Zygohistomorphic prepromorphisms: Difference between revisions

Latest revision as of 15:40, 20 July 2023

Zygohistomorphic prepromorphisms are an intentionally overcomplicated combination of recursion-schemes concepts that started as a joke^[1].

Used when you really need both semi-mutual recursion and history and to repeatedly apply a natural transformation as you get deeper into the functor. Zygo implements semi-mutual recursion like a zygomorphism. Para gives you access to your result à la paramorphism.

import Control.Morphism.Zygo
import Control.Morphism.Prepro
import Control.Morphism.Histo
import Control.Functor.Algebra
import Control.Functor.Extras

zygoHistoPrepro 
  :: (Unfoldable t, Foldable t) 
  => (Base t b -> b) 
  -> (forall c. Base t c -> Base t c) 
  -> (Base t (EnvT b (Stream (Base t)) a) -> a) 
  -> t
  -> a
zygoHistoPrepro f g t = gprepro (distZygoT f distHisto) g t
-- unless you want a generalized zygomorphism.

↑ [1] Edward Kmett on Twitter, 2019

[1] [1] Edward Kmett on Twitter, 2019

[1]

@@ Line 1: / Line 1: @@
-Used when you really need both semi-mutual recursion and history and to repeatedly apply a natural transformation as you get deeper into the functor. Zygo implements semi-mutual recursion like a zygomorphism. Para gives you access to your result à la paramorphism.
+Zygohistomorphic prepromorphisms are an intentionally overcomplicated combination of recursion-schemes concepts that started as a joke<ref>[https://archive.ph/2Jlo6] Edward Kmett on Twitter, 2019</ref>.
-<pre>
+Used when you really need both semi-mutual recursion and history and to repeatedly apply a natural transformation as you get deeper into the functor. <code>Zygo</code> implements semi-mutual recursion like a zygomorphism. ''Para'' gives you access to your result à la paramorphism.
+<haskell>
 import Control.Morphism.Zygo
 import Control.Morphism.Prepro
@@ Line 8: / Line 10: @@
 import Control.Functor.Extras
-zygohistomorphic_prepromorphism :: Functor f => Algebra f b -> GAlgebra f (Cofree f) a -> (f :~> f) -> FixF f -> a
+zygoHistoPrepro
-zygohistomorphic_prepromorphism f = g_prepro (distZygoT (liftAlgebra f) (distHisto id))
+  :: (Unfoldable t, Foldable t)
+  => (Base t b -> b)
+  -> (forall c. Base t c -> Base t c)
+  -> (Base t (EnvT b (Stream (Base t)) a) -> a)
+  -> t
+  -> a
+zygoHistoPrepro f g t = gprepro (distZygoT f distHisto) g t
 -- unless you want a generalized zygomorphism.
-</pre>
+</haskell>
+<references />
+[[Category:Code]]
+[[Category:Language extensions]]