Copyright	(c) 2009--2010 Universiteit Utrecht
License	BSD3
Maintainer	generics@haskell.org
Stability	experimental
Portability	non-portable
Safe Haskell	Safe
Language	Haskell2010

Generics.MultiRec.FoldAlg

Contents

The type family of convenient algebras.
The class to turn convenient algebras into standard algebras.
Interface
Construction of algebras

Description

A variant of fold that allows the specification of the algebra in a convenient way.

Synopsis

type family Alg (f :: (* -> *) -> * -> *) (r :: * -> *) (ix :: *) :: *
type family Comp (f :: (* -> *) -> * -> *) (r :: * -> *) (ix :: *) :: *
type Algebra phi r = forall ix. phi ix -> Alg (PF phi) r ix
class Fold (f :: (* -> *) -> * -> *) where
- alg :: Alg f r ix -> f r ix -> r ix
fold :: forall phi ix r. (Fam phi, HFunctor phi (PF phi), Fold (PF phi)) => Algebra phi r -> phi ix -> ix -> r ix
(&) :: a -> b -> (a, b)

The type family of convenient algebras.

type family Alg (f :: (* -> *) -> * -> *) (r :: * -> *) (ix :: *) :: * Source #

The type family we use to describe the convenient algebras.

Instances

type Alg U r ix Source #	For a unit, no arguments are available.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg U r ix = r ix
type Alg (K a) r ix Source #	For a constant, we take the constant value to a result.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (K a) r ix = a -> r ix
type Alg (I xi) r ix Source #	For an identity, we turn the recursive result into a final result. Note that the index can change.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (I xi) r ix = r xi -> r ix
type Alg (C c f) r ix Source #	Constructors are ignored.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (C c f) r ix = Alg f r ix
type Alg (f :.: I xi) r ix Source #
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (f :.: I xi) r ix = f (r xi) -> r ix
type Alg (f :>: xi) r ix Source #	A tag changes the index of the final result.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (f :>: xi) r ix = Alg f r xi
type Alg (f :*: g) r ix Source #	For a product where the left hand side is a constant, we take the value as an additional argument.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (f :*: g) r ix = Comp f r ix -> Alg g r ix
type Alg (f :+: g) r ix Source #	For a sum, the algebra is a pair of two algebras.
Instance details Defined in Generics.MultiRec.FoldAlg type Alg (f :+: g) r ix = (Alg f r ix, Alg g r ix)

type family Comp (f :: (* -> *) -> * -> *) (r :: * -> *) (ix :: *) :: * Source #

Instances

type Comp (K a) r ix Source #
Instance details Defined in Generics.MultiRec.FoldAlg type Comp (K a) r ix = a
type Comp (I xi) r ix Source #
Instance details Defined in Generics.MultiRec.FoldAlg type Comp (I xi) r ix = r xi
type Comp (f :.: g) r ix Source #
Instance details Defined in Generics.MultiRec.FoldAlg type Comp (f :.: g) r ix = f (Comp g r ix)

type Algebra phi r = forall ix. phi ix -> Alg (PF phi) r ix Source #

The algebras passed to the fold have to work for all index types in the family. The additional witness argument is required only to make GHC's typechecker happy.

The class to turn convenient algebras into standard algebras.

class Fold (f :: (* -> *) -> * -> *) where Source #

The class fold explains how to convert a convenient algebra Alg back into a function from functor to result, as required by the standard fold function.

Methods

alg :: Alg f r ix -> f r ix -> r ix Source #

Instances

Fold U Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg U r ix -> U r ix -> r ix Source #
Fold (K a) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (K a) r ix -> K a r ix -> r ix Source #
Fold (I xi) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (I xi) r ix -> I xi r ix -> r ix Source #
Fold f => Fold (C c f) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (C c f) r ix -> C c f r ix -> r ix Source #
Functor f => Fold (f :.: I xi) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (f :.: I xi) r ix -> (f :.: I xi) r ix -> r ix Source #
Fold f => Fold (f :>: xi) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (f :>: xi) r ix -> (f :>: xi) r ix -> r ix Source #
Fold g => Fold (K a :*: g) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (K a :: g) r ix -> (K a :: g) r ix -> r ix Source #
Fold g => Fold (I xi :*: g) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (I xi :: g) r ix -> (I xi :: g) r ix -> r ix Source #
(Fold f, Fold g) => Fold (f :+: g) Source #
Instance details Defined in Generics.MultiRec.FoldAlg Methods alg :: Alg (f :+: g) r ix -> (f :+: g) r ix -> r ix Source #

Interface

fold :: forall phi ix r. (Fam phi, HFunctor phi (PF phi), Fold (PF phi)) => Algebra phi r -> phi ix -> ix -> r ix Source #

Fold with convenient algebras.

Construction of algebras

(&) :: a -> b -> (a, b) infixr 5 Source #

For constructing algebras that are made of nested pairs rather than n-ary tuples, it is helpful to use this pairing combinator.