FunC: A Functional Compressor

FunC compresses a tree by a λ-term that evaluates to the tree. For example, a term a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a c))))))))))))))), which contains 16-time occurrences of a, is compressed into a λ-term (λf. (f f) f a c) (λs.λz.s (s z)). You can try FunC by writing a tree in the following text area and press the ”Compress“ button.

Examples

Natural Number: 9

a (a (a (a (a (a (a (a (a c))))))))

Natural Number: 16

a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a c)))))))))))))))

Seventh Fibnacci Word

[a b a a b a b a a b a a b a b a a b a b a]

Binary Numbers

/* [0,1,2,3,...,15] in MSB
   where preceding "a"s are removed. */

c [] (
c [b] (
c [b a] (
c [b b] (
c [b a a] (
c [b a b] (
c [b b a] (
c [b b b] (
c [b a a a] (
c [b a a b] (
c [b a b a] (
c [b a b b] (
c [b b a a] (
c [b b a b] (
c [b b b a] (
c [b b b b] (
n))))))))))))))))

Tree-Drawing L-System

/* Tree-Drawing Pattern generated by following L-System:
     S -> f
     f -> f[+f]f[-f]f */
[f lpar  plus f rpar f lpar  minus f rpar f lpar  plus f lpar  plus f rpar f lpar  minus f rpar f rpar f lpar  plus f rpar f lpar  minus f rpar f lpar  minus f lpar plus f rpar f lpar  minus f rpar f rpar f lpar  plus f rpar f lpar  minus f rpar f]

aⁿbⁿ

[a a a a a a a a a a a a a a a a b b b b b b b b b b b b b b b b]

abab…

[a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b ]

English-French Translation

seq (tr [I like him] [Je le aime bien]) (tr [I like her] [Je la aime bien])