fix(library/tactic/ac_tactics): allow nested ac_app macros in perm_ac macro
fixes #1442
This commit is contained in:
Leonardo de Moura
parent
970e11bf5e
commit
7a99d87cbd
2 changed files with 276 additions and 260 deletions
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@ -99,266 +99,6 @@ optional<expr> ac_manager::is_comm(expr const & e) {
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return r;
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}
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struct flat_assoc_fn {
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abstract_type_context & m_ctx;
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expr m_op;
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expr m_assoc;
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flat_assoc_fn(abstract_type_context & ctx, expr const & op, expr const & assoc):
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m_ctx(ctx), m_op(op), m_assoc(assoc) {}
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bool is_op_app(expr const & e, expr & lhs, expr & rhs) {
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if (!is_app(e)) return false;
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expr const & fn1 = app_fn(e);
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if (!is_app(fn1)) return false;
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if (app_fn(fn1) != m_op) return false;
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lhs = app_arg(fn1);
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rhs = app_arg(e);
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return true;
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}
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bool is_op_app(expr const & e) {
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if (!is_app(e)) return false;
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expr const & fn1 = app_fn(e);
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if (!is_app(fn1)) return false;
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return app_fn(fn1) == m_op;
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}
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expr mk_op(expr const & a, expr const & b) {
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return mk_app(m_op, a, b);
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}
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expr mk_assoc(expr const & a, expr const & b, expr const & c) {
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return mk_app(m_assoc, a, b, c);
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}
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expr mk_eq_refl(expr const & a) {
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return ::lean::mk_eq_refl(m_ctx, a);
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}
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expr mk_eq_trans(expr const & H1, expr const & H2) {
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return ::lean::mk_eq_trans(m_ctx, H1, H2);
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}
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expr mk_eq_trans(expr const & H1, optional<expr> const & H2) {
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if (!H2) return H1;
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return mk_eq_trans(H1, *H2);
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}
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optional<expr> mk_eq_trans(optional<expr> const & H1, optional<expr> const & H2) {
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if (!H1) return H2;
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if (!H2) return H1;
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return some_expr(mk_eq_trans(*H1, *H2));
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}
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expr mk_eq_symm(expr const & H) {
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return ::lean::mk_eq_symm(m_ctx, H);
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}
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optional<expr> mk_eq_symm(optional<expr> const & H) {
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if (!H) return none_expr();
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return some_expr(mk_eq_symm(*H));
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}
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expr mk_congr_arg(expr const & fn, expr const & H) {
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return ::lean::mk_congr_arg(m_ctx, fn, H);
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}
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pair<expr, optional<expr>> flat_with(expr const & e, expr const & rest) {
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expr lhs, rhs;
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if (is_op_app(e, lhs, rhs)) {
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auto p1 = flat_with(rhs, rest);
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if (p1.second) {
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auto p2 = flat_with(lhs, p1.first);
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// H3 is a proof for (lhs `op` rhs) `op` rest = lhs `op` (rhs `op` rest)
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expr H3 = mk_assoc(lhs, rhs, rest);
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// H4 is a proof for lhs `op` (rhs `op` rest) = lhs `op` p1.first
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expr H4 = mk_congr_arg(mk_app(m_op, lhs), *p1.second);
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expr H = mk_eq_trans(mk_eq_trans(H3, H4), p2.second);
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return mk_pair(p2.first, some_expr(H));
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} else {
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if (is_op_app(lhs)) {
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auto p2 = flat_with(lhs, p1.first);
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// H3 is a proof for (lhs `op` rhs) `op` rest = lhs `op` (rhs `op` rest)
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expr H3 = mk_assoc(lhs, rhs, rest);
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expr H = mk_eq_trans(H3, p2.second);
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return mk_pair(p2.first, some_expr(H));
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} else {
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return mk_pair(mk_op(lhs, p1.first), some_expr(mk_assoc(lhs, rhs, rest)));
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}
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}
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} else {
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return mk_pair(mk_op(e, rest), none_expr());
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}
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}
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pair<expr, optional<expr>> flat_core(expr const & e) {
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expr lhs, rhs;
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if (is_op_app(e, lhs, rhs)) {
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auto p1 = flat_core(rhs);
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if (p1.second) {
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if (is_op_app(lhs)) {
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auto p2 = flat_with(lhs, p1.first);
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expr H3 = mk_congr_arg(mk_app(m_op, lhs), *p1.second);
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expr H = mk_eq_trans(H3, p2.second);
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return mk_pair(p2.first, some_expr(H));
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} else {
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expr r = mk_op(lhs, p1.first);
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expr H = mk_congr_arg(mk_app(m_op, lhs), *p1.second);
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return mk_pair(r, some_expr(H));
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}
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} else {
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if (is_op_app(lhs)) {
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return flat_with(lhs, rhs);
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} else {
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return mk_pair(e, none_expr());
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}
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}
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} else {
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return mk_pair(e, none_expr());
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}
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}
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pair<expr, expr> flat(expr const & e) {
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auto p = flat_core(e);
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if (p.second) {
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return mk_pair(p.first, *p.second);
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} else {
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return mk_pair(e, mk_eq_refl(e));
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}
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}
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};
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#define lean_perm_ac_trace(code) lean_trace(name({"tactic", "perm_ac"}), scope_trace_env _scope1(m_ctx.env(), m_ctx); code)
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struct perm_ac_fn : public flat_assoc_fn {
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expr m_comm;
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optional<expr> m_left_comm;
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perm_ac_fn(abstract_type_context & ctx, expr const & op, expr const & assoc, expr const & comm):
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flat_assoc_fn(ctx, op, assoc), m_comm(comm) {
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}
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[[ noreturn ]] void throw_failed() {
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throw exception("perm_ac failed, arguments are not equal modulo AC");
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}
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expr mk_comm(expr const & a, expr const & b) {
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return mk_app(m_comm, a, b);
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}
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level dec_level(level const & l) {
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if (auto r = ::lean::dec_level(l))
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return *r;
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throw_failed();
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}
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expr mk_left_comm(expr const & a, expr const & b, expr const & c) {
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if (!m_left_comm) {
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expr A = m_ctx.infer(a);
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level lvl = dec_level(get_level(m_ctx, A));
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m_left_comm = mk_app(mk_constant(get_left_comm_name(), {lvl}), A, m_op, m_comm, m_assoc);
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}
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return mk_app(*m_left_comm, a, b, c);
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}
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/* Given a term \c e of the form (op t_1 (op t_2 ... (op t_{n-1} t_n))), if
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for some i, t_i == t, then produce the term
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(op t_i (op t_2 ... (op t_{n-1} t_n)))
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and a proof they are equal AC.
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Throw exception if t is not found. */
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pair<expr, expr> pull_term(expr const & t, expr const & e) {
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expr lhs1, rhs1;
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if (!is_op_app(e, lhs1, rhs1)) {
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lean_perm_ac_trace(tout() << "right-hand-side does not contain:\n" << t << "\n";);
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throw_failed();
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}
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if (t == rhs1) {
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return mk_pair(mk_op(rhs1, lhs1), mk_comm(lhs1, rhs1));
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}
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expr lhs2, rhs2;
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if (!is_op_app(rhs1, lhs2, rhs2)) {
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lean_perm_ac_trace(tout() << "right-hand-side does not contain:\n" << t << "\n";);
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throw_failed();
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}
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if (t == lhs2) {
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return mk_pair(mk_op(lhs2, mk_op(lhs1, rhs2)), mk_left_comm(lhs1, lhs2, rhs2));
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}
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/* We have e := lhs1 `op` lhs2 `op` rhs2 */
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auto p = pull_term(t, rhs1);
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expr lhs3, rhs3;
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lean_verify(is_op_app(p.first, lhs3, rhs3));
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lean_assert(t == lhs3);
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/* p.second : rhs1 = t `op` rhs3 */
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expr H1 = mk_congr_arg(mk_app(m_op, lhs1), p.second);
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/* H1 : lhs1 `op` rhs1 = lhs1 `op` t `op` rhs3 */
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expr H2 = mk_left_comm(lhs1, t, rhs3);
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/* H2 : lhs1 `op` t `op` rhs3 = t `op` lhs1 `op` rhs3 */
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return mk_pair(mk_op(t, mk_op(lhs1, rhs3)), mk_eq_trans(H1, H2));
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}
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/* Return a proof that e1 == e2 modulo AC. Return none if reflexivity.
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Throw exception if failure */
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optional<expr> perm_flat(expr const & e1, expr const & e2) {
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expr lhs1, rhs1;
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expr lhs2, rhs2;
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bool b1 = is_op_app(e1, lhs1, rhs1);
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bool b2 = is_op_app(e2, lhs2, rhs2);
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if (b1 != b2) {
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lean_perm_ac_trace(tout() << "left and right-hand-sides have different number of terms\n";);
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throw_failed();
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}
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if (!b1 && !b2) {
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if (e1 == e2) {
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return none_expr(); // reflexivity
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} else {
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lean_perm_ac_trace(tout() << "the left and right hand sides contain the terms:\n" << e1 << "\n" << e2 << "\n";);
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throw_failed();
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}
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}
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lean_assert(b1 && b2);
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if (lhs1 == lhs2) {
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optional<expr> H = perm_flat(rhs1, rhs2);
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if (!H) return none_expr();
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return some_expr(mk_congr_arg(mk_app(m_op, lhs1), *H));
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} else {
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auto p = pull_term(lhs2, e1);
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is_op_app(p.first, lhs1, rhs1);
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lean_assert(lhs1 == lhs2);
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optional<expr> H1 = perm_flat(rhs1, rhs2);
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if (!H1) return some_expr(p.second);
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expr H2 = mk_congr_arg(mk_app(m_op, lhs1), *H1);
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return some_expr(mk_eq_trans(p.second, H2));
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}
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}
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/* Return a proof that lhs == rhs modulo AC. Return none if reflexivity.
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Throw exception if failure */
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optional<expr> perm_core(expr const & lhs, expr const & rhs) {
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auto p1 = flat_core(lhs);
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auto p2 = flat_core(rhs);
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auto H = perm_flat(p1.first, p2.first);
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return mk_eq_trans(p1.second, mk_eq_trans(H, mk_eq_symm(p2.second)));
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}
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expr perm(expr const & lhs, expr const & rhs) {
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if (auto H = perm_core(lhs, rhs))
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return *H;
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else
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return mk_eq_refl(lhs);
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}
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};
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pair<expr, optional<expr>> flat_assoc(abstract_type_context & ctx, expr const & op, expr const & assoc, expr const & e) {
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return flat_assoc_fn(ctx, op, assoc).flat_core(e);
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}
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expr perm_ac(abstract_type_context & ctx, expr const & op, expr const & assoc, expr const & comm, expr const & e1, expr const & e2) {
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return perm_ac_fn(ctx, op, assoc, comm).perm(e1, e2);
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}
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static name * g_ac_app_name = nullptr;
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static macro_definition * g_ac_app_macro = nullptr;
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static std::string * g_ac_app_opcode = nullptr;
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@ -612,6 +352,271 @@ static expr expand_if_ac_app(expr const & e) {
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return e;
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}
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struct flat_assoc_fn {
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abstract_type_context & m_ctx;
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expr m_op;
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expr m_assoc;
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flat_assoc_fn(abstract_type_context & ctx, expr const & op, expr const & assoc):
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m_ctx(ctx), m_op(op), m_assoc(assoc) {}
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bool is_op_app(expr const & e, expr & lhs, expr & rhs) {
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if (!is_app(e)) return false;
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expr const & fn1 = app_fn(e);
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if (!is_app(fn1)) return false;
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if (app_fn(fn1) != m_op) return false;
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lhs = app_arg(fn1);
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rhs = app_arg(e);
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return true;
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}
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bool is_op_app(expr const & e) {
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if (!is_app(e)) return false;
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expr const & fn1 = app_fn(e);
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if (!is_app(fn1)) return false;
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return app_fn(fn1) == m_op;
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}
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expr mk_op(expr const & a, expr const & b) {
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return mk_app(m_op, a, b);
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}
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expr mk_assoc(expr const & a, expr const & b, expr const & c) {
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return mk_app(m_assoc, a, b, c);
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}
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expr mk_eq_refl(expr const & a) {
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return ::lean::mk_eq_refl(m_ctx, a);
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}
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expr mk_eq_trans(expr const & H1, expr const & H2) {
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return ::lean::mk_eq_trans(m_ctx, H1, H2);
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}
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expr mk_eq_trans(expr const & H1, optional<expr> const & H2) {
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if (!H2) return H1;
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return mk_eq_trans(H1, *H2);
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}
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optional<expr> mk_eq_trans(optional<expr> const & H1, optional<expr> const & H2) {
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if (!H1) return H2;
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if (!H2) return H1;
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return some_expr(mk_eq_trans(*H1, *H2));
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}
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expr mk_eq_symm(expr const & H) {
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return ::lean::mk_eq_symm(m_ctx, H);
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}
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optional<expr> mk_eq_symm(optional<expr> const & H) {
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if (!H) return none_expr();
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return some_expr(mk_eq_symm(*H));
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}
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expr mk_congr_arg(expr const & fn, expr const & H) {
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return ::lean::mk_congr_arg(m_ctx, fn, H);
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}
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pair<expr, optional<expr>> flat_with(expr const & e, expr const & rest) {
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expr lhs, rhs;
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if (is_op_app(e, lhs, rhs)) {
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lhs = expand_if_ac_app(lhs);
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rhs = expand_if_ac_app(rhs);
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auto p1 = flat_with(rhs, rest);
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if (p1.second) {
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auto p2 = flat_with(lhs, p1.first);
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// H3 is a proof for (lhs `op` rhs) `op` rest = lhs `op` (rhs `op` rest)
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expr H3 = mk_assoc(lhs, rhs, rest);
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// H4 is a proof for lhs `op` (rhs `op` rest) = lhs `op` p1.first
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expr H4 = mk_congr_arg(mk_app(m_op, lhs), *p1.second);
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expr H = mk_eq_trans(mk_eq_trans(H3, H4), p2.second);
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return mk_pair(p2.first, some_expr(H));
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} else {
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if (is_op_app(lhs)) {
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auto p2 = flat_with(lhs, p1.first);
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// H3 is a proof for (lhs `op` rhs) `op` rest = lhs `op` (rhs `op` rest)
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expr H3 = mk_assoc(lhs, rhs, rest);
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expr H = mk_eq_trans(H3, p2.second);
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return mk_pair(p2.first, some_expr(H));
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} else {
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return mk_pair(mk_op(lhs, p1.first), some_expr(mk_assoc(lhs, rhs, rest)));
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}
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}
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} else {
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return mk_pair(mk_op(e, rest), none_expr());
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}
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}
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pair<expr, optional<expr>> flat_core(expr e) {
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expr lhs, rhs;
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e = expand_if_ac_app(e);
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if (is_op_app(e, lhs, rhs)) {
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lhs = expand_if_ac_app(lhs);
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rhs = expand_if_ac_app(rhs);
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auto p1 = flat_core(rhs);
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if (p1.second) {
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if (is_op_app(lhs)) {
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auto p2 = flat_with(lhs, p1.first);
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expr H3 = mk_congr_arg(mk_app(m_op, lhs), *p1.second);
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expr H = mk_eq_trans(H3, p2.second);
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return mk_pair(p2.first, some_expr(H));
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} else {
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expr r = mk_op(lhs, p1.first);
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expr H = mk_congr_arg(mk_app(m_op, lhs), *p1.second);
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return mk_pair(r, some_expr(H));
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}
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} else {
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if (is_op_app(lhs)) {
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return flat_with(lhs, rhs);
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} else {
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return mk_pair(e, none_expr());
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}
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}
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} else {
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return mk_pair(e, none_expr());
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}
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}
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pair<expr, expr> flat(expr const & e) {
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auto p = flat_core(e);
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if (p.second) {
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return mk_pair(p.first, *p.second);
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} else {
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return mk_pair(e, mk_eq_refl(e));
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}
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}
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};
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#define lean_perm_ac_trace(code) lean_trace(name({"tactic", "perm_ac"}), scope_trace_env _scope1(m_ctx.env(), m_ctx); code)
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struct perm_ac_fn : public flat_assoc_fn {
|
||||
expr m_comm;
|
||||
optional<expr> m_left_comm;
|
||||
|
||||
perm_ac_fn(abstract_type_context & ctx, expr const & op, expr const & assoc, expr const & comm):
|
||||
flat_assoc_fn(ctx, op, assoc), m_comm(comm) {
|
||||
}
|
||||
|
||||
[[ noreturn ]] void throw_failed() {
|
||||
throw exception("perm_ac failed, arguments are not equal modulo AC");
|
||||
}
|
||||
|
||||
expr mk_comm(expr const & a, expr const & b) {
|
||||
return mk_app(m_comm, a, b);
|
||||
}
|
||||
|
||||
level dec_level(level const & l) {
|
||||
if (auto r = ::lean::dec_level(l))
|
||||
return *r;
|
||||
throw_failed();
|
||||
}
|
||||
|
||||
expr mk_left_comm(expr const & a, expr const & b, expr const & c) {
|
||||
if (!m_left_comm) {
|
||||
expr A = m_ctx.infer(a);
|
||||
level lvl = dec_level(get_level(m_ctx, A));
|
||||
m_left_comm = mk_app(mk_constant(get_left_comm_name(), {lvl}), A, m_op, m_comm, m_assoc);
|
||||
}
|
||||
return mk_app(*m_left_comm, a, b, c);
|
||||
}
|
||||
|
||||
/* Given a term \c e of the form (op t_1 (op t_2 ... (op t_{n-1} t_n))), if
|
||||
for some i, t_i == t, then produce the term
|
||||
|
||||
(op t_i (op t_2 ... (op t_{n-1} t_n)))
|
||||
|
||||
and a proof they are equal AC.
|
||||
Throw exception if t is not found. */
|
||||
pair<expr, expr> pull_term(expr const & t, expr const & e) {
|
||||
expr lhs1, rhs1;
|
||||
if (!is_op_app(e, lhs1, rhs1)) {
|
||||
lean_perm_ac_trace(tout() << "right-hand-side does not contain:\n" << t << "\n";);
|
||||
throw_failed();
|
||||
}
|
||||
if (t == rhs1) {
|
||||
return mk_pair(mk_op(rhs1, lhs1), mk_comm(lhs1, rhs1));
|
||||
}
|
||||
expr lhs2, rhs2;
|
||||
if (!is_op_app(rhs1, lhs2, rhs2)) {
|
||||
lean_perm_ac_trace(tout() << "right-hand-side does not contain:\n" << t << "\n";);
|
||||
throw_failed();
|
||||
}
|
||||
if (t == lhs2) {
|
||||
return mk_pair(mk_op(lhs2, mk_op(lhs1, rhs2)), mk_left_comm(lhs1, lhs2, rhs2));
|
||||
}
|
||||
/* We have e := lhs1 `op` lhs2 `op` rhs2 */
|
||||
auto p = pull_term(t, rhs1);
|
||||
expr lhs3, rhs3;
|
||||
lean_verify(is_op_app(p.first, lhs3, rhs3));
|
||||
lean_assert(t == lhs3);
|
||||
/* p.second : rhs1 = t `op` rhs3 */
|
||||
expr H1 = mk_congr_arg(mk_app(m_op, lhs1), p.second);
|
||||
/* H1 : lhs1 `op` rhs1 = lhs1 `op` t `op` rhs3 */
|
||||
expr H2 = mk_left_comm(lhs1, t, rhs3);
|
||||
/* H2 : lhs1 `op` t `op` rhs3 = t `op` lhs1 `op` rhs3 */
|
||||
return mk_pair(mk_op(t, mk_op(lhs1, rhs3)), mk_eq_trans(H1, H2));
|
||||
}
|
||||
|
||||
/* Return a proof that e1 == e2 modulo AC. Return none if reflexivity.
|
||||
Throw exception if failure */
|
||||
optional<expr> perm_flat(expr const & e1, expr const & e2) {
|
||||
expr lhs1, rhs1;
|
||||
expr lhs2, rhs2;
|
||||
bool b1 = is_op_app(e1, lhs1, rhs1);
|
||||
bool b2 = is_op_app(e2, lhs2, rhs2);
|
||||
if (b1 != b2) {
|
||||
lean_perm_ac_trace(tout() << "left and right-hand-sides have different number of terms\n";);
|
||||
throw_failed();
|
||||
}
|
||||
if (!b1 && !b2) {
|
||||
if (e1 == e2) {
|
||||
return none_expr(); // reflexivity
|
||||
} else {
|
||||
lean_perm_ac_trace(tout() << "the left and right hand sides contain the terms:\n" << e1 << "\n" << e2 << "\n";);
|
||||
throw_failed();
|
||||
}
|
||||
}
|
||||
lean_assert(b1 && b2);
|
||||
if (lhs1 == lhs2) {
|
||||
optional<expr> H = perm_flat(rhs1, rhs2);
|
||||
if (!H) return none_expr();
|
||||
return some_expr(mk_congr_arg(mk_app(m_op, lhs1), *H));
|
||||
} else {
|
||||
auto p = pull_term(lhs2, e1);
|
||||
is_op_app(p.first, lhs1, rhs1);
|
||||
lean_assert(lhs1 == lhs2);
|
||||
optional<expr> H1 = perm_flat(rhs1, rhs2);
|
||||
if (!H1) return some_expr(p.second);
|
||||
expr H2 = mk_congr_arg(mk_app(m_op, lhs1), *H1);
|
||||
return some_expr(mk_eq_trans(p.second, H2));
|
||||
}
|
||||
}
|
||||
|
||||
/* Return a proof that lhs == rhs modulo AC. Return none if reflexivity.
|
||||
Throw exception if failure */
|
||||
optional<expr> perm_core(expr const & lhs, expr const & rhs) {
|
||||
auto p1 = flat_core(lhs);
|
||||
auto p2 = flat_core(rhs);
|
||||
auto H = perm_flat(p1.first, p2.first);
|
||||
return mk_eq_trans(p1.second, mk_eq_trans(H, mk_eq_symm(p2.second)));
|
||||
}
|
||||
|
||||
expr perm(expr const & lhs, expr const & rhs) {
|
||||
if (auto H = perm_core(lhs, rhs))
|
||||
return *H;
|
||||
else
|
||||
return mk_eq_refl(lhs);
|
||||
}
|
||||
};
|
||||
|
||||
pair<expr, optional<expr>> flat_assoc(abstract_type_context & ctx, expr const & op, expr const & assoc, expr const & e) {
|
||||
return flat_assoc_fn(ctx, op, assoc).flat_core(e);
|
||||
}
|
||||
|
||||
expr perm_ac(abstract_type_context & ctx, expr const & op, expr const & assoc, expr const & comm, expr const & e1, expr const & e2) {
|
||||
return perm_ac_fn(ctx, op, assoc, comm).perm(e1, e2);
|
||||
}
|
||||
|
||||
static name * g_perm_ac_name = nullptr;
|
||||
static macro_definition * g_perm_ac_macro = nullptr;
|
||||
static std::string * g_perm_ac_opcode = nullptr;
|
||||
|
|
|
|||
11
tests/lean/run/1442.lean
Normal file
11
tests/lean/run/1442.lean
Normal file
|
|
@ -0,0 +1,11 @@
|
|||
protected def rel : ℤ × ℤ → ℤ × ℤ → Prop
|
||||
| ⟨n₁, d₁⟩ ⟨n₂, d₂⟩ := n₁ * d₂ = n₂ * d₁
|
||||
|
||||
private def mul' : ℤ × ℤ → ℤ × ℤ → ℤ × ℤ
|
||||
| ⟨n₁, d₁⟩ ⟨n₂, d₂⟩ := ⟨n₁ * n₂, d₁ * d₂⟩
|
||||
|
||||
example : ∀(a b c d : ℤ × ℤ), rel a c → rel b d → rel (mul' a b) (mul' c d) :=
|
||||
λ⟨n₁, d₁⟩ ⟨n₂, d₂⟩ ⟨n₃, d₃⟩ ⟨n₄, d₄⟩,
|
||||
assume (h₁ : n₁ * d₃ = n₃ * d₁) (h₂ : n₂ * d₄ = n₄ * d₂),
|
||||
show (n₁ * n₂) * (d₃ * d₄) = (n₃ * n₄) * (d₁ * d₂),
|
||||
by cc
|
||||
Loading…
Add table
Reference in a new issue