I want a function that takes an integer and returns that number in the form of a church encoded function.
I have achieved this in newlisp:
(define (reduce stencil sq) (apply stencil sq 2))
(define (num n) (cond
((= n 0) 'x)
((< n 2) '(f x))
(true (reduce (fn (l i) (list 'f l)) (cons '(f x) (sequence 2 n)) ))))
(define (church-encode n)
(letex ((body (num n)))
(fn (f x) body)))
If I call (church-encode 0) I get back a lambda of the church-encoded zero:
(lambda (f x) x)
And (church-encode 3) will yield:
(lambda (f x) (f (f (f x))))
But I want to do the same in Javascript. Preferably without resorting to string jank like I have done here:
(function (_) {
var asnum = function(x) { return x((function(x) {return x+1;}), 0); };
function church_encode(n) {
function genBody() {
return _.reduce(_.range(n), function(e,x) {
return e.replace("x", "f(x)");
}, "x");
}
eval("var crap = function (f, x) { return "+genBody()+"; }");
return crap;
}
var encoded_nums = _.map(_.range(11), church_encode);
var numerics = _.map(encoded_nums, asnum);
console.log(numerics);
})(require('lodash'));
(function () {
function range(n){
var l = [];
for(var i = 0; i < n; i++){
l.push(i);
}
return l;
}
function church_encode(n) {
if(n < 1)
return function(f, x) { return x; };
if(n === 1)
return function(f, x) { return f(x); };
function succ (n) {
return function(f,x) {
return n(f,f(x));
}
}
return range(n).reduce(function(a){
return succ(a);
}, function (f,x) { return x; });
}
function to_int(f){
var i = 0;
f(function(){ i++ });
return i;
};
console.log(to_int(church_encode(5)));
})();