Safe Haskell	None
Language	Haskell2010

LAoP.Utils.Internal

Contents

Natural data type
Coerce auxiliar functions to help promote Int typed functions to
List data type
Category type class
Orphan instances

Synopsis

newtype Natural (start :: Nat) (end :: Nat) = Nat Int
nat :: forall n m. (KnownNat n, KnownNat m) => Int -> Natural n m
coerceNat :: (Int -> Int -> Int) -> Natural a a' -> Natural b b' -> Natural c c'
coerceNat2 :: ((Int, Int) -> Int -> Int) -> (Natural a a', Natural b b') -> Natural c c' -> Natural d d'
coerceNat3 :: (Int -> Int -> a) -> Natural b b' -> Natural c c' -> a
newtype List a = L [a]
class Category k where
- type Object k o :: Constraint
- id :: Object k a => k a a
- (.) :: k b c -> k a b -> k a c

`Natural` data type

newtype Natural (start :: Nat) (end :: Nat) Source #

Wrapper around Ints that have a restrictive semantic associated. A value of type Natural n m can only be instanciated with some Int i that's n <= i <= m.

Constructors

Nat Int

Instances

(KnownNat n, KnownNat m) => Bounded (Natural n m) Source #
Instance details Defined in LAoP.Utils.Internal Methods minBound :: Natural n m # maxBound :: Natural n m #
(KnownNat n, KnownNat m) => Enum (Natural n m) Source #
Instance details Defined in LAoP.Utils.Internal Methods succ :: Natural n m -> Natural n m # pred :: Natural n m -> Natural n m # toEnum :: Int -> Natural n m # fromEnum :: Natural n m -> Int # enumFrom :: Natural n m -> [Natural n m] # enumFromThen :: Natural n m -> Natural n m -> [Natural n m] # enumFromTo :: Natural n m -> Natural n m -> [Natural n m] # enumFromThenTo :: Natural n m -> Natural n m -> Natural n m -> [Natural n m] #
Eq (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal Methods (==) :: Natural start end -> Natural start end -> Bool # (/=) :: Natural start end -> Natural start end -> Bool #
(KnownNat n, KnownNat m) => Num (Natural n m) Source #	Throws a runtime error if any of the operations overflows or underflows.
Instance details Defined in LAoP.Utils.Internal Methods (+) :: Natural n m -> Natural n m -> Natural n m # (-) :: Natural n m -> Natural n m -> Natural n m # (*) :: Natural n m -> Natural n m -> Natural n m # negate :: Natural n m -> Natural n m # abs :: Natural n m -> Natural n m # signum :: Natural n m -> Natural n m # fromInteger :: Integer -> Natural n m #
Ord (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal Methods compare :: Natural start end -> Natural start end -> Ordering # (<) :: Natural start end -> Natural start end -> Bool # (<=) :: Natural start end -> Natural start end -> Bool # (>) :: Natural start end -> Natural start end -> Bool # (>=) :: Natural start end -> Natural start end -> Bool # max :: Natural start end -> Natural start end -> Natural start end # min :: Natural start end -> Natural start end -> Natural start end #
Read (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal Methods readsPrec :: Int -> ReadS (Natural start end) # readList :: ReadS [Natural start end] # readPrec :: ReadPrec (Natural start end) # readListPrec :: ReadPrec [Natural start end] #
Show (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal Methods showsPrec :: Int -> Natural start end -> ShowS # show :: Natural start end -> String # showList :: [Natural start end] -> ShowS #
Generic (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal Associated Types type Rep (Natural start end) :: Type -> Type # Methods from :: Natural start end -> Rep (Natural start end) x # to :: Rep (Natural start end) x -> Natural start end #
NFData (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal Methods rnf :: Natural start end -> () #
type Rep (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal type Rep (Natural start end) = D1 (MetaData "Natural" "LAoP.Utils.Internal" "laop-0.1.1.0-77r4sagBL01x6jU5Cku3u" True) (C1 (MetaCons "Nat" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Int)))

nat :: forall n m. (KnownNat n, KnownNat m) => Int -> Natural n m Source #

Natural constructor function. Throws a runtime error if the Int value is greater than the corresponding m or lower than n in the Natural n m type.

Coerce auxiliar functions to help promote `Int` typed functions to

coerceNat :: (Int -> Int -> Int) -> Natural a a' -> Natural b b' -> Natural c c' Source #

Auxiliary function that promotes binary Int functions to Natural binary functions.

coerceNat2 :: ((Int, Int) -> Int -> Int) -> (Natural a a', Natural b b') -> Natural c c' -> Natural d d' Source #

Auxiliary function that promotes ternary (binary) Int functions to Natural functions.

coerceNat3 :: (Int -> Int -> a) -> Natural b b' -> Natural c c' -> a Source #

Auxiliary function that promotes ternary (binary) Int functions to Natural functions.

`List` data type

newtype List a Source #

Powerset data type.

This data type is a newtype wrapper around '[]'. This exists in order to implement an Enum and Bounded instance that cannot be harmful for the outside.

Constructors

L [a]

Instances

(Enum a, Bounded a) => Bounded (List a) Source #
Instance details Defined in LAoP.Utils.Internal Methods minBound :: List a # maxBound :: List a #
(Bounded a, Enum a, Eq a) => Enum (List a) Source #
Instance details Defined in LAoP.Utils.Internal Methods succ :: List a -> List a # pred :: List a -> List a # toEnum :: Int -> List a # fromEnum :: List a -> Int # enumFrom :: List a -> [List a] # enumFromThen :: List a -> List a -> [List a] # enumFromTo :: List a -> List a -> [List a] # enumFromThenTo :: List a -> List a -> List a -> [List a] #
Eq a => Eq (List a) Source #
Instance details Defined in LAoP.Utils.Internal Methods (==) :: List a -> List a -> Bool # (/=) :: List a -> List a -> Bool #
Read a => Read (List a) Source #
Instance details Defined in LAoP.Utils.Internal Methods readsPrec :: Int -> ReadS (List a) # readList :: ReadS [List a] # readPrec :: ReadPrec (List a) # readListPrec :: ReadPrec [List a] #
Show a => Show (List a) Source #
Instance details Defined in LAoP.Utils.Internal Methods showsPrec :: Int -> List a -> ShowS # show :: List a -> String # showList :: [List a] -> ShowS #

Category type class

class Category k where Source #

Constrained category instance

Associated Types

type Object k o :: Constraint Source #

Methods

id :: Object k a => k a a Source #

(.) :: k b c -> k a b -> k a c Source #

Instances

Category Relation Source #	It is possible to implement a constrained version of the category type class.
Instance details Defined in LAoP.Relation.Internal Associated Types type Object Relation o :: Constraint Source # Methods id :: Object Relation a => Relation a a Source # (.) :: Relation b c -> Relation a b -> Relation a c Source #
Num e => Category (Matrix e) Source #	It is possible to implement a constrained version of the category type class.
Instance details Defined in LAoP.Matrix.Internal Associated Types type Object (Matrix e) o :: Constraint Source # Methods id :: Object (Matrix e) a => Matrix e a a Source # (.) :: Matrix e b c -> Matrix e a b -> Matrix e a c Source #
Num e => Category (Matrix e) Source #	It is possible to implement a constrained version of the category type class.
Instance details Defined in LAoP.Matrix.Type Associated Types type Object (Matrix e) o :: Constraint Source # Methods id :: Object (Matrix e) a => Matrix e a a Source # (.) :: Matrix e b c -> Matrix e a b -> Matrix e a c Source #
Category ((->) :: Type -> Type -> Type) Source #
Instance details Defined in LAoP.Utils.Internal Associated Types type Object (->) o :: Constraint Source # Methods id :: Object (->) a => a -> a Source # (.) :: (b -> c) -> (a -> b) -> a -> c Source #

Orphan instances

(Bounded a, Bounded b) => Bounded (Either a b) Source #
Instance details Methods minBound :: Either a b # maxBound :: Either a b #
(Enum a, Bounded a, Enum b, Bounded b) => Enum (Either a b) Source #
Instance details Methods succ :: Either a b -> Either a b # pred :: Either a b -> Either a b # toEnum :: Int -> Either a b # fromEnum :: Either a b -> Int # enumFrom :: Either a b -> [Either a b] # enumFromThen :: Either a b -> Either a b -> [Either a b] # enumFromTo :: Either a b -> Either a b -> [Either a b] # enumFromThenTo :: Either a b -> Either a b -> Either a b -> [Either a b] #
(Enum a, Enum b, Bounded b) => Enum (a, b) Source #	Optimized `Enum` instance for tuples that comply with the given constraints.
Instance details Methods succ :: (a, b) -> (a, b) # pred :: (a, b) -> (a, b) # toEnum :: Int -> (a, b) # fromEnum :: (a, b) -> Int # enumFrom :: (a, b) -> [(a, b)] # enumFromThen :: (a, b) -> (a, b) -> [(a, b)] # enumFromTo :: (a, b) -> (a, b) -> [(a, b)] # enumFromThenTo :: (a, b) -> (a, b) -> (a, b) -> [(a, b)] #

Natural data type

Coerce auxiliar functions to help promote Int typed functions to

List data type

Category type class

Orphan instances

`Natural` data type

Coerce auxiliar functions to help promote `Int` typed functions to

`List` data type