Module

Data.Ring

Package: purescript-prelude
Repository: purescript/purescript-prelude

#Ring Source

class (Semiring a) <= Ring a  where

The Ring class is for types that support addition, multiplication, and subtraction operations.

Instances must satisfy the following law in addition to the Semiring laws:

Additive inverse: a - a = (zero - a) + a = zero

Members

sub :: a -> a -> a

Instances

Ring Int
Ring Number
Ring Unit
(Ring b) => Ring (a -> b)
(RowToList row list, RingRecord list row row) => Ring (Record row)

#negate Source

negate :: forall a. Ring a => a -> a

negate x can be used as a shorthand for zero - x.

#(-) Source

Operator alias for Data.Ring.sub (left-associative / precedence 6)

#RingRecord Source

class (SemiringRecord rowlist row subrow) <= RingRecord rowlist row subrow | rowlist -> subrow where

A class for records where all fields have Ring instances, used to implement the Ring instance for records.

Members

subRecord :: RLProxy rowlist -> Record row -> Record row -> Record subrow

Instances

RingRecord Nil row ()
(IsSymbol key, Cons key focus subrowTail subrow, RingRecord rowlistTail row subrowTail, Ring focus) => RingRecord (Cons key focus rowlistTail) row subrow

Re-exports from Data.Semiring

#Semiring Source

class Semiring a  where

The Semiring class is for types that support an addition and multiplication operation.

Instances must satisfy the following laws:

Commutative monoid under addition:
- Associativity: (a + b) + c = a + (b + c)
- Identity: zero + a = a + zero = a
- Commutative: a + b = b + a
Monoid under multiplication:
- Associativity: (a * b) * c = a * (b * c)
- Identity: one * a = a * one = a
Multiplication distributes over addition:
- Left distributivity: a * (b + c) = (a * b) + (a * c)
- Right distributivity: (a + b) * c = (a * c) + (b * c)
Annihilation: zero * a = a * zero = zero

Note: The Number and Int types are not fully law abiding members of this class hierarchy due to the potential for arithmetic overflows, and in the case of Number, the presence of NaN and Infinity values. The behaviour is unspecified in these cases.

Members

add :: a -> a -> a
zero :: a
mul :: a -> a -> a
one :: a

Instances

Semiring Int
Semiring Number
(Semiring b) => Semiring (a -> b)
Semiring Unit
(RowToList row list, SemiringRecord list row row) => Semiring (Record row)

#SemiringRecord Source

class SemiringRecord rowlist row subrow | rowlist -> subrow

A class for records where all fields have Semiring instances, used to implement the Semiring instance for records.

Instances

SemiringRecord Nil row ()
(IsSymbol key, Cons key focus subrowTail subrow, SemiringRecord rowlistTail row subrowTail, Semiring focus) => SemiringRecord (Cons key focus rowlistTail) row subrow

#(+) Source

Operator alias for Data.Semiring.add (left-associative / precedence 6)

#(*) Source

Operator alias for Data.Semiring.mul (left-associative / precedence 7)