feat(library/simplifier): add is_permutation_ceq predicate
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
7fb0aa4800
commit
3238c7e2a0
3 changed files with 133 additions and 56 deletions
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@ -156,6 +156,70 @@ bool is_ceq(ro_environment const & env, expr e) {
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}
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}
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static bool is_permutation(expr const & lhs, expr const & rhs, unsigned offset, buffer<optional<unsigned>> & p) {
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if (lhs.kind() != rhs.kind())
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return false;
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switch (lhs.kind()) {
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case expr_kind::Constant: case expr_kind::Type: case expr_kind::Value: case expr_kind::MetaVar:
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return lhs == rhs;
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case expr_kind::Var:
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if (var_idx(lhs) < offset) {
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return lhs == rhs; // locally bound variable
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} else if (var_idx(lhs) - offset < p.size()) {
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if (p[var_idx(lhs) - offset]) {
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return *(p[var_idx(lhs) - offset]) == var_idx(rhs);
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} else {
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p[var_idx(lhs) - offset] = var_idx(rhs);
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return true;
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}
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} else {
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return lhs == rhs; // free variable
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}
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case expr_kind::Lambda: case expr_kind::Pi:
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return
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is_permutation(abst_domain(lhs), abst_domain(rhs), offset, p) &&
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is_permutation(abst_body(lhs), abst_body(rhs), offset+1, p);
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case expr_kind::HEq:
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return
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is_permutation(heq_lhs(lhs), heq_lhs(rhs), offset, p) &&
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is_permutation(heq_rhs(lhs), heq_rhs(rhs), offset, p);
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case expr_kind::App:
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if (num_args(lhs) == num_args(rhs)) {
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for (unsigned i = 0; i < num_args(lhs); i++) {
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if (!is_permutation(arg(lhs, i), arg(rhs, i), offset, p))
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return false;
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}
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return true;
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} else {
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return false;
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}
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case expr_kind::Let:
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if (static_cast<bool>(let_type(lhs)) != static_cast<bool>(let_type(rhs)))
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return false;
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if (static_cast<bool>(let_type(lhs)) && !is_permutation(*let_type(lhs), *let_type(rhs), offset, p))
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return false;
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return
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is_permutation(let_value(lhs), let_value(rhs), offset, p) &&
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is_permutation(let_body(lhs), let_value(rhs), offset+1, p);
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}
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lean_unreachable();
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}
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bool is_permutation_ceq(expr e) {
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unsigned num_args = 0;
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while (is_pi(e)) {
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e = abst_body(e);
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num_args++;
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}
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if (!is_eq(e))
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return false;
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expr lhs = arg(e, 2);
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expr rhs = arg(e, 3);
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buffer<optional<unsigned>> permutation;
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permutation.resize(num_args);
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return is_permutation(lhs, rhs, 0, permutation);
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}
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static int to_ceqs(lua_State * L) {
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ro_shared_environment env(L, 1);
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auto r = to_ceqs(env, to_expr(L, 2), to_expr(L, 3));
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@ -179,8 +243,14 @@ static int is_ceq(lua_State * L) {
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return 1;
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}
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static int is_permutation_ceq(lua_State * L) {
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lua_pushboolean(L, is_permutation_ceq(to_expr(L, 1)));
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return 1;
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}
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void open_ceq(lua_State * L) {
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SET_GLOBAL_FUN(to_ceqs, "to_ceqs");
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SET_GLOBAL_FUN(is_ceq, "is_ceq");
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SET_GLOBAL_FUN(is_permutation_ceq, "is_permutation_ceq");
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}
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}
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@ -41,7 +41,10 @@ list<expr_pair> to_ceqs(ro_environment const & env, expr const & e, expr const &
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when \c A is not a proposition.
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*/
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bool is_ceq(ro_environment const & env, expr e);
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/**
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\brief Return true iff the lhs is identical to the rhs modulo a
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permutation of the conditional equation arguments.
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*/
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bool is_permutation_ceq(expr e);
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void open_ceq(lua_State * L);
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}
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@ -3,17 +3,22 @@ assert(env:find_object("neq_elim"))
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function show_ceqs(ceqs)
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for i = 1, #ceqs do
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print(ceqs[i][1], ceqs[i][2])
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print(ceqs[i][1], ceqs[i][2], is_permutation_ceq(ceqs[i][1]))
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env:type_check(ceqs[i][2])
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assert(is_ceq(env, ceqs[i][1]))
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end
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end
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function test_ceq(name, expected)
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function test_ceq(name, expected, is_perm)
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local obj = env:find_object(name)
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local r = to_ceqs(env, obj:get_type(), Const(name))
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show_ceqs(r)
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assert(#r == expected)
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if is_perm ~= nil then
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for i = 1, #r do
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assert(is_permutation_ceq(r[i][1]) == is_perm)
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end
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end
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end
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parse_lean_cmds([[
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@ -35,55 +40,54 @@ test_ceq("Ax4", 0)
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test_ceq("Ax5", 1)
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test_ceq("Ax6", 1)
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test_ceq("eta", 1)
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test_ceq("not_not_eq", 1)
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test_ceq("or_comm", 1)
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test_ceq("or_assoc", 1)
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test_ceq("or_id", 1)
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test_ceq("or_falsel", 1)
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test_ceq("or_falser", 1)
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test_ceq("or_truel", 1)
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test_ceq("or_truer", 1)
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test_ceq("or_tauto", 1)
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test_ceq("and_comm", 1)
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test_ceq("and_assoc", 1)
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test_ceq("and_id", 1)
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test_ceq("and_falsel", 1)
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test_ceq("and_falser", 1)
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test_ceq("and_truel", 1)
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test_ceq("and_truer", 1)
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test_ceq("and_absurd", 1)
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test_ceq("imp_truer", 1)
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test_ceq("imp_truel", 1)
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test_ceq("imp_falser", 1)
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test_ceq("imp_falsel", 1)
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test_ceq("not_and", 1)
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test_ceq("not_or", 1)
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test_ceq("not_iff", 1)
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test_ceq("not_implies", 1)
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test_ceq("or_left_comm", 1)
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test_ceq("and_left_comm", 1)
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test_ceq("forall_or_distributer", 1)
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test_ceq("forall_or_distributel", 1)
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test_ceq("forall_and_distribute", 1)
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test_ceq("exists_and_distributer", 1)
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test_ceq("exists_and_distributel", 1)
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test_ceq("exists_or_distribute", 1)
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test_ceq({"Nat", "add_zeror"}, 1)
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test_ceq({"Nat", "add_zerol"}, 1)
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test_ceq({"Nat", "add_comm"}, 1)
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test_ceq({"Nat", "add_assoc"}, 1)
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test_ceq({"Nat", "mul_zerol"}, 1)
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test_ceq({"Nat", "mul_zeror"}, 1)
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test_ceq({"Nat", "mul_onel"}, 1)
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test_ceq({"Nat", "mul_oner"}, 1)
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test_ceq({"Nat", "mul_comm"}, 1)
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test_ceq({"Nat", "mul_assoc"}, 1)
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test_ceq({"Nat", "add_comm"}, 1)
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test_ceq({"Nat", "add_assoc"}, 1)
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test_ceq({"Nat", "distributer"}, 1)
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test_ceq({"Nat", "distributel"}, 1)
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test_ceq({"Nat", "le_refl"}, 1)
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test_ceq({"Nat", "le_zero"}, 1)
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test_ceq({"Nat", "not_lt_0"}, 1)
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test_ceq({"Nat", "lt_nrefl"}, 1)
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test_ceq("not_not_eq", 1, false)
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test_ceq("or_comm", 1, true)
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test_ceq("or_assoc", 1, false)
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test_ceq("or_id", 1, false)
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test_ceq("or_falsel", 1, false)
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test_ceq("or_falser", 1, false)
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test_ceq("or_truel", 1, false)
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test_ceq("or_truer", 1, false)
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test_ceq("or_tauto", 1, false)
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test_ceq("and_comm", 1, true)
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test_ceq("and_assoc", 1, false)
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test_ceq("and_id", 1, false)
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test_ceq("and_falsel", 1, false)
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test_ceq("and_falser", 1, false)
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test_ceq("and_truel", 1, false)
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test_ceq("and_truer", 1, false)
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test_ceq("and_absurd", 1, false)
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test_ceq("imp_truer", 1, false)
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test_ceq("imp_truel", 1, false)
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test_ceq("imp_falser", 1, false)
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test_ceq("imp_falsel", 1, false)
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test_ceq("not_and", 1, false)
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test_ceq("not_or", 1, false)
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test_ceq("not_iff", 1, false)
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test_ceq("not_implies", 1, false)
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test_ceq("or_left_comm", 1, true)
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test_ceq("and_left_comm", 1, true)
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test_ceq("forall_or_distributer", 1, false)
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test_ceq("forall_or_distributel", 1, false)
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test_ceq("forall_and_distribute", 1, false)
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test_ceq("exists_and_distributer", 1, false)
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test_ceq("exists_and_distributel", 1, false)
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test_ceq("exists_or_distribute", 1, false)
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test_ceq({"Nat", "add_zeror"}, 1, false)
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test_ceq({"Nat", "add_zerol"}, 1, false)
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test_ceq({"Nat", "add_comm"}, 1 , true)
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test_ceq({"Nat", "add_assoc"}, 1, false)
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test_ceq({"Nat", "mul_zerol"}, 1, false)
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test_ceq({"Nat", "mul_zeror"}, 1, false)
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test_ceq({"Nat", "mul_onel"}, 1, false)
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test_ceq({"Nat", "mul_oner"}, 1, false)
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test_ceq({"Nat", "mul_comm"}, 1, true)
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test_ceq({"Nat", "mul_assoc"}, 1, false)
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test_ceq({"Nat", "add_comm"}, 1, true)
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test_ceq({"Nat", "add_assoc"}, 1, false)
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test_ceq({"Nat", "distributer"}, 1, false)
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test_ceq({"Nat", "distributel"}, 1, false)
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test_ceq({"Nat", "le_refl"}, 1, false)
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test_ceq({"Nat", "le_zero"}, 1, false)
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test_ceq({"Nat", "not_lt_0"}, 1, false)
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test_ceq({"Nat", "lt_nrefl"}, 1, false)
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