Negate Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods negate :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing Source #
(l == Negate r, Zero Rational ('Just '(i, l)) ('Just '(i, r))) => Negate Rational ('Just '(i, l) :: L Rational :: Type) ('Just '(i, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods negate :: I Rational ('Just '(i, l)) ('Just '(i, r)) -> I Rational ('Just '(i, l)) ('Just '(i, r)) Source #
(Zero Integer ('Just l) ('Just r), l == Negate r) => Negate Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods negate :: I Integer ('Just l) ('Just r) -> I Integer ('Just l) ('Just r) Source #

class Interval x l r => Plus (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals where addition is known to be a closed operation.

Methods

plus :: I x l r -> I x l r -> I x l r Source #

plus a b adds a and b.

Correspondence with plus'

forall (a :: I x l r) (b :: I x l r).
  (Plus x l r) =>
    plus' a b  ==  Just (plus a b)

Instances

Instances details

Interval Natural l ('Nothing :: Maybe Natural) => Plus Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods plus :: I Natural l 'Nothing -> I Natural l 'Nothing -> I Natural l 'Nothing Source #
Plus Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods plus :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing Source #
Plus Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods plus :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '(ir, r)), r <= (0 / 1)) => Plus Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '(ir, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods plus :: I Rational0 'Nothing ('Just '(ir, r)) -> I Rational0 'Nothing ('Just '(ir, r)) -> I Rational0 'Nothing ('Just '(ir, r)) Source #
(Interval Integer ('Nothing :: Maybe Integer) ('Just r), r <= P 0) => Plus Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods plus :: I Integer0 'Nothing ('Just r) -> I Integer0 'Nothing ('Just r) -> I Integer0 'Nothing ('Just r) Source #
(Interval Rational ('Just '(il, l)) ('Nothing :: Maybe (Bool, Rational)), (0 / 1) <= l) => Plus Rational ('Just '(il, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods plus :: I Rational0 ('Just '(il, l)) 'Nothing -> I Rational0 ('Just '(il, l)) 'Nothing -> I Rational0 ('Just '(il, l)) 'Nothing Source #
(Interval Integer ('Just l) ('Nothing :: Maybe Integer), P 0 <= l) => Plus Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods plus :: I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing Source #

class Interval x l r => Mult (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals where multiplication is known to be a closed operation.

Methods

mult :: I x l r -> I x l r -> I x l r Source #

mult a b multiplies a times b.

Correspondence with mult'

forall (a :: I x l r) (b :: I x l r).
  (Mult x l r) =>
    mult' a b  ==  Just (mult a b)

Instances

Instances details

Interval Natural l ('Nothing :: Maybe Natural) => Mult Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods mult :: I Natural l 'Nothing -> I Natural l 'Nothing -> I Natural l 'Nothing Source #
Mult Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods mult :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing Source #
Mult Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods mult :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing Source #
(Interval Rational ('Just '(il, l)) ('Nothing :: Maybe (Bool, Rational)), (1 / 1) <= l) => Mult Rational ('Just '(il, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods mult :: I Rational0 ('Just '(il, l)) 'Nothing -> I Rational0 ('Just '(il, l)) 'Nothing -> I Rational0 ('Just '(il, l)) 'Nothing Source #
(Interval Integer ('Just l) ('Nothing :: Maybe Integer), P 0 <= l) => Mult Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods mult :: I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing -> I Integer0 ('Just l) 'Nothing Source #
(Interval Rational ('Just '(il, l)) ('Just '(ir, r)), (0 / 1) <= l, r <= (1 / 1)) => Mult Rational ('Just '(il, l) :: L Rational :: Type) ('Just '(ir, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods mult :: I Rational ('Just '(il, l)) ('Just '(ir, r)) -> I Rational ('Just '(il, l)) ('Just '(ir, r)) -> I Rational ('Just '(il, l)) ('Just '(ir, r)) Source #

class Zero x l r => Minus (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals where subtraction is known to be a closed operation.

Methods

minus :: I x l r -> I x l r -> I x l r Source #

minus a b substracts b from a

Correspondence with minus'

forall (a :: I x l r) (b :: I x l r).
  (Minus x l r) =>
    minus' a b  ==  Just (minus a b)

Instances

Instances details

Minus Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods minus :: I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing -> I Rational0 'Nothing 'Nothing Source #
Minus Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods minus :: I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing -> I Integer0 'Nothing 'Nothing Source #

class Interval x l r => Div (x :: Type) (l :: L x) (r :: R x) where Source #

Intervals where division is known to be a closed operation.

Methods

div :: I x l r -> I x l r -> I x l r Source #

div a b divides a by b.

Correspondence with div'

forall (a :: I x l r) (b :: I x l r).
  (Div x l r) =>
    div' a b  ==  Just (div a b)

Instances

Instances details

((0 / 1) < l, r <= (1 / 1), Interval Rational ('Just '(il, l)) ('Just '(ir, r))) => Div Rational ('Just '(il, l) :: L Rational :: Type) ('Just '(ir, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods div :: I Rational ('Just '(il, l)) ('Just '(ir, r)) -> I Rational ('Just '(il, l)) ('Just '(ir, r)) -> I Rational ('Just '(il, l)) ('Just '(ir, r)) Source #

Known

class (Interval x l r, KnownCtx x l r t) => Known (x :: Type) (l :: L x) (r :: R x) (t :: T x) where Source #

Proof that t is known to be within l and r in I x l r.

NB: When defining Known instances, instead of mentioning any necessary constraints in the instance context, mention them them in KnownCtx. By doing so, when an instance of Known x l r is satisfied, KnownCtx x l r is satisfied as well. If you don't do this, with won't behave as you would expect.

Associated Types

type KnownCtx x l r t :: Constraint Source #

Constraints to be satisfied by t if it is known to be within the I x l r interval.

type KnownCtx x l r t = ()

Methods

known' :: Proxy t -> I x l r Source #

Obtain a term-level representation of t as I x l r.

Also consider using known, an alternative version of this function designed to be used with -XTypeApplications.

Instances

Instances details

(Interval CChar l r, KnownCtx CChar l r t) => Known CChar (l :: L CChar :: Type) (r :: R CChar :: Type) (t :: T CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Associated Types type KnownCtx CChar l r t Source # Methods known' :: Proxy t -> I CChar l r Source #
(Interval CInt l r, KnownCtx CInt l r t) => Known CInt (l :: L CInt :: Type) (r :: R CInt :: Type) (t :: T CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Associated Types type KnownCtx CInt l r t Source # Methods known' :: Proxy t -> I CInt l r Source #
(Interval CIntMax l r, KnownCtx CIntMax l r t) => Known CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) (t :: T CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Associated Types type KnownCtx CIntMax l r t Source # Methods known' :: Proxy t -> I CIntMax l r Source #
(Interval CIntPtr l r, KnownCtx CIntPtr l r t) => Known CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) (t :: T CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Associated Types type KnownCtx CIntPtr l r t Source # Methods known' :: Proxy t -> I CIntPtr l r Source #
(Interval CLLong l r, KnownCtx CLLong l r t) => Known CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) (t :: T CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Associated Types type KnownCtx CLLong l r t Source # Methods known' :: Proxy t -> I CLLong l r Source #
(Interval CLong l r, KnownCtx CLong l r t) => Known CLong (l :: L CLong :: Type) (r :: R CLong :: Type) (t :: T CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Associated Types type KnownCtx CLong l r t Source # Methods known' :: Proxy t -> I CLong l r Source #
(Interval CPtrdiff l r, KnownCtx CPtrdiff l r t) => Known CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) (t :: T CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Associated Types type KnownCtx CPtrdiff l r t Source # Methods known' :: Proxy t -> I CPtrdiff l r Source #
(Interval CSChar l r, KnownCtx CSChar l r t) => Known CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) (t :: T CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Associated Types type KnownCtx CSChar l r t Source # Methods known' :: Proxy t -> I CSChar l r Source #
(Interval CShort l r, KnownCtx CShort l r t) => Known CShort (l :: L CShort :: Type) (r :: R CShort :: Type) (t :: T CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Associated Types type KnownCtx CShort l r t Source # Methods known' :: Proxy t -> I CShort l r Source #
(Interval CSize l r, KnownCtx CSize l r t) => Known CSize (l :: L CSize :: Type) (r :: R CSize :: Type) (t :: T CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Associated Types type KnownCtx CSize l r t Source # Methods known' :: Proxy t -> I CSize l r Source #
(Interval CUChar l r, KnownCtx CUChar l r t) => Known CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) (t :: T CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Associated Types type KnownCtx CUChar l r t Source # Methods known' :: Proxy t -> I CUChar l r Source #
(Interval CUInt l r, KnownCtx CUInt l r t) => Known CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) (t :: T CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Associated Types type KnownCtx CUInt l r t Source # Methods known' :: Proxy t -> I CUInt l r Source #
(Interval CUIntMax l r, KnownCtx CUIntMax l r t) => Known CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) (t :: T CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Associated Types type KnownCtx CUIntMax l r t Source # Methods known' :: Proxy t -> I CUIntMax l r Source #
(Interval CUIntPtr l r, KnownCtx CUIntPtr l r t) => Known CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) (t :: T CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Associated Types type KnownCtx CUIntPtr l r t Source # Methods known' :: Proxy t -> I CUIntPtr l r Source #
(Interval CULLong l r, KnownCtx CULLong l r t) => Known CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) (t :: T CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Associated Types type KnownCtx CULLong l r t Source # Methods known' :: Proxy t -> I CULLong l r Source #
(Interval CULong l r, KnownCtx CULong l r t) => Known CULong (l :: L CULong :: Type) (r :: R CULong :: Type) (t :: T CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Associated Types type KnownCtx CULong l r t Source # Methods known' :: Proxy t -> I CULong l r Source #
(Interval CUShort l r, KnownCtx CUShort l r t) => Known CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) (t :: T CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Associated Types type KnownCtx CUShort l r t Source # Methods known' :: Proxy t -> I CUShort l r Source #
(Interval CWchar l r, KnownCtx CWchar l r t) => Known CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) (t :: T CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Associated Types type KnownCtx CWchar l r t Source # Methods known' :: Proxy t -> I CWchar l r Source #
(Interval Int16 l r, KnownCtx Int16 l r t) => Known Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) (t :: T Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Associated Types type KnownCtx Int16 l r t Source # Methods known' :: Proxy t -> I Int16 l r Source #
(Interval Int32 l r, KnownCtx Int32 l r t) => Known Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) (t :: T Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Associated Types type KnownCtx Int32 l r t Source # Methods known' :: Proxy t -> I Int32 l r Source #
(Interval Int64 l r, KnownCtx Int64 l r t) => Known Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) (t :: T Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Associated Types type KnownCtx Int64 l r t Source # Methods known' :: Proxy t -> I Int64 l r Source #
(Interval Int8 l r, KnownCtx Int8 l r t) => Known Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) (t :: T Int8 :: Type) Source #
Instance details Defined in I.Int8 Associated Types type KnownCtx Int8 l r t Source # Methods known' :: Proxy t -> I Int8 l r Source #
(Interval Word16 l r, KnownCtx Word16 l r t) => Known Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) (t :: T Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Associated Types type KnownCtx Word16 l r t Source # Methods known' :: Proxy t -> I Word16 l r Source #
(Interval Word32 l r, KnownCtx Word32 l r t) => Known Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) (t :: T Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Associated Types type KnownCtx Word32 l r t Source # Methods known' :: Proxy t -> I Word32 l r Source #
(Interval Word64 l r, KnownCtx Word64 l r t) => Known Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) (t :: T Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Associated Types type KnownCtx Word64 l r t Source # Methods known' :: Proxy t -> I Word64 l r Source #
(Interval Word8 l r, KnownCtx Word8 l r t) => Known Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) (t :: T Word8 :: Type) Source #
Instance details Defined in I.Word8 Associated Types type KnownCtx Word8 l r t Source # Methods known' :: Proxy t -> I Word8 l r Source #
(Interval Int l r, KnownCtx Int l r t) => Known Int (l :: L Int :: Type) (r :: R Int :: Type) (t :: T Int :: Type) Source #
Instance details Defined in I.Autogen.Int Associated Types type KnownCtx Int l r t Source # Methods known' :: Proxy t -> I Int l r Source #
(Interval Word l r, KnownCtx Word l r t) => Known Word (l :: L Word :: Type) (r :: R Word :: Type) (t :: T Word :: Type) Source #
Instance details Defined in I.Autogen.Word Associated Types type KnownCtx Word l r t Source # Methods known' :: Proxy t -> I Word l r Source #
(Interval Natural l ('Nothing :: Maybe Natural), KnownCtx Natural l ('Nothing :: Maybe Natural) t) => Known Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) (t :: T Natural :: Type) Source #
Instance details Defined in I.Natural Associated Types type KnownCtx Natural l 'Nothing t Source # Methods known' :: Proxy t -> I Natural l 'Nothing Source #
(Interval Natural l ('Just r), KnownCtx Natural l ('Just r) t) => Known Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) (t :: T Natural :: Type) Source #
Instance details Defined in I.Natural Associated Types type KnownCtx Natural l ('Just r) t Source # Methods known' :: Proxy t -> I Natural l ('Just r) Source #
KnownCtx Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) t => Known Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational 'Nothing 'Nothing t Source # Methods known' :: Proxy t -> I Rational0 'Nothing 'Nothing Source #
KnownCtx Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) t => Known Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) (t :: T Integer :: Type) Source #
Instance details Defined in I.Integer Associated Types type KnownCtx Integer 'Nothing 'Nothing t Source # Methods known' :: Proxy t -> I Integer0 'Nothing 'Nothing Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)), KnownCtx Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)) t) => Known Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r) :: R Rational :: Type) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational 'Nothing ('Just '('False, r)) t Source # Methods known' :: Proxy t -> I Rational0 'Nothing ('Just '('False, r)) Source #
(Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)), KnownCtx Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)) t) => Known Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational 'Nothing ('Just '('True, r)) t Source # Methods known' :: Proxy t -> I Rational0 'Nothing ('Just '('True, r)) Source #
(Interval Integer ('Nothing :: Maybe Integer) ('Just r), KnownCtx Integer ('Nothing :: Maybe Integer) ('Just r) t) => Known Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) (t :: T Integer :: Type) Source #
Instance details Defined in I.Integer Associated Types type KnownCtx Integer 'Nothing ('Just r) t Source # Methods known' :: Proxy t -> I Integer0 'Nothing ('Just r) Source #
(Interval Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)), KnownCtx Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)) t) => Known Rational ('Just '('False, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational ('Just '('False, l)) 'Nothing t Source # Methods known' :: Proxy t -> I Rational0 ('Just '('False, l)) 'Nothing Source #
(Interval Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)), KnownCtx Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)) t) => Known Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational ('Just '('True, l)) 'Nothing t Source # Methods known' :: Proxy t -> I Rational0 ('Just '('True, l)) 'Nothing Source #
(Interval Integer ('Just l) ('Nothing :: Maybe Integer), KnownCtx Integer ('Just l) ('Nothing :: Maybe Integer) t) => Known Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) (t :: T Integer :: Type) Source #
Instance details Defined in I.Integer Associated Types type KnownCtx Integer ('Just l) 'Nothing t Source # Methods known' :: Proxy t -> I Integer0 ('Just l) 'Nothing Source #
(Interval Rational ('Just '('False, l)) ('Just '('False, r)), KnownCtx Rational ('Just '('False, l)) ('Just '('False, r)) t) => Known Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational ('Just '('False, l)) ('Just '('False, r)) t Source # Methods known' :: Proxy t -> I Rational ('Just '('False, l)) ('Just '('False, r)) Source #
(Interval Rational ('Just '('False, l)) ('Just '('True, r)), KnownCtx Rational ('Just '('False, l)) ('Just '('True, r)) t) => Known Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational ('Just '('False, l)) ('Just '('True, r)) t Source # Methods known' :: Proxy t -> I Rational ('Just '('False, l)) ('Just '('True, r)) Source #
(Interval Rational ('Just '('True, l)) ('Just '('False, r)), KnownCtx Rational ('Just '('True, l)) ('Just '('False, r)) t) => Known Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational ('Just '('True, l)) ('Just '('False, r)) t Source # Methods known' :: Proxy t -> I Rational ('Just '('True, l)) ('Just '('False, r)) Source #
(Interval Rational ('Just '('True, l)) ('Just '('True, r)), KnownCtx Rational ('Just '('True, l)) ('Just '('True, r)) t) => Known Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) (t :: T Rational :: Type) Source #
Instance details Defined in I.Rational Associated Types type KnownCtx Rational ('Just '('True, l)) ('Just '('True, r)) t Source # Methods known' :: Proxy t -> I Rational ('Just '('True, l)) ('Just '('True, r)) Source #
(Interval Integer ('Just l) ('Just r), KnownCtx Integer ('Just l) ('Just r) t) => Known Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) (t :: T Integer :: Type) Source #
Instance details Defined in I.Integer Associated Types type KnownCtx Integer ('Just l) ('Just r) t Source # Methods known' :: Proxy t -> I Integer ('Just l) ('Just r) Source #

known :: forall {x} t l r. Known x l r t => I x l r Source #

Alternative version of known', designed to be used with -XTypeApplications. It works only when x can be inferred by other means.

> :type known
known :: forall {x :: Type} (t :: T x) (l :: L x) (r :: R x). Known x l r t => I x l r

> :type known @55 :: Known Word8 l r 55 => I Word8 l r
known @55 :: Known Word8 l r 55 => I Word8 l r

> :type known @55 @33 :: Known Word8 33 r 55 => I Word8 33 r
known @55 @33 :: Known Word8 33 r 55 => I Word8 33 r

> :type known @55 @33 @77 :: I Word8 33 77
known @55 @33 @77 :: I Word8 33 77 :: I Word8 33 77

> known @55 @33 @77 :: I Word8 33 77
55

class Interval x l r => With (x :: Type) (l :: L x) (r :: R x) where Source #

Proof that I x l r contains a value of type x whose type-level representation t :: T x satisfies a Known x l r t.

Methods

with :: I x l r -> (forall (t :: T x). Known x l r t => Proxy t -> b) -> b Source #

Bring to scope the type-level representation of x as t :: T x, together with the constraints that prove that t is Known to be in the interval I x l r.

Identity law

x  ==  with x known'

Instances

Instances details

Interval CChar l r => With CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods with :: I CChar l r -> (forall (t :: T CChar). Known CChar l r t => Proxy t -> b) -> b Source #
Interval CInt l r => With CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods with :: I CInt l r -> (forall (t :: T CInt). Known CInt l r t => Proxy t -> b) -> b Source #
Interval CIntMax l r => With CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods with :: I CIntMax l r -> (forall (t :: T CIntMax). Known CIntMax l r t => Proxy t -> b) -> b Source #
Interval CIntPtr l r => With CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods with :: I CIntPtr l r -> (forall (t :: T CIntPtr). Known CIntPtr l r t => Proxy t -> b) -> b Source #
Interval CLLong l r => With CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods with :: I CLLong l r -> (forall (t :: T CLLong). Known CLLong l r t => Proxy t -> b) -> b Source #
Interval CLong l r => With CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods with :: I CLong l r -> (forall (t :: T CLong). Known CLong l r t => Proxy t -> b) -> b Source #
Interval CPtrdiff l r => With CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods with :: I CPtrdiff l r -> (forall (t :: T CPtrdiff). Known CPtrdiff l r t => Proxy t -> b) -> b Source #
Interval CSChar l r => With CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods with :: I CSChar l r -> (forall (t :: T CSChar). Known CSChar l r t => Proxy t -> b) -> b Source #
Interval CShort l r => With CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods with :: I CShort l r -> (forall (t :: T CShort). Known CShort l r t => Proxy t -> b) -> b Source #
Interval CSize l r => With CSize (l :: L CSize :: Type) (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods with :: I CSize l r -> (forall (t :: T CSize). Known CSize l r t => Proxy t -> b) -> b Source #
Interval CUChar l r => With CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods with :: I CUChar l r -> (forall (t :: T CUChar). Known CUChar l r t => Proxy t -> b) -> b Source #
Interval CUInt l r => With CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods with :: I CUInt l r -> (forall (t :: T CUInt). Known CUInt l r t => Proxy t -> b) -> b Source #
Interval CUIntMax l r => With CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods with :: I CUIntMax l r -> (forall (t :: T CUIntMax). Known CUIntMax l r t => Proxy t -> b) -> b Source #
Interval CUIntPtr l r => With CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods with :: I CUIntPtr l r -> (forall (t :: T CUIntPtr). Known CUIntPtr l r t => Proxy t -> b) -> b Source #
Interval CULLong l r => With CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods with :: I CULLong l r -> (forall (t :: T CULLong). Known CULLong l r t => Proxy t -> b) -> b Source #
Interval CULong l r => With CULong (l :: L CULong :: Type) (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods with :: I CULong l r -> (forall (t :: T CULong). Known CULong l r t => Proxy t -> b) -> b Source #
Interval CUShort l r => With CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods with :: I CUShort l r -> (forall (t :: T CUShort). Known CUShort l r t => Proxy t -> b) -> b Source #
Interval CWchar l r => With CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods with :: I CWchar l r -> (forall (t :: T CWchar). Known CWchar l r t => Proxy t -> b) -> b Source #
Interval Int16 l r => With Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods with :: I Int16 l r -> (forall (t :: T Int16). Known Int16 l r t => Proxy t -> b) -> b Source #
Interval Int32 l r => With Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods with :: I Int32 l r -> (forall (t :: T Int32). Known Int32 l r t => Proxy t -> b) -> b Source #
Interval Int64 l r => With Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods with :: I Int64 l r -> (forall (t :: T Int64). Known Int64 l r t => Proxy t -> b) -> b Source #
Interval Int8 l r => With Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods with :: I Int8 l r -> (forall (t :: T Int8). Known Int8 l r t => Proxy t -> b) -> b Source #
Interval Word16 l r => With Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods with :: I Word16 l r -> (forall (t :: T Word16). Known Word16 l r t => Proxy t -> b) -> b Source #
Interval Word32 l r => With Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods with :: I Word32 l r -> (forall (t :: T Word32). Known Word32 l r t => Proxy t -> b) -> b Source #
Interval Word64 l r => With Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods with :: I Word64 l r -> (forall (t :: T Word64). Known Word64 l r t => Proxy t -> b) -> b Source #
Interval Word8 l r => With Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods with :: I Word8 l r -> (forall (t :: T Word8). Known Word8 l r t => Proxy t -> b) -> b Source #
Interval Int l r => With Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods with :: I Int l r -> (forall (t :: T Int). Known Int l r t => Proxy t -> b) -> b Source #
Interval Word l r => With Word (l :: L Word :: Type) (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods with :: I Word l r -> (forall (t :: T Word). Known Word l r t => Proxy t -> b) -> b Source #
Interval Natural l ('Nothing :: Maybe Natural) => With Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods with :: I Natural l 'Nothing -> (forall (t :: T Natural). Known Natural l 'Nothing t => Proxy t -> b) -> b Source #
Interval Natural l ('Just r) => With Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods with :: I Natural l ('Just r) -> (forall (t :: T Natural). Known Natural l ('Just r) t => Proxy t -> b) -> b Source #
With Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods with :: I Rational0 'Nothing 'Nothing -> (forall (t :: T Rational0). Known Rational0 'Nothing 'Nothing t => Proxy t -> b) -> b Source #
With Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods with :: I Integer0 'Nothing 'Nothing -> (forall (t :: T Integer0). Known Integer0 'Nothing 'Nothing t => Proxy t -> b) -> b Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)) => With Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods with :: I Rational0 'Nothing ('Just '('False, r)) -> (forall (t :: T Rational0). Known Rational0 'Nothing ('Just '('False, r)) t => Proxy t -> b) -> b Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)) => With Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods with :: I Rational0 'Nothing ('Just '('True, r)) -> (forall (t :: T Rational0). Known Rational0 'Nothing ('Just '('True, r)) t => Proxy t -> b) -> b Source #
Interval Integer ('Nothing :: Maybe Integer) ('Just r) => With Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods with :: I Integer0 'Nothing ('Just r) -> (forall (t :: T Integer0). Known Integer0 'Nothing ('Just r) t => Proxy t -> b) -> b Source #
Interval Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)) => With Rational ('Just '('False, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods with :: I Rational0 ('Just '('False, l)) 'Nothing -> (forall (t :: T Rational0). Known Rational0 ('Just '('False, l)) 'Nothing t => Proxy t -> b) -> b Source #
Interval Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)) => With Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods with :: I Rational0 ('Just '('True, l)) 'Nothing -> (forall (t :: T Rational0). Known Rational0 ('Just '('True, l)) 'Nothing t => Proxy t -> b) -> b Source #
Interval Integer ('Just l) ('Nothing :: Maybe Integer) => With Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods with :: I Integer0 ('Just l) 'Nothing -> (forall (t :: T Integer0). Known Integer0 ('Just l) 'Nothing t => Proxy t -> b) -> b Source #
Interval Rational ('Just '('False, l)) ('Just '('False, r)) => With Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods with :: I Rational ('Just '('False, l)) ('Just '('False, r)) -> (forall (t :: T Rational). Known Rational ('Just '('False, l)) ('Just '('False, r)) t => Proxy t -> b) -> b Source #
Interval Rational ('Just '('False, l)) ('Just '('True, r)) => With Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods with :: I Rational ('Just '('False, l)) ('Just '('True, r)) -> (forall (t :: T Rational). Known Rational ('Just '('False, l)) ('Just '('True, r)) t => Proxy t -> b) -> b Source #
Interval Rational ('Just '('True, l)) ('Just '('False, r)) => With Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods with :: I Rational ('Just '('True, l)) ('Just '('False, r)) -> (forall (t :: T Rational). Known Rational ('Just '('True, l)) ('Just '('False, r)) t => Proxy t -> b) -> b Source #
Interval Rational ('Just '('True, l)) ('Just '('True, r)) => With Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods with :: I Rational ('Just '('True, l)) ('Just '('True, r)) -> (forall (t :: T Rational). Known Rational ('Just '('True, l)) ('Just '('True, r)) t => Proxy t -> b) -> b Source #
Interval Integer ('Just l) ('Just r) => With Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods with :: I Integer ('Just l) ('Just r) -> (forall (t :: T Integer). Known Integer ('Just l) ('Just r) t => Proxy t -> b) -> b Source #

min :: forall x l r. Known x l r (MinI x l r) => I x l r Source #

Minimum value in the interval, if MinI x is defined.

max :: forall x l r. Known x l r (MaxI x l r) => I x l r Source #

Maximum value in the interval, if MaxI x is defined.

single :: forall x l r. (MinI x l r ~ MaxI x l r, Known x l r (MinI x l r)) => I x l r Source #

If an Interval contains a single inhabitant, obtain it.

Testing

class Interval x l r => Shove (x :: Type) (l :: L x) (r :: R x) where Source #

Shove an x into an interval I x l r, somehow.

Note: This class is for testing purposes only. For example, if you want to generate random values of type I x l r for testing purposes, all you have to do is generate random values of type x and then shove them into I x l r.

Note: We don't like this too much. If there was a good way to export generators for Hedgehog or QuickCheck without depending on these libraries, we'd probably export that instead.

Methods

shove :: x -> I x l r Source #

No guarantees are made about the x value that ends up in I x l r. In particular, you can't expect id == unwrap . shove, not even for x values for which from == Just. All shove guarantees is a more or less uniform distribution.

Instances

Instances details

Interval CChar l r => Shove CChar (l :: L CChar :: Type) (r :: R CChar :: Type) Source #
Instance details Defined in I.Autogen.CChar Methods shove :: CChar -> I CChar l r Source #
Interval CInt l r => Shove CInt (l :: L CInt :: Type) (r :: R CInt :: Type) Source #
Instance details Defined in I.Autogen.CInt Methods shove :: CInt -> I CInt l r Source #
Interval CIntMax l r => Shove CIntMax (l :: L CIntMax :: Type) (r :: R CIntMax :: Type) Source #
Instance details Defined in I.Autogen.CIntMax Methods shove :: CIntMax -> I CIntMax l r Source #
Interval CIntPtr l r => Shove CIntPtr (l :: L CIntPtr :: Type) (r :: R CIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CIntPtr Methods shove :: CIntPtr -> I CIntPtr l r Source #
Interval CLLong l r => Shove CLLong (l :: L CLLong :: Type) (r :: R CLLong :: Type) Source #
Instance details Defined in I.Autogen.CLLong Methods shove :: CLLong -> I CLLong l r Source #
Interval CLong l r => Shove CLong (l :: L CLong :: Type) (r :: R CLong :: Type) Source #
Instance details Defined in I.Autogen.CLong Methods shove :: CLong -> I CLong l r Source #
Interval CPtrdiff l r => Shove CPtrdiff (l :: L CPtrdiff :: Type) (r :: R CPtrdiff :: Type) Source #
Instance details Defined in I.Autogen.CPtrdiff Methods shove :: CPtrdiff -> I CPtrdiff l r Source #
Interval CSChar l r => Shove CSChar (l :: L CSChar :: Type) (r :: R CSChar :: Type) Source #
Instance details Defined in I.Autogen.CSChar Methods shove :: CSChar -> I CSChar l r Source #
Interval CShort l r => Shove CShort (l :: L CShort :: Type) (r :: R CShort :: Type) Source #
Instance details Defined in I.Autogen.CShort Methods shove :: CShort -> I CShort l r Source #
Interval CSize l r => Shove CSize (l :: L CSize :: Type) (r :: R CSize :: Type) Source #
Instance details Defined in I.Autogen.CSize Methods shove :: CSize -> I CSize l r Source #
Interval CUChar l r => Shove CUChar (l :: L CUChar :: Type) (r :: R CUChar :: Type) Source #
Instance details Defined in I.Autogen.CUChar Methods shove :: CUChar -> I CUChar l r Source #
Interval CUInt l r => Shove CUInt (l :: L CUInt :: Type) (r :: R CUInt :: Type) Source #
Instance details Defined in I.Autogen.CUInt Methods shove :: CUInt -> I CUInt l r Source #
Interval CUIntMax l r => Shove CUIntMax (l :: L CUIntMax :: Type) (r :: R CUIntMax :: Type) Source #
Instance details Defined in I.Autogen.CUIntMax Methods shove :: CUIntMax -> I CUIntMax l r Source #
Interval CUIntPtr l r => Shove CUIntPtr (l :: L CUIntPtr :: Type) (r :: R CUIntPtr :: Type) Source #
Instance details Defined in I.Autogen.CUIntPtr Methods shove :: CUIntPtr -> I CUIntPtr l r Source #
Interval CULLong l r => Shove CULLong (l :: L CULLong :: Type) (r :: R CULLong :: Type) Source #
Instance details Defined in I.Autogen.CULLong Methods shove :: CULLong -> I CULLong l r Source #
Interval CULong l r => Shove CULong (l :: L CULong :: Type) (r :: R CULong :: Type) Source #
Instance details Defined in I.Autogen.CULong Methods shove :: CULong -> I CULong l r Source #
Interval CUShort l r => Shove CUShort (l :: L CUShort :: Type) (r :: R CUShort :: Type) Source #
Instance details Defined in I.Autogen.CUShort Methods shove :: CUShort -> I CUShort l r Source #
Interval CWchar l r => Shove CWchar (l :: L CWchar :: Type) (r :: R CWchar :: Type) Source #
Instance details Defined in I.Autogen.CWchar Methods shove :: CWchar -> I CWchar l r Source #
Interval Int16 l r => Shove Int16 (l :: L Int16 :: Type) (r :: R Int16 :: Type) Source #
Instance details Defined in I.Autogen.Int16 Methods shove :: Int16 -> I Int16 l r Source #
Interval Int32 l r => Shove Int32 (l :: L Int32 :: Type) (r :: R Int32 :: Type) Source #
Instance details Defined in I.Autogen.Int32 Methods shove :: Int32 -> I Int32 l r Source #
Interval Int64 l r => Shove Int64 (l :: L Int64 :: Type) (r :: R Int64 :: Type) Source #
Instance details Defined in I.Autogen.Int64 Methods shove :: Int64 -> I Int64 l r Source #
Interval Int8 l r => Shove Int8 (l :: L Int8 :: Type) (r :: R Int8 :: Type) Source #
Instance details Defined in I.Int8 Methods shove :: Int8 -> I Int8 l r Source #
Interval Word16 l r => Shove Word16 (l :: L Word16 :: Type) (r :: R Word16 :: Type) Source #
Instance details Defined in I.Autogen.Word16 Methods shove :: Word16 -> I Word16 l r Source #
Interval Word32 l r => Shove Word32 (l :: L Word32 :: Type) (r :: R Word32 :: Type) Source #
Instance details Defined in I.Autogen.Word32 Methods shove :: Word32 -> I Word32 l r Source #
Interval Word64 l r => Shove Word64 (l :: L Word64 :: Type) (r :: R Word64 :: Type) Source #
Instance details Defined in I.Autogen.Word64 Methods shove :: Word64 -> I Word64 l r Source #
Interval Word8 l r => Shove Word8 (l :: L Word8 :: Type) (r :: R Word8 :: Type) Source #
Instance details Defined in I.Word8 Methods shove :: Word8 -> I Word8 l r Source #
Interval Int l r => Shove Int (l :: L Int :: Type) (r :: R Int :: Type) Source #
Instance details Defined in I.Autogen.Int Methods shove :: Int -> I Int l r Source #
Interval Word l r => Shove Word (l :: L Word :: Type) (r :: R Word :: Type) Source #
Instance details Defined in I.Autogen.Word Methods shove :: Word -> I Word l r Source #
Interval Natural l ('Nothing :: Maybe Natural) => Shove Natural (l :: L Natural :: Type) ('Nothing :: Maybe Natural) Source #
Instance details Defined in I.Natural Methods shove :: Natural -> I Natural l 'Nothing Source #
Interval Natural l ('Just r) => Shove Natural (l :: L Natural :: Type) ('Just r :: R Natural :: Type) Source #
Instance details Defined in I.Natural Methods shove :: Natural -> I Natural l ('Just r) Source #
Shove Rational ('Nothing :: Maybe (Bool, Rational)) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods shove :: Rational0 -> I Rational0 'Nothing 'Nothing Source #
Interval Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) => Shove Integer ('Nothing :: Maybe Integer) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods shove :: Integer0 -> I Integer0 'Nothing 'Nothing Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r)) => Shove Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods shove :: Rational0 -> I Rational0 'Nothing ('Just '('False, r)) Source #
Interval Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r)) => Shove Rational ('Nothing :: Maybe (Bool, Rational)) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods shove :: Rational0 -> I Rational0 'Nothing ('Just '('True, r)) Source #
Interval Integer ('Nothing :: Maybe Integer) ('Just r) => Shove Integer ('Nothing :: Maybe Integer) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods shove :: Integer0 -> I Integer0 'Nothing ('Just r) Source #
Interval Rational ('Just '('False, l)) ('Nothing :: Maybe (Bool, Rational)) => Shove Rational ('Just '('False, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods shove :: Rational0 -> I Rational0 ('Just '('False, l)) 'Nothing Source #
Interval Rational ('Just '('True, l)) ('Nothing :: Maybe (Bool, Rational)) => Shove Rational ('Just '('True, l) :: L Rational :: Type) ('Nothing :: Maybe (Bool, Rational)) Source #
Instance details Defined in I.Rational Methods shove :: Rational0 -> I Rational0 ('Just '('True, l)) 'Nothing Source #
Interval Integer ('Just l) ('Nothing :: Maybe Integer) => Shove Integer ('Just l :: L Integer :: Type) ('Nothing :: Maybe Integer) Source #
Instance details Defined in I.Integer Methods shove :: Integer0 -> I Integer0 ('Just l) 'Nothing Source #
Interval Rational ('Just '('False, l)) ('Just '('False, r)) => Shove Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods shove :: Rational -> I Rational ('Just '('False, l)) ('Just '('False, r)) Source #
Interval Rational ('Just '('False, l)) ('Just '('True, r)) => Shove Rational ('Just '('False, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods shove :: Rational -> I Rational ('Just '('False, l)) ('Just '('True, r)) Source #
Interval Rational ('Just '('True, l)) ('Just '('False, r)) => Shove Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('False, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods shove :: Rational -> I Rational ('Just '('True, l)) ('Just '('False, r)) Source #
Interval Rational ('Just '('True, l)) ('Just '('True, r)) => Shove Rational ('Just '('True, l) :: L Rational :: Type) ('Just '('True, r) :: R Rational :: Type) Source #
Instance details Defined in I.Rational Methods shove :: Rational -> I Rational ('Just '('True, l)) ('Just '('True, r)) Source #
Interval Integer ('Just l) ('Just r) => Shove Integer ('Just l :: L Integer :: Type) ('Just r :: R Integer :: Type) Source #
Instance details Defined in I.Integer Methods shove :: Integer -> I Integer ('Just l) ('Just r) Source #

Danger

unsafest :: forall x l r. x -> I x l r Source #

unsafest allows you to wrap an x in an I x l r without checking whether the x is within the interval ends.

WARNING: This function is fast because it doesn't do any work, but also it is very dangerous because it ignores all the safety supposedly given by the I x l r type. Don't use this unless you have proved by other means that the x is within the I x l r interval. Please use from instead, or even unsafe.