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const intToName = (num) => {
let out = "";
for (let n = num + 1; n > 0; n--) {
out += String.fromCharCode(97 + (--n % 26));
n = Math.floor(n / 26);
}
return out;
};
// ------------
// CONSTRUCTORS
// ------------
const abstraction = (name) => (body) => ({
constructor: "abstraction",
name,
body,
});
const higherOrderAbstraction = (f) => ({ constructor: "h-abstraction", f });
const application = (left) => (right) => ({
constructor: "application",
left,
right,
});
const higherOrderApplication = (left) =>
left.constructor == "h-abstraction" ? left.f : application(left);
const symbol = (name) => ({ constructor: "symbol", name });
const definition = (name) => ({ constructor: "definition", name });
const show = (term) => {
switch (term.constructor) {
case "abstraction":
return `λ${term.name}.${show(term.body)}`;
case "application":
return `(${show(term.left)} ${show(term.right)})`;
case "symbol":
return `${term.name}`;
}
};
// ---------
// REDUCTION
// ---------
const toHigherOrder = (t) => {
const go = (env) => (t) => {
switch (t.constructor) {
case "application":
return higherOrderApplication(go(env)(t.left))(go(env)(t.right));
case "abstraction":
return higherOrderAbstraction((x) =>
go({ ...env, [t.name]: x })(t.body),
);
case "symbol":
if (t.name in env) return env[t.name];
throw Error("unbound symbol " + t.name);
default:
throw Error("unexpected " + t.constructor);
}
};
return go({})(t);
};
const fromHigherOrder = (t) => {
const go = (d) => (t) => {
// t = t();
switch (t.constructor) {
case "application":
return application(go(d)(t.left))(go(d)(t.right));
case "h-abstraction":
const name = intToName(d);
return abstraction(name)(go(d + 1)(t.f(symbol(name))));
case "symbol":
return t;
default:
throw Error("unexpected " + t.constructor);
}
};
return go(0)(t);
};
const reduce = (term) => {
return fromHigherOrder(toHigherOrder(term));
};
// -------
// PARSING
// -------
const consume = (str) => (predicate) => {
let out = "";
while (str && predicate(str[0])) {
out += str[0];
str = str.slice(1);
}
return [out, str.trim()];
};
const isSymbol = (x) => x >= "a" && x <= "z";
const isDefinition = (x) => (x >= "A" && x <= "Z") || (x >= "0" && x <= "9");
const parseTerm = (program) => {
const go = (str) => {
// skip spaces
str = str.trim();
const head = str[0];
const tail = str.slice(1).trim();
// abstraction start
if ("\\λ".includes(head)) {
const [name, tail1] = consume(tail)(isSymbol);
const tail2 = tail1.slice(1).trim(); // skip .
const [body, tail3] = go(tail2);
return [abstraction(name)(body), tail3];
}
// application start
if (head == "(") {
const [left, tail1] = go(tail);
const [right, tail2] = go(tail1);
return [application(left)(right), tail2.trim().slice(1)];
}
// application end - already consumed above
if (head == ")") {
throw Error("unexpected " + head);
}
// symbol / variable (lowercase letters)
if (isSymbol(head)) {
const [sym, tail1] = consume(str)(isSymbol);
return [symbol(sym), tail1];
}
// definition (uppercase letters)
if (isDefinition(head)) {
const [name, tail1] = consume(str)(isDefinition);
return [definition(name), tail1];
}
throw Error("unexpected " + head);
};
const [term, tail] = go(program);
if (tail != "") throw Error("unexpected " + tail);
return term;
};
const parse = (program) => {
const definitions = {};
const substituteDefinition = (t) => {
switch (t.constructor) {
case "application":
return application(substituteDefinition(t.left))(
substituteDefinition(t.right),
);
case "abstraction":
return abstraction(t.name)(substituteDefinition(t.body));
case "symbol":
return t;
case "definition":
if (t.name in definitions) return definitions[t.name];
else throw Error("invalid definition " + t.name);
default:
throw Error("unexpected " + t.constructor);
}
};
program
.trim()
.split("\n")
.filter((line) => !(line.startsWith("//") || line.trim() == ""))
.forEach((line) => {
const [definition, term] = line.split("=");
definitions[definition.trim()] = substituteDefinition(
parseTerm(term.trim()),
);
});
if (!("MAIN" in definitions)) throw Error("no 'MAIN' definition");
return definitions["MAIN"];
};
// ---
// CLI
// ---
const data = require("fs").readFileSync("/dev/stdin");
console.log(show(reduce(parse(data + ""))));
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