Data.Ring
#Ring
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
#(-)
Operator alias for Data.Ring.sub (left-associative / precedence 6)
#RingRecord
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
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
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
#(+)
Operator alias for Data.Semiring.add (left-associative / precedence 6)
#(*)
Operator alias for Data.Semiring.mul (left-associative / precedence 7)
Packages
assert
catenable-lists
const
convertable-options
datetime-parsing
debug
distributive
erl-atom
erl-gun
erl-lager
erl-logger
erl-maps
erl-modules
erl-nativerefs
erl-opentelemetry
- OpenTelemetry.Metrics
- OpenTelemetry.Metrics.Counter
- OpenTelemetry.Metrics.Meter
- OpenTelemetry.Metrics.SumObserver
- OpenTelemetry.Metrics.UpDownCounter
- OpenTelemetry.Metrics.UpDownSumObserver
- OpenTelemetry.Metrics.ValueObserver
- OpenTelemetry.Metrics.ValueRecorder
- OpenTelemetry.Tracing
- OpenTelemetry.Tracing.Baggage
- OpenTelemetry.Tracing.Ctx
- OpenTelemetry.Tracing.Propagator.TextMap
- OpenTelemetry.Tracing.Span
- OpenTelemetry.Tracing.Tracer
- Tracing.Attributes
erl-process
erl-queue
erl-ranch
erl-simplebus
erl-ssl
erl-test-eunit
erl-test-eunit-discovery
erl-tuples
erl-untagged-union
exceptions
exists
expect-inferred
functions
graphs
heterogeneous
identity
integers
invariant
js-uri
lazy
lcg
math
media-types
newtype
nonempty
nullable
ordered-collections
partial
prelude
- 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
- Record.Unsafe
- Type.Data.Row
- Type.Data.RowList
- Type.Proxy
profunctor-lenses
- Data.Lens.AffineTraversal
- Data.Lens.At
- Data.Lens.Common
- Data.Lens.Fold
- Data.Lens.Fold.Partial
- Data.Lens.Getter
- Data.Lens.Grate
- Data.Lens.Index
- Data.Lens.Indexed
- Data.Lens.Internal.Bazaar
- Data.Lens.Internal.Exchange
- Data.Lens.Internal.Focusing
- Data.Lens.Internal.Forget
- Data.Lens.Internal.Grating
- Data.Lens.Internal.Indexed
- Data.Lens.Internal.Market
- Data.Lens.Internal.Re
- Data.Lens.Internal.Shop
- Data.Lens.Internal.Stall
- Data.Lens.Internal.Tagged
- Data.Lens.Internal.Wander
- Data.Lens.Internal.Zipping
- Data.Lens.Iso
- Data.Lens.Iso.Newtype
- Data.Lens.Lens
- Data.Lens.Lens.Product
- Data.Lens.Lens.Tuple
- Data.Lens.Lens.Unit
- Data.Lens.Lens.Void
- Data.Lens.Prism
- Data.Lens.Prism.Coproduct
- Data.Lens.Prism.Either
- Data.Lens.Prism.Maybe
- Data.Lens.Record
- Data.Lens.Setter
- Data.Lens.Traversal
- Data.Lens.Types
- Data.Lens.Zoom
psci-support
quickcheck-laws
- Test.QuickCheck.Laws
- Test.QuickCheck.Laws.Control.Alt
- Test.QuickCheck.Laws.Control.Alternative
- Test.QuickCheck.Laws.Control.Applicative
- Test.QuickCheck.Laws.Control.Apply
- Test.QuickCheck.Laws.Control.Bind
- Test.QuickCheck.Laws.Control.Category
- Test.QuickCheck.Laws.Control.Comonad
- Test.QuickCheck.Laws.Control.Extend
- Test.QuickCheck.Laws.Control.Monad
- Test.QuickCheck.Laws.Control.MonadPlus
- Test.QuickCheck.Laws.Control.MonadZero
- Test.QuickCheck.Laws.Control.Plus
- Test.QuickCheck.Laws.Control.Semigroupoid
- Test.QuickCheck.Laws.Data.BooleanAlgebra
- Test.QuickCheck.Laws.Data.Bounded
- Test.QuickCheck.Laws.Data.BoundedEnum
- Test.QuickCheck.Laws.Data.CommutativeRing
- Test.QuickCheck.Laws.Data.DivisionRing
- Test.QuickCheck.Laws.Data.Eq
- Test.QuickCheck.Laws.Data.EuclideanRing
- Test.QuickCheck.Laws.Data.Field
- Test.QuickCheck.Laws.Data.Foldable
- Test.QuickCheck.Laws.Data.Functor
- Test.QuickCheck.Laws.Data.FunctorWithIndex
- Test.QuickCheck.Laws.Data.HeytingAlgebra
- Test.QuickCheck.Laws.Data.Monoid
- Test.QuickCheck.Laws.Data.Ord
- Test.QuickCheck.Laws.Data.Ring
- Test.QuickCheck.Laws.Data.Semigroup
- Test.QuickCheck.Laws.Data.Semiring
random
rationals
record-prefix
refs
safe-coerce
semirings
simple-json
strings
- Data.Char
- Data.Char.Gen
- Data.String.CaseInsensitive
- Data.String.CodePoints
- Data.String.CodeUnits
- Data.String.Common
- Data.String.Gen
- Data.String.NonEmpty.CaseInsensitive
- Data.String.NonEmpty.CodePoints
- Data.String.NonEmpty.CodeUnits
- Data.String.NonEmpty.Internal
- Data.String.Pattern
- Data.String.Regex
- Data.String.Regex.Flags
- Data.String.Regex.Unsafe
- Data.String.Unsafe
tailrec
transformers
- Control.Comonad.Env
- Control.Comonad.Env.Class
- Control.Comonad.Env.Trans
- Control.Comonad.Store
- Control.Comonad.Store.Class
- Control.Comonad.Store.Trans
- Control.Comonad.Traced
- Control.Comonad.Traced.Class
- Control.Comonad.Traced.Trans
- Control.Comonad.Trans.Class
- Control.Monad.Cont
- Control.Monad.Cont.Class
- Control.Monad.Cont.Trans
- Control.Monad.Error.Class
- Control.Monad.Except
- Control.Monad.Except.Trans
- Control.Monad.Identity.Trans
- Control.Monad.List.Trans
- Control.Monad.Maybe.Trans
- Control.Monad.RWS
- Control.Monad.RWS.Trans
- Control.Monad.Reader
- Control.Monad.Reader.Class
- Control.Monad.Reader.Trans
- Control.Monad.State
- Control.Monad.State.Class
- Control.Monad.State.Trans
- Control.Monad.Trans.Class
- Control.Monad.Writer
- Control.Monad.Writer.Class
- Control.Monad.Writer.Trans
type-equality
undefinable
unfoldable
unsafe-coerce
unsafe-reference
uri
- URI.AbsoluteURI
- URI.Authority
- URI.Common
- URI.Extra.MultiHostPortPair
- URI.Extra.QueryPairs
- URI.Extra.UserPassInfo
- URI.Fragment
- URI.HierarchicalPart
- URI.Host
- URI.Host.Gen
- URI.Host.IPv4Address
- URI.Host.IPv6Address
- URI.Host.RegName
- URI.HostPortPair
- URI.HostPortPair.Gen
- URI.Path
- URI.Path.Absolute
- URI.Path.NoScheme
- URI.Path.Rootless
- URI.Path.Segment
- URI.Port
- URI.Port.Gen
- URI.Query
- URI.RelativePart
- URI.RelativeRef
- URI.Scheme
- URI.Scheme.Common
- URI.URI
- URI.URIRef
- URI.UserInfo