Data.Ring
- Package
- prelude
- Repository
- purerl/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 laws in addition to the Semiring
laws:
- Additive inverse:
a - a = zero
- Compatibility of
sub
andnegate
:a - b = a + (zero - b)
Members
sub :: a -> a -> a
Instances
#RingRecord Source
class RingRecord :: RowList Type -> Row Type -> Row Type -> Constraint
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
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
- Associativity:
- Monoid under multiplication:
- Associativity:
(a * b) * c = a * (b * c)
- Identity:
one * a = a * one = a
- Associativity:
- Multiplication distributes over addition:
- Left distributivity:
a * (b + c) = (a * b) + (a * c)
- Right distributivity:
(a + b) * c = (a * c) + (b * c)
- Left distributivity:
- 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
Instances
#SemiringRecord Source
class SemiringRecord :: RowList Type -> Row Type -> Row Type -> Constraint
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
- Modules
- Control.
Applicative - Control.
Apply - Control.
Bind - Control.
Category - Control.
Monad - Control.
Semigroupoid - Data.
Boolean - Data.
BooleanAlgebra - Data.
Bounded - Data.
Bounded. Generic - Data.
CommutativeRing - Data.
DivisionRing - Data.
Eq - Data.
Eq. Generic - Data.
EuclideanRing - Data.
Field - Data.
Function - Data.
Functor - Data.
Generic. Rep - Data.
HeytingAlgebra - Data.
HeytingAlgebra. Generic - Data.
Monoid - Data.
Monoid. Additive - Data.
Monoid. Conj - Data.
Monoid. Disj - Data.
Monoid. Dual - Data.
Monoid. Endo - Data.
Monoid. Generic - Data.
Monoid. Multiplicative - Data.
NaturalTransformation - Data.
Ord - Data.
Ord. Generic - Data.
Ordering - Data.
Ring - Data.
Ring. Generic - Data.
Semigroup - Data.
Semigroup. First - Data.
Semigroup. Generic - Data.
Semigroup. Last - Data.
Semiring - Data.
Semiring. Generic - Data.
Show - Data.
Show. Generic - Data.
Symbol - Data.
Unit - Data.
Void - Prelude
- Record.
Unsafe - Type.
Data. Row - Type.
Data. RowList - Type.
Proxy