TreeF is functor for Trees. TreeF has Map-instance (on structure).

A function to transform a Tree into fixed structure that can be used by Cata and Ana.

See the implementation of Size for an example.

Sum the nodes of TreeF containing Nats.

See the implementation of Fib for an example.

Count the nodes of TreeF.

See the Size for an example.

Size of the Tree is the number of nodes in it.

Example

Size is defined as Cata CountNodesAlg =<< TreeToFix tr and can be used with the following.

>>> data BuildNode :: Nat -> Exp (Nat,[Nat])
>>> :{
  type instance Eval (BuildNode x) =
      If (Eval ((2 TL.* x TL.+ 1) >= 8))
          '(x, '[])
          '(x, '[ 2 TL.* x, (2 TL.* x) TL.+ 1 ])
:}

>>> :kind! Eval (Size =<< UnfoldTree BuildNode 1)
Eval (Size =<< UnfoldTree BuildNode 1) :: Nat
= 7

CoAlgebra to build TreeF's. This is an example from containers-package. See Size and example in there.

:kind! Eval (Ana BuildNodeCoA 1) :kind! Eval (Hylo CountNodesAlg BuildNodeCoA 1)

CoAlgebra for the Fib-function.

Fibonaccis with Hylo, not efficient

Example

>>> :kind! Eval (Fib 10)
Eval (Fib 10) :: Nat
= 55

BTreeF is a btree functor. At the moment, it is used to build sorting algorithms.

Use this if you want to sort symbols into increasing order.

Use this if you want to sort symbols into decreasing order.

Qsort - give the comparison function a -> a -> Exp Bool comparing your list elements and then Qsort will order the list.

Example

>>> :kind! Eval (Qsort (<) '[5,3,1,9,4,6,3])
Eval (Qsort (<) '[5,3,1,9,4,6,3]) :: [Nat]
= '[1, 3, 3, 4, 5, 6, 9]

>>> :kind! Eval (Qsort SymbolCompareInc '[ "bb", "e", "a", "e", "d" ])
Eval (Qsort SymbolCompareInc '[ "bb", "e", "a", "e", "d" ]) :: [TL.Symbol]
= '["a", "bb", "d", "e", "e"]