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test(library/rewriter): add test for depth RW

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This commit is contained in:
Soonho Kong 2013-12-01 01:58:23 -05:00
parent 064e3fe20d
commit 6a6b69ddf4
1 changed files with 48 additions and 0 deletions
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48
src/tests/library/rewriter/rewriter.cpp
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@ -590,6 +590,53 @@ static void repeat_rewriter2_tst() {
env.add_theorem("repeat_thm2", concl, proof);
}
static void depth_rewriter1_tst() {
cout << "=== depth_rewriter1_tst() ===" << std::endl;
// Theorem: Pi(x y : N), x + y = y + x := ADD_COMM x y
// Term : f (a + b)
// Result : (f (b + a), ADD_COMM a b)
expr a = Const("a"); // a : Nat
expr b = Const("b"); // b : Nat
expr f1 = Const("f1"); // f : Nat -> Nat
expr f2 = Const("f2"); // f : Nat -> Nat -> Nat
expr f3 = Const("f3"); // f : Nat -> Nat -> Nat -> Nat
expr f4 = Const("f4"); // f : Nat -> Nat -> Nat -> Nat -> Nat
expr zero = nVal(0); // zero : Nat
expr a_plus_b = nAdd(a, b);
expr b_plus_a = nAdd(b, a);
expr add_comm_thm_type = Pi("x", Nat,
Pi("y", Nat,
Eq(nAdd(Const("x"), Const("y")), nAdd(Const("y"), Const("x")))));
expr add_comm_thm_body = Const("ADD_COMM");
environment env = mk_toplevel();
env.add_var("f1", Nat >> Nat);
env.add_var("f2", Nat >> (Nat >> Nat));
env.add_var("f3", Nat >> (Nat >> (Nat >> Nat)));
env.add_var("f4", Nat >> (Nat >> (Nat >> (Nat >> Nat))));
env.add_var("a", Nat);
env.add_var("b", Nat);
env.add_axiom("ADD_COMM", add_comm_thm_type); // ADD_COMM : Pi (x, y: N), x + y = y + z
// Rewriting
rewriter add_comm_thm_rewriter = mk_theorem_rewriter(add_comm_thm_type, add_comm_thm_body);
rewriter try_rewriter = mk_try_rewriter(add_comm_thm_rewriter);
rewriter depth_rewriter = mk_depth_rewriter(try_rewriter);
context ctx;
cout << "RW = " << depth_rewriter << std::endl;
expr v = nAdd(f1(nAdd(a, b)), f3(a, b, nAdd(a, b)));
pair<expr, expr> result = depth_rewriter(env, ctx, v);
expr concl = mk_eq(v, result.first);
expr proof = result.second;
cout << "Concl = " << concl << std::endl
<< "Proof = " << proof << std::endl;
lean_assert_eq(concl, mk_eq(v, nAdd(f3(a, b, nAdd(b, a)), f1(nAdd(b, a)))));
env.add_theorem("depth_rewriter1", concl, proof);
cout << "====================================================" << std::endl;
}
int main() {
theorem_rewriter1_tst();
theorem_rewriter2_tst();
@ -602,5 +649,6 @@ int main() {
app_rewriter1_tst();
repeat_rewriter1_tst();
repeat_rewriter2_tst();
depth_rewriter1_tst();
return has_violations() ? 1 : 0;
}