Safe Haskell	None
Language	Haskell2010

Data.Semilattice.Upper

Description

Upper bounds, related to Bounded, Join, Meet, and Ord.

Synopsis

class Upper s where

Documentation

class Upper s where Source #

The least upper bound of s.

Laws:

If s is Bounded, we require upperBound and maxBound to agree:

upperBound = maxBound

If s is a Meet semilattice, upperBound must be the identity of /\:

upperBound /\ a = a

If s is a Join semilattice, upperBound must be the absorbing element of \/:

upperBound \/ a = upperBound

If s is Ordered, upperBound must be at least as large as every terminating value:

compare upperBound a /= LT

Methods

upperBound :: s Source #

upperBound :: Bounded s => s Source #

Instances

Upper Bool Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Bool Source #
Upper Char Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Char Source #
Upper Int Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Int Source #
Upper Int8 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Int8 Source #
Upper Int16 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Int16 Source #
Upper Int32 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Int32 Source #
Upper Int64 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Int64 Source #
Upper Ordering Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Ordering Source #
Upper Word8 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Word8 Source #
Upper Word16 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Word16 Source #
Upper Word32 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Word32 Source #
Upper Word64 Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Word64 Source #
Upper () Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: () Source #
Upper CDev Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CDev Source #
Upper CIno Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CIno Source #
Upper CMode Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CMode Source #
Upper COff Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: COff Source #
Upper CPid Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CPid Source #
Upper CSsize Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CSsize Source #
Upper CGid Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CGid Source #
Upper CNlink Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CNlink Source #
Upper CUid Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CUid Source #
Upper CTcflag Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CTcflag Source #
Upper CRLim Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CRLim Source #
Upper CBlkSize Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CBlkSize Source #
Upper CBlkCnt Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CBlkCnt Source #
Upper CClockId Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CClockId Source #
Upper CFsBlkCnt Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CFsBlkCnt Source #
Upper CFsFilCnt Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CFsFilCnt Source #
Upper CId Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CId Source #
Upper CKey Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CKey Source #
Upper Fd Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Fd Source #
Upper All Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: All Source #
Upper Any Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Any Source #
Upper Associativity Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Associativity Source #
Upper SourceUnpackedness Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: SourceUnpackedness Source #
Upper SourceStrictness Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: SourceStrictness Source #
Upper DecidedStrictness Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: DecidedStrictness Source #
Upper CChar Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CChar Source #
Upper CSChar Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CSChar Source #
Upper CUChar Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CUChar Source #
Upper CShort Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CShort Source #
Upper CUShort Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CUShort Source #
Upper CInt Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CInt Source #
Upper CUInt Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CUInt Source #
Upper CLong Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CLong Source #
Upper CULong Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CULong Source #
Upper CLLong Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CLLong Source #
Upper CULLong Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CULLong Source #
Upper CBool Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CBool Source #
Upper CPtrdiff Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CPtrdiff Source #
Upper CSize Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CSize Source #
Upper CWchar Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CWchar Source #
Upper CSigAtomic Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CSigAtomic Source #
Upper CIntPtr Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CIntPtr Source #
Upper CUIntPtr Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CUIntPtr Source #
Upper CIntMax Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CIntMax Source #
Upper CUIntMax Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: CUIntMax Source #
Upper WordPtr Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: WordPtr Source #
Upper IntPtr Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: IntPtr Source #
Upper GeneralCategory Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: GeneralCategory Source #
Upper a => Upper (Min a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Min a Source #
Upper a => Upper (Max a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Max a Source #
Upper a => Upper (First a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: First a Source #
Upper a => Upper (Last a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Last a Source #
Upper a => Upper (WrappedMonoid a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: WrappedMonoid a Source #
Upper a => Upper (Identity a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Identity a Source #
Upper a => Upper (Dual a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Dual a Source #
Upper a => Upper (Sum a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Sum a Source #
Upper a => Upper (Product a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Product a Source #
Upper a => Upper (Meeting a) Source #
Instance details Defined in Data.Semilattice.Meet Methods upperBound :: Meeting a Source #
Lower a => Upper (Tumble a) Source #
Instance details Defined in Data.Semilattice.Tumble Methods upperBound :: Tumble a Source #
Upper a => Upper (Order a) Source #
Instance details Defined in Data.Semilattice.Order Methods upperBound :: Order a Source #
Bounded a => Upper (Bound a) Source #
Instance details Defined in Data.Semilattice.Bound Methods upperBound :: Bound a Source #
Upper b => Upper (a -> b) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: a -> b Source #
(Upper a, Upper b) => Upper (a, b) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b) Source #
Upper (Proxy a) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Proxy a Source #
(Upper a, Upper b, Upper c) => Upper (a, b, c) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c) Source #
Upper a => Upper (Const a b) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Const a b Source #
Coercible a b => Upper (Coercion a b) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: Coercion a b Source #
a ~ b => Upper (a :~: b) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: a :~: b Source #
(Upper a, Upper b, Upper c, Upper d) => Upper (a, b, c, d) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d) Source #
a ~~ b => Upper (a :~~: b) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: a :~~: b Source #
(Upper a, Upper b, Upper c, Upper d, Upper e) => Upper (a, b, c, d, e) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f) => Upper (a, b, c, d, e, f) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g) => Upper (a, b, c, d, e, f, g) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h) => Upper (a, b, c, d, e, f, g, h) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i) => Upper (a, b, c, d, e, f, g, h, i) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i, Upper j) => Upper (a, b, c, d, e, f, g, h, i, j) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i, j) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i, Upper j, Upper k) => Upper (a, b, c, d, e, f, g, h, i, j, k) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i, j, k) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i, Upper j, Upper k, Upper l) => Upper (a, b, c, d, e, f, g, h, i, j, k, l) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i, Upper j, Upper k, Upper l, Upper m) => Upper (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i, Upper j, Upper k, Upper l, Upper m, Upper n) => Upper (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #
(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g, Upper h, Upper i, Upper j, Upper k, Upper l, Upper m, Upper n, Upper o) => Upper (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #
Instance details Defined in Data.Semilattice.Upper Methods upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

Bounded:

upperBound == (maxBound :: Bool)

Identity of /\:

upperBound /\ a == (a :: Bool)

Absorbing element of \/:

upperBound \/ a == (upperBound :: Bool)

Ord:

compare upperBound (a :: Bool) /= LT

>>> import Data.Semilattice.Join
>>> import Data.Semilattice.Meet
>>> import Test.QuickCheck (Arbitrary(..))
>>> import Test.QuickCheck.Function