Data.Semilattice.Upper

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

Documentation

class Upper s where

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

upperBound :: Bounded s => s

Instances

Upper Bool

Defined in Data.Semilattice.Upper

Methods

upperBound :: Bool

Upper Char

Defined in Data.Semilattice.Upper

Methods

upperBound :: Char

Upper Int

Defined in Data.Semilattice.Upper

Methods

upperBound :: Int

Upper Int8

Defined in Data.Semilattice.Upper

Methods

upperBound :: Int8

Upper Int16

Defined in Data.Semilattice.Upper

Methods

upperBound :: Int16

Upper Int32

Defined in Data.Semilattice.Upper

Methods

upperBound :: Int32

Upper Int64

Defined in Data.Semilattice.Upper

Methods

upperBound :: Int64

Upper Ordering

Defined in Data.Semilattice.Upper

Methods

upperBound :: Ordering

Upper Word8

Defined in Data.Semilattice.Upper

Methods

upperBound :: Word8

Upper Word16

Defined in Data.Semilattice.Upper

Methods

upperBound :: Word16

Upper Word32

Defined in Data.Semilattice.Upper

Methods

upperBound :: Word32

Upper Word64

Defined in Data.Semilattice.Upper

Methods

upperBound :: Word64

Upper ()

Defined in Data.Semilattice.Upper

Methods

upperBound :: ()

Upper CDev

Defined in Data.Semilattice.Upper

Methods

upperBound :: CDev

Upper CIno

Defined in Data.Semilattice.Upper

Methods

upperBound :: CIno

Upper CMode

Defined in Data.Semilattice.Upper

Methods

upperBound :: CMode

Upper COff

Defined in Data.Semilattice.Upper

Methods

upperBound :: COff

Upper CPid

Defined in Data.Semilattice.Upper

Methods

upperBound :: CPid

Upper CSsize

Defined in Data.Semilattice.Upper

Methods

upperBound :: CSsize

Upper CGid

Defined in Data.Semilattice.Upper

Methods

upperBound :: CGid

Upper CNlink

Defined in Data.Semilattice.Upper

Methods

upperBound :: CNlink

Upper CUid

Defined in Data.Semilattice.Upper

Methods

upperBound :: CUid

Upper CTcflag

Defined in Data.Semilattice.Upper

Methods

upperBound :: CTcflag

Upper CRLim

Defined in Data.Semilattice.Upper

Methods

upperBound :: CRLim

Upper CBlkSize

Defined in Data.Semilattice.Upper

Methods

upperBound :: CBlkSize

Upper CBlkCnt

Defined in Data.Semilattice.Upper

Methods

upperBound :: CBlkCnt

Upper CClockId

Defined in Data.Semilattice.Upper

Methods

upperBound :: CClockId

Upper CFsBlkCnt

Defined in Data.Semilattice.Upper

Methods

upperBound :: CFsBlkCnt

Upper CFsFilCnt

Defined in Data.Semilattice.Upper

Methods

upperBound :: CFsFilCnt

Upper CId

Defined in Data.Semilattice.Upper

Methods

upperBound :: CId

Upper CKey

Defined in Data.Semilattice.Upper

Methods

upperBound :: CKey

Upper Fd

Defined in Data.Semilattice.Upper

Methods

upperBound :: Fd

Upper All

Defined in Data.Semilattice.Upper

Methods

upperBound :: All

Upper Any

Defined in Data.Semilattice.Upper

Methods

upperBound :: Any

Upper Associativity

Defined in Data.Semilattice.Upper

Methods

upperBound :: Associativity

Upper SourceUnpackedness

Defined in Data.Semilattice.Upper

Methods

upperBound :: SourceUnpackedness

Upper SourceStrictness

Defined in Data.Semilattice.Upper

Methods

upperBound :: SourceStrictness

Upper DecidedStrictness

Defined in Data.Semilattice.Upper

Methods

upperBound :: DecidedStrictness

Upper CChar

Defined in Data.Semilattice.Upper

Methods

upperBound :: CChar

Upper CSChar

Defined in Data.Semilattice.Upper

Methods

upperBound :: CSChar

Upper CUChar

Defined in Data.Semilattice.Upper

Methods

upperBound :: CUChar

Upper CShort

Defined in Data.Semilattice.Upper

Methods

upperBound :: CShort

Upper CUShort

Defined in Data.Semilattice.Upper

Methods

upperBound :: CUShort

Upper CInt

Defined in Data.Semilattice.Upper

Methods

upperBound :: CInt

Upper CUInt

Defined in Data.Semilattice.Upper

Methods

upperBound :: CUInt

Upper CLong

Defined in Data.Semilattice.Upper

Methods

upperBound :: CLong

Upper CULong

Defined in Data.Semilattice.Upper

Methods

upperBound :: CULong

Upper CLLong

Defined in Data.Semilattice.Upper

Methods

upperBound :: CLLong

Upper CULLong

Defined in Data.Semilattice.Upper

Methods

upperBound :: CULLong

Upper CBool

Defined in Data.Semilattice.Upper

Methods

upperBound :: CBool

Upper CPtrdiff

Defined in Data.Semilattice.Upper

Methods

upperBound :: CPtrdiff

Upper CSize

Defined in Data.Semilattice.Upper

Methods

upperBound :: CSize

Upper CWchar

Defined in Data.Semilattice.Upper

Methods

upperBound :: CWchar

Upper CSigAtomic

Defined in Data.Semilattice.Upper

Methods

upperBound :: CSigAtomic

Upper CIntPtr

Defined in Data.Semilattice.Upper

Methods

upperBound :: CIntPtr

Upper CUIntPtr

Defined in Data.Semilattice.Upper

Methods

upperBound :: CUIntPtr

Upper CIntMax

Defined in Data.Semilattice.Upper

Methods

upperBound :: CIntMax

Upper CUIntMax

Defined in Data.Semilattice.Upper

Methods

upperBound :: CUIntMax

Upper WordPtr

Defined in Data.Semilattice.Upper

Methods

upperBound :: WordPtr

Upper IntPtr

Defined in Data.Semilattice.Upper

Methods

upperBound :: IntPtr

Upper GeneralCategory

Defined in Data.Semilattice.Upper

Methods

upperBound :: GeneralCategory

Upper a => Upper (Min a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Min a

Upper a => Upper (Max a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Max a

Upper a => Upper (First a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: First a

Upper a => Upper (Last a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Last a

Upper a => Upper (WrappedMonoid a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: WrappedMonoid a

Upper a => Upper (Identity a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Identity a

Upper a => Upper (Dual a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Dual a

Upper a => Upper (Sum a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Sum a

Upper a => Upper (Product a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Product a

Upper a => Upper (Meeting a)

Defined in Data.Semilattice.Meet

Methods

upperBound :: Meeting a

Lower a => Upper (Tumble a)

Defined in Data.Semilattice.Tumble

Methods

upperBound :: Tumble a

Upper a => Upper (Order a)

Defined in Data.Semilattice.Order

Methods

upperBound :: Order a

Bounded a => Upper (Bound a)

Defined in Data.Semilattice.Bound

Methods

upperBound :: Bound a

Upper b => Upper (a -> b)

Defined in Data.Semilattice.Upper

Methods

upperBound :: a -> b

(Upper a, Upper b) => Upper (a, b)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b)

Upper (Proxy a)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Proxy a

(Upper a, Upper b, Upper c) => Upper (a, b, c)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c)

Upper a => Upper (Const a b)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Const a b

Coercible a b => Upper (Coercion a b)

Defined in Data.Semilattice.Upper

Methods

upperBound :: Coercion a b

a ~ b => Upper (a :~: b)

Defined in Data.Semilattice.Upper

Methods

upperBound :: a :~: b

(Upper a, Upper b, Upper c, Upper d) => Upper (a, b, c, d)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d)

a ~~ b => Upper (a :~~: b)

Defined in Data.Semilattice.Upper

Methods

upperBound :: a :~~: b

(Upper a, Upper b, Upper c, Upper d, Upper e) => Upper (a, b, c, d, e)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e)

(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f) => Upper (a, b, c, d, e, f)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f)

(Upper a, Upper b, Upper c, Upper d, Upper e, Upper f, Upper g) => Upper (a, b, c, d, e, f, g)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i, j)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i, j, k)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

(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)

Defined in Data.Semilattice.Upper

Methods

upperBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

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