plsandbox/stlc-bidir/simple.test.ts

import { test, expect, describe } from "bun:test";
import {
  abs1,
  abs2,
  app1,
  app2,
  arr,
  convertToDebruijn,
  infer,
  parseExpr,
  parseTy,
  unitTy,
  var1,
  var2,
} from ".";

const kCombinator = `lam (x : ()) . lam (y : ()) . x`;
const kCombinatorTy = `() -> (() -> ())`;

const sCombinator = `lam (x : () -> (() -> ())) . lam (y : () -> ()) . lam (z : ()) . (x z) (y z)`;

describe("parser", () => {
  test("K combinator", () => {
    const parsed = parseExpr(kCombinator);
    const expr = abs1("x", unitTy(), abs1("y", unitTy(), var1("x")));
    expect(parsed).toEqual(expr);
  });

  test("S combinator", () => {
    const parsed = parseExpr(sCombinator);
    const expr = abs1(
      "x",
      arr(unitTy(), arr(unitTy(), unitTy())),
      abs1(
        "y",
        arr(unitTy(), unitTy()),
        abs1(
          "z",
          unitTy(),
          app1(app1(var1("x"), var1("z")), app1(var1("y"), var1("z"))),
        ),
      ),
    );
    expect(parsed).toEqual(expr);
  });
});

describe("convertToDeBruijn", () => {
  test("K combinator", () => {
    const expr = parseExpr(kCombinator);
    const expr2 = abs2(unitTy(), abs2(unitTy(), var2(1)));

    expect(convertToDebruijn(expr)).toEqual(expr2);
  });

  test("S combinator", () => {
    const expr = abs1(
      "x",
      arr(unitTy(), arr(unitTy(), unitTy())),
      abs1(
        "y",
        arr(unitTy(), unitTy()),
        abs1(
          "z",
          unitTy(),
          app1(app1(var1("x"), var1("z")), app1(var1("y"), var1("z"))),
        ),
      ),
    );
    const expr2 = abs2(
      arr(unitTy(), arr(unitTy(), unitTy())),
      abs2(
        arr(unitTy(), unitTy()),
        abs2(unitTy(), app2(app2(var2(2), var2(0)), app2(var2(1), var2(0)))),
      ),
    );

    expect(convertToDebruijn(expr)).toEqual(expr2);
  });
});

describe("infer", () => {
  test("K combinator", () => {
    const expr = parseExpr(kCombinator);
    const expr2 = convertToDebruijn(expr);
    const ty = parseTy(kCombinatorTy);

    expect(infer(expr2)).toEqual(ty);
  });

  test("K combinator negative", () => {
    const expr = parseExpr(kCombinator);
    const expr2 = convertToDebruijn(expr);
    const ty = parseTy(`() -> (() -> (() -> ()))`);

    expect(infer(expr2)).not.toEqual(ty);
  });
});