Integral -package:aeson-optics -package:optics-core -package:lens-aeson -package:prelude-compat -package:lens

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.

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.

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

Print integral numbers in common positional numeral systems.

Parsers for integral numbers written in positional numeral systems.

Safe overrides of the methods of class Integral.

Generates a random integral number in the given [inclusive,inclusive] range. When the generator tries to shrink, it will shrink towards the origin of the specified Range. For example, the following generator will produce a number between 1970 and 2100, but will shrink towards 2000:

integral (Range.constantFrom 2000 1970 2100) :: Gen Int

Some sample outputs from this generator might look like:

=== Outcome ===
1973
=== Shrinks ===
2000
1987
1980
1976
1974

=== Outcome ===
2061
=== Shrinks ===
2000
2031
2046
2054
2058
2060

Integration using the rectangle rule.

Constructor for a simple integral type.

Integral symbol. Use integralFromTo if you want to specify the limits of the integral.

helper function to create a FieldInteger

Memoize an integral type.

matches an Integral value Note that the combinator (rPair . integral . integral) is ill-defined because the parse canwell. not tell where it is supposed to split the sequence of digits to produced two ints.

Integrate the input signal over time.

• Depends: before now.

Compute an indefinite integral of the polynomial, setting the constant term to zero.

>>> integral (3 * X^2 + 3) :: UPoly Double
1.0 * X^3 + 0.0 * X^2 + 3.0 * X + 0.0