Math.Combinatorics.Species.AST.Instances

Type class instances for TSpeciesAST, ESpeciesAST, and SpeciesAST, in a separate module to avoid a dependency cycle between Math.Combinatorics.Species.AST and Math.Combinatorics.Species.Class.

This module also contains functions for reifying species expressions to ASTs and reflecting ASTs back into other species instances, which are in this module since they depend on the AST type class instances.

Documentation

reify :: SpeciesAST -> SpeciesAST

Reify a species expression into an AST. (Actually, this is just the identity function with a usefully restricted type.) For example:

> reify octopus
C . TL+
> reify (ksubset 3)
E3 * TE

reifyE :: ESpeciesAST -> ESpeciesAST

The same as reify, but produce a typed, size-annotated AST.

reflect :: Species s => SpeciesAST -> s

Reflect an AST back into any instance of the Species class.

reflectT :: Species s => TSpeciesAST f -> s

Reflect a typed AST back into any instance of the Species class.

reflectE :: Species s => ESpeciesAST -> s

Reflect an existentially wrapped typed AST back into any instance of the Species class.

Orphan instances

Eq SpeciesAST

Species expressions can be compared for structural equality. (Note that if s1 and s2 are isomorphic species we do not necessarily have s1 == s2.)

Note, however, that species containing an OfSize constructor will always compare as False with any other species, since we cannot decide function equality.

Methods

(==) :: SpeciesAST -> SpeciesAST -> Bool

(/=) :: SpeciesAST -> SpeciesAST -> Bool

Ord SpeciesAST

An (arbitrary) Ord instance, so that we can put species expressions in canonical order when simplifying.

Methods

compare :: SpeciesAST -> SpeciesAST -> Ordering

(<) :: SpeciesAST -> SpeciesAST -> Bool

(<=) :: SpeciesAST -> SpeciesAST -> Bool

(>) :: SpeciesAST -> SpeciesAST -> Bool

(>=) :: SpeciesAST -> SpeciesAST -> Bool

max :: SpeciesAST -> SpeciesAST -> SpeciesAST

min :: SpeciesAST -> SpeciesAST -> SpeciesAST

Show ESpeciesAST

Methods

showsPrec :: Int -> ESpeciesAST -> ShowS

show :: ESpeciesAST -> String

showList :: [ESpeciesAST] -> ShowS

Show SpeciesAST

Display species expressions in a nice human-readable form. Note that we commit the unforgivable sin of omitting a corresponding Read instance. This will hopefully be remedied in a future version.

Methods

showsPrec :: Int -> SpeciesAST -> ShowS

show :: SpeciesAST -> String

showList :: [SpeciesAST] -> ShowS

C ESpeciesAST

Methods

differentiate :: ESpeciesAST -> ESpeciesAST

C SpeciesAST

Species expressions are differentiable.

Methods

differentiate :: SpeciesAST -> SpeciesAST

C ESpeciesAST

Methods

(*) :: ESpeciesAST -> ESpeciesAST -> ESpeciesAST

one :: ESpeciesAST

fromInteger :: Integer -> ESpeciesAST

(^) :: ESpeciesAST -> Integer -> ESpeciesAST

C SpeciesAST

Species expressions form a ring. Well, sort of. Of course the ring laws actually only hold up to isomorphism of species, not up to structural equality.

Methods

(*) :: SpeciesAST -> SpeciesAST -> SpeciesAST

one :: SpeciesAST

fromInteger :: Integer -> SpeciesAST

(^) :: SpeciesAST -> Integer -> SpeciesAST

C ESpeciesAST

Methods

zero :: ESpeciesAST

(+) :: ESpeciesAST -> ESpeciesAST -> ESpeciesAST

(-) :: ESpeciesAST -> ESpeciesAST -> ESpeciesAST

negate :: ESpeciesAST -> ESpeciesAST

C SpeciesAST

Species expressions are additive.

Methods

zero :: SpeciesAST

(+) :: SpeciesAST -> SpeciesAST -> SpeciesAST

(-) :: SpeciesAST -> SpeciesAST -> SpeciesAST

negate :: SpeciesAST -> SpeciesAST

Species ESpeciesAST

Methods

singleton :: ESpeciesAST

set :: ESpeciesAST

cycle :: ESpeciesAST

bracelet :: ESpeciesAST

linOrd :: ESpeciesAST

subset :: ESpeciesAST

ksubset :: Integer -> ESpeciesAST

element :: ESpeciesAST

o :: ESpeciesAST -> ESpeciesAST -> ESpeciesAST

(><) :: ESpeciesAST -> ESpeciesAST -> ESpeciesAST

(@@) :: ESpeciesAST -> ESpeciesAST -> ESpeciesAST

ofSize :: ESpeciesAST -> (Integer -> Bool) -> ESpeciesAST

ofSizeExactly :: ESpeciesAST -> Integer -> ESpeciesAST

nonEmpty :: ESpeciesAST -> ESpeciesAST

rec :: ASTFunctor f => f -> ESpeciesAST

omega :: ESpeciesAST

Species SpeciesAST

Species expressions are an instance of the Species class, so we can use the Species class DSL to build species expression ASTs.

Methods

singleton :: SpeciesAST

set :: SpeciesAST

cycle :: SpeciesAST

bracelet :: SpeciesAST

linOrd :: SpeciesAST

subset :: SpeciesAST

ksubset :: Integer -> SpeciesAST

element :: SpeciesAST

o :: SpeciesAST -> SpeciesAST -> SpeciesAST

(><) :: SpeciesAST -> SpeciesAST -> SpeciesAST

(@@) :: SpeciesAST -> SpeciesAST -> SpeciesAST

ofSize :: SpeciesAST -> (Integer -> Bool) -> SpeciesAST

ofSizeExactly :: SpeciesAST -> Integer -> SpeciesAST

nonEmpty :: SpeciesAST -> SpeciesAST

rec :: ASTFunctor f => f -> SpeciesAST

omega :: SpeciesAST

Show (TSpeciesAST s)

Methods

showsPrec :: Int -> TSpeciesAST s -> ShowS

show :: TSpeciesAST s -> String

showList :: [TSpeciesAST s] -> ShowS