add typescript exercise

misc/casetree.ts

@@ -0,0 +1,180 @@
+// why I'm not doing this in a real language, I don't know
+
+// It might be interesting to add some types and flesh this out
+// but time may be better spent on the real deal (where I have easy
+// access to types)
+
+// the array version is always a constructor application
+type Pattern = string | [string, ...Pattern[]];
+type Constraint = [Pattern, Pattern];
+type Exp = string | Exp[];
+
+type Clause = [Constraint[], Pattern[], Exp];
+type Problem = Clause[];
+
+type Tree =
+  | ["Lam", string, Tree]
+  | ["Done", Exp]
+  | ["Case", string, [string[], Tree][]];
+
+// These are essentially sexpr
+const showExp = (exp: Exp): string => {
+  if (exp instanceof Array) {
+    return "(" + exp.map(showExp).join(" ") + ")";
+  }
+  return exp;
+};
+
+const printProb = (prob: Problem) => {
+  for (let [cs, ps, exp] of prob) {
+    console.log(
+      `[${cs
+        .map(([a, b]) => `${showExp(a)} /? ${showExp(b)}`)
+        .join(", ")}] ${ps} => ${showExp(exp)}`
+    );
+  }
+};
+
+const printTree = (tree: Tree, indent = "") => {
+  switch (tree[0]) {
+    case "Lam":
+      console.log(indent + "Lam", tree[1]);
+      printTree(tree[2], indent + "  ");
+      break;
+    case "Done":
+      console.log(indent, showExp(tree[1]));
+      break;
+    case "Case":
+      console.log(indent + "Case", tree[1]);
+      for (let [l, r] of tree[2]) {
+        console.log(indent + "  " + showExp(l), "=>");
+        printTree(r, indent + "    ");
+      }
+      break;
+    default:
+      console.log("FIXME");
+  }
+};
+
+let problem: Problem = [
+  [[], [["Z"], "j"], "j"],
+  [[], ["i", ["Z"]], "i"],
+  [
+    [],
+    [
+      ["S", "k"],
+      ["S", "l"],
+    ],
+    ["S", ["max", "k", "l"]],
+  ],
+];
+let next = 0;
+const free = () => "i" + next++;
+
+// intro applies if everybody has shape [n, ...ns]
+function intro(prob: Problem): Tree {
+  let name = free();
+  console.log("INTRO", name);
+  let prob2: Problem = prob.map(([cs, [n, ...ns], exp]) => [
+    [...cs, [name, n]],
+    ns,
+    exp,
+  ]);
+  printProb(prob2);
+  return ["Lam", name, solve(prob2)];
+}
+
+function substPat(prob: Problem, name: string, pat: Pattern): Tree {
+  console.log("subproblem", pat);
+  let prob2: Problem = [];
+  OUTER: for (let [cs, ps, exp] of prob) {
+    let cs2: Constraint[] = [];
+    for (let [a, b] of cs) {
+      if (a === name) {
+        if (b instanceof Array) {
+          if (b[0] !== pat[0]) {
+            console.log("drop mismatch", pat, "/?", b);
+            // drop entire clause
+            continue OUTER;
+          } else {
+            console.log("zip");
+            // zip
+            if (pat.length !== b.length) {
+              console.error("length mismatch", pat, "/?", b);
+              throw new Error();
+            }
+            for (let i = 1; i < pat.length; i++) {
+              cs2.push([pat[i], b[i]]);
+            }
+          }
+          // REVIEW can name occur anywhere else?
+        } else {
+          cs2.push([pat, b]);
+        }
+      } else {
+        cs2.push([a, b]);
+      }
+    }
+    prob2.push([cs2, ps, exp]);
+  }
+
+  printProb(prob2);
+  return solve(prob2);
+}
+
+function split(prob: Problem, name: string): Tree {
+  console.log("SPLIT", name);
+  // here we're assuming Nat for our example
+  let arg = free();
+  return [
+    "Case",
+    name,
+    [
+      [["Z"], substPat(prob, name, ["Z"])],
+      [["S", arg], substPat(prob, name, ["S", arg])],
+    ],
+  ];
+}
+
+const canIntro = (prob: Problem) => prob.every((cl) => cl[1].length);
+
+console.log(canIntro(problem));
+
+function subst(exp: Exp, x: string, y: Pattern): Exp {
+  if (exp === x) return y;
+  if (typeof exp === "string") return exp;
+  return exp.map((e) => subst(e, x, y));
+}
+
+function solve(prob: Problem): Tree {
+  if (canIntro(prob)) return intro(prob);
+
+  // Done if no copattern and constraints all solved on first clause...
+
+  // SplitCon if first clause has a x /? c p1... with x having appropriate type
+  let [cs, ps, exp] = prob[0];
+  let cs2: Constraint[] = [];
+  for (let [x, y] of cs) {
+    // need to check types too
+    if (y instanceof Array && typeof x === "string") {
+      return split(prob, x);
+    }
+    // subst and see if there is anything left.
+    if (typeof y === "string") {
+      exp = subst(exp, y, x);
+    } else {
+      cs2.push([x, y]);
+    }
+  }
+  if (!cs2.length && !ps.length) return ["Done", exp];
+
+  // SplitEmpty if first clause has a x /? ø with x of empty type
+
+  // SplitEq if first clause has a x /? refl with appropriate type
+  // here a substitution is generated from the unification of the refl
+
+  printProb(prob);
+  throw new Error(`stuck`);
+}
+
+printTree(intro(problem));