Fcf.Alg.Morphism

Structure that Cata can fold and that is a result structure of Ana.

Commonly used name describing the method Cata eats.

Commonly used name describing the method Ana eats.

Commonly used name describing the method Para eats.

Write the function to give a Fix, and feed it in together with an Algebra.

Check Fcf.Alg.List to see example algebras in use. There we have e.g. ListToFix-function.

Ana can also be used to build a Fix structure.

Example

data NToOneCoA :: CoAlgebra (ListF Nat) Nat
:{

type instance Eval (NToOneCoA b) = If (Eval (b < 1) ) 'NilF ('ConsF b ( b TL.- 1)) :}

:kind! Eval (Ana NToOneCoA 3)

Eval (Ana NToOneCoA 3) :: Fix (ListF TL.Natural) = 'Fix ('ConsF 3 ('Fix ('ConsF 2 ('Fix ('ConsF 1 ('Fix 'NilF))))))

Hylomorphism uses first Ana to build a structure (unfold) and then Cata to process the structure (fold).

Example

data NToOneCoA :: CoAlgebra (ListF Nat) Nat
:{

type instance Eval (NToOneCoA b) = If (Eval (b < 1) ) 'NilF ('ConsF b ( b TL.- 1)) :}

:kind! Eval (Hylo SumAlg NToOneCoA 5)

Eval (Hylo SumAlg NToOneCoA 5) :: TL.Natural = 15

Write a function to give a Fix, and feed it in together with an RAlgebra

Check Fcf.Alg.List to see example algebras in use. There we have e.g. ListToParaFix-function.

Annotate (f r) with attribute a (from Recursion Schemes by example, Tim Williams).

Annotated fixed-point type. A cofree comonad (from Recursion Schemes by example, Tim Williams).

Attribute of the root node (from Recursion Schemes by example, Tim Williams).

Strip attribute from root (from Recursion Schemes by example, Tim Williams).

Annotation constructor (from Recursion Schemes by example, Tim Williams).

Synthesized attributes are created in a bottom-up traversal using a catamorphism (from Recursion Schemes by example, Tim Williams).

This is the algebra that is fed to the cata.

Synthesized attributes are created in a bottom-up traversal using a catamorphism (from Recursion Schemes by example, Tim Williams).

For the example, see Fcf.Data.Alg.Tree.Sizes.

Histo takes annotation algebra and takes a Fix-structure (from Recursion Schemes by example, Tim Williams).

This is a helper for Histo as it is implemented with Cata.

Histo takes annotation algebra and takes a Fix-structure (from Recursion Schemes by example, Tim Williams).

Examples can be found from Fcf.Data.Alg.Tree and Fcf.Data.Alg.List modules.

Type-level First. Tuples (,) and Either have First-instances.

Example

:kind! Eval (First ((+) 1) '(3,"a"))

Eval (First ((+) 1) '(3,"a")) :: (TL.Natural, TL.Symbol) = '(4, "a")

Type-level Second. Tuples (,) and Either have Second-instances.

Example

:kind! Eval (Second ((+) 1) '("a",3))

Eval (Second ((+) 1) '("a",3)) :: (TL.Symbol, TL.Natural) = '("a", 4)