Edward Cherlin Paper Pure functions in APL and J
https://dl.acm.org/doi/10.1145/114055.114065 Jared. On Sat, Jul 2, 2022 at 12:21, Jacques Bailhache <jacques.bailha...@gmail.com> wrote: > I am trying to implement combinatory logic in J. I succeeded for > combinators I and K : > > ap =: 4 : 'x @.(]@1) y' > I =: ]`] > I ap 5 > 5 > K =: ]`(3 : ']`(]@y)') > (K ap 6) ap 8 > 6 > > but I don't see how to implement the combinator S. > It must satisfy : > ((S ap a) ap b) ap c = (a ap c) ap (b ap c) > For example : > ((S ap add) ap double) ap 10 = (add ap 10) ap (double ap 10) > where add and double are defined as follow : > > add =: ]`(3 : ']`(+ & y)') > (add ap 3) ap 5 > 8 > double =: ]`+: > double ap 10 > 20 > (add ap 10) ap (double ap 10) > 30 > > I found that (S ap add) ap double = ]`((add & ap) ap (double & ap)) : > > (]`((add & ap) ap (double & ap))) ap 10 > 30 > > The next steps consists in defining S ap add by abstracting double from > this expression, but I don't see how to do this. > Does someone have an idea ? > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
