almost there

nothing-helper.js

@@ -1,4 +1,53 @@
-module.exports = {
-  to_int: (f) => f(n => n+1)(0),
-  to_boolean: (f) => f(true)(false),
+const nothing = require('./nothing.js');
+
+const charset = '0123456789BFiuz';
+const from_int = (n) => {
+  let f = nothing.ZERO;
+  for (let _ = 0; _ < n; _++) f = nothing.INC(f);
+  return f;
+};
+const to_int = (f) => nothing.TIMES(f)(i => i+1)(0);
+const from_bool = (b) => b ? nothing.TRUE : nothing.FALSE;
+const to_bool = (f) => f(true)(false);
+const to_array = (l) => {
+  let a = [];
+
+  while (!to_bool(nothing.IS_EMPTY(l))) {
+    a.push(nothing.FIRST(l));
+    l = nothing.REST(l);
+  }
+
+  return a;
+};
+const from_array = (a) => {
+  let l = nothing.EMPTY;
+
+  while (a.length) l = nothing.UNSHIFT(l)(a.pop());
+
+  return l;
+};
+const to_char = (c) => charset[to_int(c)];
+const from_char = (c) => from_int(charset.indexOf(c));
+const to_string = (s) => to_array(s).map(to_char).join('');
+const from_string = (s) => from_array(s.split('').map(from_char));
+const representation_of = (v) => {
+  if (typeof v == "number") return from_int(v);
+  if (typeof v == "boolean") return from_bool(v);
+  if (typeof v == "string") return from_string(v);
+  if (Array.isArray(v)) return from_array(v.map(representation_of));
+  throw Error(`Oops, I don’t know how represent this: ${v}`);
+};
+const zip = (a, b) => a.map((e, i) => [e, b[i]]);
+const check_represent = function(r, v) {
+  if (typeof v == "number") return to_int(r) == v;
+  if (typeof v == "boolean") return to_bool(r) == v;
+  if (typeof v == "string") { console.log("checking ", to_array(r).map(to_int), " against ", v); return to_string(r) == v; }
+  if (Array.isArray(v)) {
+    let a = to_array(r);
+    return a.length == v.length && zip(a, v).every(([r, v]) => check_represent(r,v));
+  }
+  throw Error(`Oops, I don’t know how check this: ${v}`);
+};
+module.exports = {
+  to_string, to_array, representation_of, check_represent, to_int, to_char
 };