Integral -package:aeson-optics -package:optics-core -package:lens-aeson is:exact -is:module

class (Real a, Enum a) => Integral a

Integral numbers, supporting integer division. The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs. In addition, toInteger should be total, and fromInteger should be a left inverse for it, i.e. fromInteger (toInteger i) = i.

pattern Integral :: Integral a => a -> Integer

lens Numeric.Lens

class (Real a, Enum a) => Integral a

hedgehog Hedgehog.Internal.Prelude, base-compat Prelude.Compat, Cabal-syntax Distribution.Compat.Prelude, ihaskell IHaskellPrelude, dimensional Numeric.Units.Dimensional.Prelude, rebase Rebase.Prelude, LambdaHack Game.LambdaHack.Core.Prelude, cabal-install-solver Distribution.Solver.Compat.Prelude, faktory Faktory.Prelude

Integral numbers, supporting integer division. The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs. In addition, toInteger should be total, and fromInteger should be a left inverse for it, i.e. fromInteger (toInteger i) = i.

class (Real a, Enum a) => Integral a

ghc GHC.Prelude.Basic

class (Real a, Enum a) => Integral a

rio RIO.Prelude.Types, base-prelude BasePrelude, classy-prelude ClassyPrelude, clash-prelude Clash.HaskellPrelude, constrained-categories Control.Category.Constrained.Prelude Control.Category.Hask, yesod-paginator Yesod.Paginator.Prelude, distribution-opensuse OpenSuse.Prelude

Integral numbers, supporting integer division. The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

class (Real a, Enum a) => Integral a

basic-prelude CorePrelude

Integral numbers, supporting integer division.

class Integral a

basement Basement.Compat.Base Basement.Compat.NumLiteral Basement.Imports, foundation Foundation

Integral Literal support e.g. 123 :: Integer 123 :: Word8

class Distributive a => Integral a

numhask NumHask NumHask.Data.Integral

An Integral is anything that satisfies the law:

\a b -> b == zero || b * (a `div` b) + (a `mod` b) == a

>>> 3 `divMod` 2
(1,1)

>>> (-3) `divMod` 2
(-2,1)

>>> (-3) `quotRem` 2
(-1,-1)

class (Real a, Enum a) => Integral a

prelude-compat Prelude2010

Integral numbers, supporting integer division. The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the 'div'/'mod' and 'quot'/'rem' pairs, given suitable Euclidean functions f and g:

x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

Integral :: FormatType

PyF PyF.Formatters

Integral :: Class

dotparse DotParse.Examples.NumHask