Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Data.Reducible

Contents

Reducible

Description

reducing values to there canonical value.

Synopsis

class Reducible e where
- reduce :: e -> e
reduceWith :: (x -> Rdc x) -> x -> x
(>>>=) :: (x -> Rdc x) -> (x -> Rdc x) -> x -> Rdc x
type Rdc = Action RdcState
data RdcState
- = Unchanged
- | Changed
reducesTo :: x -> Rdc x

Reducible

class Reducible e where Source #

types admitting reducible values.

Definition reduce e is called the algebraic value of e.

Reducing an e twice yield the 'same' value and the idea is that in an algebraic calculation it will be 'safe' to substitute any occurrence of e by its reduced value, i.e. both calculations will yield the same result.

Property Let e be a reducible type admitting equality, then for all e in e holds: reduce (reduce e) == reduce e.

Minimal complete definition

Nothing

Methods

reduce :: e -> e Source #

reducing e to its algebraic value.

Note The default implementation is reduce = id.

Instances

Instances details

Eq i => Reducible (PermutationForm i) Source #
Instance details Defined in OAlg.Entity.Sequence.Permutation Methods reduce :: PermutationForm i -> PermutationForm i Source #
(Oriented a, Integral r) => Reducible (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods reduce :: ProductForm r a -> ProductForm r a Source #
(Fibred a, Ord a, Semiring r, Commutative r) => Reducible (SumForm r a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods reduce :: SumForm r a -> SumForm r a Source #
Reducible (PathHomOp s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition Methods reduce :: PathHomOp s a b -> PathHomOp s a b Source #
Reducible (PathOpMap f s a b) Source #
Instance details Defined in OAlg.Hom.Oriented.Definition Methods reduce :: PathOpMap f s a b -> PathOpMap f s a b Source #

reduceWith :: (x -> Rdc x) -> x -> x Source #

reduces x by the given rules until no more reductions are applicable.

(>>>=) :: (x -> Rdc x) -> (x -> Rdc x) -> x -> Rdc x infixr 1 Source #

composition of two reductions.

type Rdc = Action RdcState Source #

Action according to the state type RdcState.

data RdcState Source #

reduction state.

Constructors

Unchanged	no reduction has been applied.
Changed	a reduction has been applied.

Instances

Instances details

Bounded RdcState Source #
Instance details Defined in OAlg.Data.Reducible Methods minBound :: RdcState # maxBound :: RdcState #
Enum RdcState Source #
Instance details Defined in OAlg.Data.Reducible Methods succ :: RdcState -> RdcState # pred :: RdcState -> RdcState # toEnum :: Int -> RdcState # fromEnum :: RdcState -> Int # enumFrom :: RdcState -> [RdcState] # enumFromThen :: RdcState -> RdcState -> [RdcState] # enumFromTo :: RdcState -> RdcState -> [RdcState] # enumFromThenTo :: RdcState -> RdcState -> RdcState -> [RdcState] #
Read RdcState Source #
Instance details Defined in OAlg.Data.Reducible Methods readsPrec :: Int -> ReadS RdcState # readList :: ReadS [RdcState] # readPrec :: ReadPrec RdcState # readListPrec :: ReadPrec [RdcState] #
Show RdcState Source #
Instance details Defined in OAlg.Data.Reducible Methods showsPrec :: Int -> RdcState -> ShowS # show :: RdcState -> String # showList :: [RdcState] -> ShowS #
Eq RdcState Source #
Instance details Defined in OAlg.Data.Reducible Methods (==) :: RdcState -> RdcState -> Bool # (/=) :: RdcState -> RdcState -> Bool #
Ord RdcState Source #
Instance details Defined in OAlg.Data.Reducible Methods compare :: RdcState -> RdcState -> Ordering # (<) :: RdcState -> RdcState -> Bool # (<=) :: RdcState -> RdcState -> Bool # (>) :: RdcState -> RdcState -> Bool # (>=) :: RdcState -> RdcState -> Bool # max :: RdcState -> RdcState -> RdcState # min :: RdcState -> RdcState -> RdcState #

reducesTo :: x -> Rdc x Source #

indicates that a term has the given reduction step, i.e. returns the given value and sets the state to Changed.