Documentation

Data structure represents the rational number. Rational number can be represented as a pair of natural numbers n and m where m is nor equal to zero.

More convenient name for promoted constructor of Rat.

Type family for normalized pair of Nats — Rat.

Overloaded multiplication.

Overloaded division.

The result kind of overloaded multiplication.

The result kind of overloaded division.

Greatest common divisor for type-level naturals.

Example:

>>> :kind! Gcd 9 11
Gcd 9 11 :: Nat
= 1

>>> :kind! Gcd 9 12
Gcd 9 12 :: Nat
= 3

Normalization of type-level rational.

Example:

>>> :kind! Normalize (9 % 11)
Normalize (9 % 11) :: Rat
= 9 :% 11

>>> :kind! Normalize (9 % 12)
Normalize (9 % 12) :: Rat
= 3 :% 4

Division of type-level rationals.

If there are Rat with Nats a and b and another Rat with c d then the following formula should be applied: \[ \frac{a}{b} / \frac{c}{d} = \frac{a * d}{b * c} \]

Example:

>>> :kind! DivRat (9 % 11) (9 % 11)
DivRat (9 % 11) (9 % 11) :: Rat
= 1 :% 1

Comparison of type-level rationals, as a function.

>>> :kind! (1 :% 42) >=% (5 :% 42)
(1 :% 42) >=% (5 :% 42) :: Bool
= 'False

>>> :kind! (5 :% 42) >=% (1 :% 42)
(5 :% 42) >=% (1 :% 42) :: Bool
= 'True

>>> :kind! (42 :% 1) >=% (42 :% 1)
(42 :% 1) >=% (42 :% 1) :: Bool
= 'True

Rational numbers, with numerator and denominator of Natural type.

This class gives the integer associated with a type-level rational.

Performs action with introduced DivRat constraint for rational numbers.

Constraint alias for DivRat units.