Add FDoc.RecursionSchemes and anamorphism example

src/FDoc/RecursionSchemes.hs

@@ -0,0 +1,33 @@
+{-# LANGUAGE DataKinds, ScopedTypeVariables, TypeFamilies, TypeOperators #-}
+module FDoc.RecursionSchemes where
+
+import Data.Record
+import Range
+import Category
+import Term
+import Syntax
+import Prologue
+import Prelude
+import Data.Functor.Foldable hiding (ListF)
+import FDoc.Term
+
+data NewField = NewField deriving (Show)
+
+{-
+Anamorphism
+
+ana :: (a -> Base t a) -- ^ a (Base t)-coalgebra
+    -> a               -- ^ seed
+    -> t               -- ^ resulting fixed point
+
+Anamorphism as a recursion scheme "builds up" a recursive structure.
+Anamorphisms work by using a coalgebra, which maps a seed value to a fixed point structure.
+
+The example below adds a new field to the `Record` fields.
+
+-}
+
+indexedTermAna :: [leaf] -> Term (Syntax leaf) (Record '[NewField, Range, Category])
+indexedTermAna childrenLeaves = ana coalgebra (indexedTerm childrenLeaves)
+  where
+    coalgebra term = (NewField .: (extract term)) :< (unwrap term)