Integral

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. 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.

TextShow instances and monomorphic functions for integral types. Since: 2

Functions for parsing and producing Integral values from/to ByteStrings based on the "Char8" encoding. That is, we assume an ASCII-compatible encoding of alphanumeric characters. Since: 0.3.0

Integral numbers, supporting integer division.

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

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 classes

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.

Parsers for integral numbers written in positional numeral systems.

Print integral numbers in common positional numeral systems.

Integral class operators applied point-wise on streams.

Safe overrides of the methods of class Integral.

This Prism can be used to model the fact that every Integral type is a subset of Integer. Embedding through the Prism only succeeds if the Integer would pass through unmodified when re-extracted.