Clue (oklopol)/SKI calculus

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deep first ~ {. 1 -> 1
              . 2 -> 2 }
deep first ~ {:. [[1 2] 3] -> 1
               : [1 2] -> 1
              :. [1 [2 3]] -> 1
	       : 1 -> 1 }
deep first ~ is list?; cons; car; cdr

depth of first ~ {. 0 -> 0
                  . 5 -> 0 }
depth of first ~ {:. [[1 2] [3 4]] -> 2
                   : [1 2] -> 1
                  :. [[[1 2 3] 4] 5] -> 3
                   : [[1 2 3] 4] -> 2}
depth of first ~ is list?; cons; car; cdr; inc; 0

make singleton ~ {. 1 -> [1]
                  . [1 2 3] -> [[1 2 3]]}
make singleton ~ cons; []

pair ~ {. 1 2 -> [1 2]
        . [3] [4 5] -> [[3] [4 5]]}
pair ~ make singleton; cons

more than 3 ~ {. 0 -> 0 }
more than 3 ~ {. 1 -> 0 }
more than 3 ~ {. 2 -> 0 }
more than 3 ~ {. 3 -> 0 }
more than 3 ~ {. 4 -> 1
               . 5 -> 1 }
more than 3 ~ 0; 1

deep first with cutoff ~ {. 0 -> 0
                          . [1 0] -> 1
                          . [[3 2] 1] -> 3
                          . [[[5 4] 3] 2] -> 5 }
deep first with cutoff ~ {. [[[[1 2]]]] -> 4
                          . [[[[[1 2] 3] 4] 5] 6] -> 4 }
deep first with cutoff ~ depth of first; more than 3
deep first with cutoff ~ deep first; 4

ski type? ~ {. 1 -> 0 }
ski type? ~ {. 2 -> 0 }
ski type? ~ {. 3 -> 0 }
ski type? ~ {. [2 1] -> 0
             . [2 3] -> 0 }
ski type? ~ {. [[3 2] 1] -> 0
             . [[3 4] 5] -> 0 }
ski type? ~ {. [3 2] -> 0
             . [3 4] -> 0 }
ski type? ~ {. [1 0] -> 1
             . [[2 1] 0] -> 2
             . [[[3 2] 1] 0] -> 3
             . [[[[1 2]]]] -> 4
             . [[[[[1 2] 3] 4] 5] 6] -> 4 }
ski type? ~ make singleton; cons; deep first
ski type? ~ depth of first; deep first with cutoff; #; 1

cadaar ~ {. [[[1 [2]]]] -> [2]
          . [[[3 [2 2]] [2 1]] 5] -> [2 2] }
cadaar ~ car; cdr

cadar ~ {. [[1,[2]]] -> [2]
         . [[[3 [2 2]] [2 1]] 5] -> [2 1] }
cadar ~ car; cdr

ski apply ~ {. 3 -> 3
             . [2 2] -> [2 2] }
ski apply ~ {:. [1 [1 2]] -> 2
              : [1 2] -> 2 }
ski apply ~ {:. [[2 [1 3]] 2] -> 3
              : [1 3] -> 3 }
ski apply ~ {:. [[[3 [2 2]] [2 1]] 5] -> [2 1]
              : [[2 2] 5] -> 2
              : [[2 1] 5] -> 1
              : [2 1] -> [2 1]
             :. [[[3 1] 1] 1] -> 1
              : [1 1] -> 1
              : [1 1] -> 1
              : [1 1] -> 1 }
ski apply ~ {:. [[[[1 2] 1] 2] 1] -> 1
              : [[[1 2] 1] 2] -> 1
              : [1 1] -> 1
             :. [[[[[3 2] 3] 2] 3] 1] -> 3
              : [[[[3 2] 3] 2] 3] -> [2 3]
              : [[2 3] 1] -> 3 }
ski apply ~ ski type?
ski apply ~ pair; car; cdr; cadaar; cadar