why-fp-foldtree-substitution-labelstree.hs

labelsTree' numberNodes
-----------------------------------------------------------------
labelsTree' (Node 1 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
foldtree' (:) (++) [] (Node 1 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
foldnode' (:) (++) [] (Node 1 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
(+) 1 (foldnodes' (:) (++) [] [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
(:) 1 (
    (++) (foldnode' (:) (++) [] (Node 2 [Node 4 []))
         (foldnodes' (:) (++) [] [Node 5 []]))
-----------------------------------------------------------------
(:) 1 (
    (++) (foldnode' (:) (++) [] (Node 2 [Node 4 []))
         ((++) (foldnode' (:) (++) [] (Node 5 []))
             (foldnodes' (:) (++) [] [])))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
            (foldnodes' (:) (++) [] [Node 4 []))
         ((++) (foldnode' (:) (++) [] (Node 5 []))
               (foldnodes' (:) (++) [] [])))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              (foldnodes' (:) (++) [] [Node 4 []))
         ((++) (foldnode' (:) (++) [] (Node 5 []))
              []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
             ((++) (foldnode' (:) (++) [] (Node 4 []))
                   (foldnodes' (:) (++) [] [])))
         ((++) (foldnode' (:) (++) [] (Node 5 []))
               []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
             ((++) (foldnode' (:) (++) [] (Node 4 []))
                   []))
        ((++) (foldnode' (:) (++) [] (Node 5 []))
              []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              ((++) (foldnode' (:) (++) [] (Node 4 []))
                    []))
        ((++) ((:) 5 (foldnodes []))
              []))
-----------------------------------------------------------------
(+) 1 (
    (++) ((:) 2 
              ((++) (foldnode' (:) (++) [] (Node 4 []))
                   []))
         ((++) ((:) 5 [])
               []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              ((++) ((:) 4 (foldnodes' (:) (++) [] []))
                  []))
        ((++) ((:) 5 [])
             []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              ((++) ((:) 4 [])
                   []))
         ((++) ((:) 5 [])
               []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              ((++) [4]
                  []))
        ((++) ((:) 5 [])
             []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              ((++) [4]
                  []))
        ((++) [5]
              []))
-----------------------------------------------------------------
(:) 1 (
    (++) ((:) 2 
              [4])
        ((++) [5]
              []))
-----------------------------------------------------------------
(:) 1 (
    (++) [2, 4]
         ((++) [5]
               []))
-----------------------------------------------------------------
(:) 1 (
    (++) [2, 4]
         [5])
-----------------------------------------------------------------
(:) 1
    [2, 4, 5]
-----------------------------------------------------------------
[1, 2, 4, 5]

why-fp-foldtree-substitution-sumtree.hs

sumTree' numberNodes
-----------------------------------------------------------------
sumTree' (Node 1 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
foldtree' (+) (+) 0 (Node 1 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
foldnode' (+) (+) 0 (Node 1 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
(+) 1 (foldnodes' (+) (+) 0 [Node 2 [Node 4 []], Node 5 []])
-----------------------------------------------------------------
(+) 1 (
    (+) (foldnode' (+) (+) 0 (Node 2 [Node 4 []))
        (foldnodes' (+) (+) 0 [Node 5 []]))
-----------------------------------------------------------------
(+) 1 (
    (+) (foldnode' (+) (+) 0 (Node 2 [Node 4 []))
        ((+) (foldnode' (+) (+) 0 (Node 5 []))
             (foldnodes' (+) (+) 0 [])))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
            (foldnodes' (+) (+) 0 [Node 4 []))
        ((+) (foldnode' (+) (+) 0 (Node 5 []))
             (foldnodes' (+) (+) 0 [])))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             (foldnodes' (+) (+) 0 [Node 4 []))
        ((+) (foldnode' (+) (+) 0 (Node 5 []))
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) (foldnode' (+) (+) 0 (Node 4 []))
                 (foldnodes' (+) (+) 0 [])))
        ((+) (foldnode' (+) (+) 0 (Node 5 []))
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) (foldnode' (+) (+) 0 (Node 4 []))
                 0))
        ((+) (foldnode' (+) (+) 0 (Node 5 []))
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) (foldnode' (+) (+) 0 (Node 4 []))
                  0))
        ((+) ((+) 5 (foldnodes []))
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) (foldnode' (+) (+) 0 (Node 4 []))
                  0))
        ((+) ((+) 5 0)
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) ((+) 4 (foldnodes' (+) (+) 0 []))
                  0))
        ((+) ((+) 5 0)
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) ((+) 4 0)
                  0))
        ((+) ((+) 5 0)
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             ((+) 4
                  0))
        ((+) ((+) 5 0)
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) ((+) 2 
             4)
        ((+) ((+) 5 0)
             0))
-----------------------------------------------------------------             
(+) 1 (
    (+) 6
        ((+) ((+) 5 0)
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) 6
        ((+) 5
             0))
-----------------------------------------------------------------
(+) 1 (
    (+) 6
        5)
-----------------------------------------------------------------
(+) 1 11
-----------------------------------------------------------------
12