Integral is:exact -package:LambdaHack -is:module

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.
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.
Pattern synonym that can be used to construct or pattern match on an Integer as if it were of any Integral type.
Integral numbers, supporting integer division.
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)
Integral Literal support e.g. 123 :: Integer 123 :: Word8
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.