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https://github.com/Z3Prover/z3
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add c-cube's recursive function theory
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
commit
c7d0d4e191
23 changed files with 1590 additions and 21 deletions
370
src/smt/theory_recfun.cpp
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370
src/smt/theory_recfun.cpp
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#include "util/stats.h"
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#include "ast/ast_util.h"
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#include "smt/theory_recfun.h"
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#include "smt/params/smt_params_helper.hpp"
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#define DEBUG(x) TRACE("recfun", tout << x << '\n';)
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namespace smt {
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theory_recfun::theory_recfun(ast_manager & m)
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: theory(m.mk_family_id("recfun")),
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m_plugin(*reinterpret_cast<recfun_decl_plugin*>(m.get_plugin(get_family_id()))),
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m_util(m_plugin.u()),
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m_trail(*this),
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m_guards(), m_max_depth(0), m_q_case_expand(), m_q_body_expand(), m_q_clauses()
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{
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}
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theory_recfun::~theory_recfun() {
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reset_queues();
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for (auto & kv : m_guards) {
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m().dec_ref(kv.m_key);
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}
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m_guards.reset();
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}
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char const * theory_recfun::get_name() const { return "recfun"; }
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void theory_recfun::setup_params() {
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// obtain max depth via parameters
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smt_params_helper p(get_context().get_params());
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set_max_depth(p.recfun_max_depth());
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}
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theory* theory_recfun::mk_fresh(context* new_ctx) {
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return alloc(theory_recfun, new_ctx->get_manager());
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}
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bool theory_recfun::internalize_atom(app * atom, bool gate_ctx) {
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context & ctx = get_context();
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if (! ctx.e_internalized(atom)) {
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unsigned num_args = atom->get_num_args();
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for (unsigned i = 0; i < num_args; ++i)
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ctx.internalize(atom->get_arg(i), false);
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ctx.mk_enode(atom, false, true, false);
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}
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if (! ctx.b_internalized(atom)) {
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bool_var v = ctx.mk_bool_var(atom);
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ctx.set_var_theory(v, get_id());
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}
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return true;
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}
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bool theory_recfun::internalize_term(app * term) {
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context & ctx = get_context();
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for (expr* e : *term) ctx.internalize(e, false);
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// the internalization of the arguments may have triggered the internalization of term.
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if (ctx.e_internalized(term))
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return true;
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ctx.mk_enode(term, false, false, true);
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return true; // the theory doesn't actually map terms to variables
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}
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void theory_recfun::reset_queues() {
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m_q_case_expand.reset();
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m_q_body_expand.reset();
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m_q_clauses.reset();
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}
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void theory_recfun::reset_eh() {
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m_trail.reset();
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reset_queues();
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m_stats.reset();
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theory::reset_eh();
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}
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/*
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* when `n` becomes relevant, if it's `f(t1…tn)` with `f` defined,
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* then case-expand `n`. If it's a macro we can also immediately
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* body-expand it.
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*/
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void theory_recfun::relevant_eh(app * n) {
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SASSERT(get_context().relevancy());
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if (u().is_defined(n)) {
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DEBUG("relevant_eh: (defined) " << mk_pp(n, m()));
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case_expansion e(u(), n);
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push_case_expand(std::move(e));
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}
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}
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void theory_recfun::push_scope_eh() {
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DEBUG("push_scope");
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theory::push_scope_eh();
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m_trail.push_scope();
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}
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void theory_recfun::pop_scope_eh(unsigned num_scopes) {
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DEBUG("pop_scope " << num_scopes);
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m_trail.pop_scope(num_scopes);
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theory::pop_scope_eh(num_scopes);
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reset_queues();
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}
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void theory_recfun::restart_eh() {
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DEBUG("restart");
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reset_queues();
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theory::restart_eh();
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}
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bool theory_recfun::can_propagate() {
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return ! (m_q_case_expand.empty() &&
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m_q_body_expand.empty() &&
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m_q_clauses.empty());
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}
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void theory_recfun::propagate() {
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context & ctx = get_context();
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for (literal_vector & c : m_q_clauses) {
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DEBUG("add axiom " << pp_lits(ctx, c.size(), c.c_ptr()));
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ctx.mk_th_axiom(get_id(), c.size(), c.c_ptr());
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}
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m_q_clauses.clear();
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for (case_expansion & e : m_q_case_expand) {
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if (e.m_def->is_fun_macro()) {
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// body expand immediately
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assert_macro_axiom(e);
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}
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else {
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// case expand
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SASSERT(e.m_def->is_fun_defined());
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assert_case_axioms(e);
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}
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}
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m_q_case_expand.clear();
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for (body_expansion & e : m_q_body_expand) {
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assert_body_axiom(e);
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}
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m_q_body_expand.clear();
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}
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void theory_recfun::max_depth_conflict() {
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DEBUG("max-depth conflict");
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context & ctx = get_context();
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literal_vector c;
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// make clause `depth_limit => V_{g : guards} ~ g`
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{
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// first literal must be the depth limit one
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app_ref dlimit = m_util.mk_depth_limit_pred(get_max_depth());
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ctx.internalize(dlimit, false);
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c.push_back(~ ctx.get_literal(dlimit));
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SASSERT(ctx.get_assignment(ctx.get_literal(dlimit)) == l_true);
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}
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for (auto& kv : m_guards) {
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expr * g = & kv.get_key();
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c.push_back(~ ctx.get_literal(g));
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}
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DEBUG("max-depth limit: add clause " << pp_lits(ctx, c.size(), c.c_ptr()));
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SASSERT(std::all_of(c.begin(), c.end(), [&](literal & l) { return ctx.get_assignment(l) == l_false; })); // conflict
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m_q_clauses.push_back(std::move(c));
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}
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// if `is_true` and `v = C_f_i(t1…tn)`, then body-expand i-th case of `f(t1…tn)`
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void theory_recfun::assign_eh(bool_var v, bool is_true) {
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expr* e = get_context().bool_var2expr(v);
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if (!is_true) return;
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if (!is_app(e)) return;
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app* a = to_app(e);
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if (u().is_case_pred(a)) {
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DEBUG("assign_case_pred_true "<< mk_pp(e,m()));
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// add to set of local assumptions, for depth-limit purpose
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{
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m_guards.insert(e, empty());
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m().inc_ref(e);
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insert_ref_map<theory_recfun,guard_set,ast_manager,expr*> trail_elt(m(), m_guards, e);
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m_trail.push(trail_elt);
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}
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if (m_guards.size() > get_max_depth()) {
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// too many body-expansions: depth-limit conflict
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max_depth_conflict();
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}
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else {
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// body-expand
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body_expansion b_e(u(), a);
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push_body_expand(std::move(b_e));
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}
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}
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}
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// replace `vars` by `args` in `e`
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expr_ref theory_recfun::apply_args(recfun::vars const & vars,
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ptr_vector<expr> const & args,
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expr * e) {
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// check that var order is standard
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SASSERT(vars.size() == 0 || vars[vars.size()-1]->get_idx() == 0);
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var_subst subst(m(), true);
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expr_ref new_body(m());
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new_body = subst(e, args.size(), args.c_ptr());
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get_context().get_rewriter()(new_body); // simplify
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return new_body;
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}
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app_ref theory_recfun::apply_pred(recfun::case_pred const & p,
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ptr_vector<expr> const & args){
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app_ref res(u().mk_case_pred(p, args), m());
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return res;
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}
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void theory_recfun::assert_macro_axiom(case_expansion & e) {
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DEBUG("assert_macro_axiom " << pp_case_expansion(e,m()));
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SASSERT(e.m_def->is_fun_macro());
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expr_ref lhs(e.m_lhs, m());
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context & ctx = get_context();
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auto & vars = e.m_def->get_vars();
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// substitute `e.args` into the macro RHS
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expr_ref rhs(apply_args(vars, e.m_args, e.m_def->get_macro_rhs()), m());
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DEBUG("macro expansion yields" << mk_pp(rhs,m()));
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// now build the axiom `lhs = rhs`
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ctx.internalize(rhs, false);
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// add unit clause `lhs=rhs`
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literal l(mk_eq(lhs, rhs, true));
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ctx.mark_as_relevant(l);
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literal_vector lits;
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lits.push_back(l);
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DEBUG("assert_macro_axiom: " << pp_lits(ctx, lits.size(), lits.c_ptr()));
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ctx.mk_th_axiom(get_id(), lits.size(), lits.c_ptr());
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}
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void theory_recfun::assert_case_axioms(case_expansion & e) {
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DEBUG("assert_case_axioms "<< pp_case_expansion(e,m())
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<< " with " << e.m_def->get_cases().size() << " cases");
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SASSERT(e.m_def->is_fun_defined());
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context & ctx = get_context();
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// add case-axioms for all case-paths
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auto & vars = e.m_def->get_vars();
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for (recfun::case_def const & c : e.m_def->get_cases()) {
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// applied predicate to `args`
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app_ref pred_applied = apply_pred(c.get_pred(), e.m_args);
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SASSERT(u().owns_app(pred_applied));
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// substitute arguments in `path`
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expr_ref_vector path(m());
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for (auto & g : c.get_guards()) {
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expr_ref g_applied = apply_args(vars, e.m_args, g);
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path.push_back(g_applied);
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}
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// assert `p(args) <=> And(guards)` (with CNF on the fly)
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ctx.internalize(pred_applied, false);
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ctx.mark_as_relevant(ctx.get_bool_var(pred_applied));
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literal concl = ctx.get_literal(pred_applied);
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{
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// assert `guards=>p(args)`
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literal_vector c;
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c.push_back(concl);
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for (expr* g : path) {
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ctx.internalize(g, false);
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c.push_back(~ ctx.get_literal(g));
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}
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//TRACE("recfun", tout << "assert_case_axioms " << pp_case_expansion(e)
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// << " axiom " << mk_pp(*l) <<"\n";);
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DEBUG("assert_case_axiom " << pp_lits(get_context(), path.size()+1, c.c_ptr()));
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get_context().mk_th_axiom(get_id(), path.size()+1, c.c_ptr());
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}
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{
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// assert `p(args) => guards[i]` for each `i`
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for (expr * _g : path) {
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SASSERT(ctx.b_internalized(_g));
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literal g = ctx.get_literal(_g);
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literal c[2] = {~ concl, g};
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DEBUG("assert_case_axiom " << pp_lits(get_context(), 2, c));
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get_context().mk_th_axiom(get_id(), 2, c);
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}
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}
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// also body-expand paths that do not depend on any defined fun
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if (c.is_immediate()) {
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body_expansion be(c, e.m_args);
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assert_body_axiom(be);
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}
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}
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}
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void theory_recfun::assert_body_axiom(body_expansion & e) {
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DEBUG("assert_body_axioms "<< pp_body_expansion(e,m()));
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context & ctx = get_context();
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recfun::def & d = *e.m_cdef->get_def();
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auto & vars = d.get_vars();
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auto & args = e.m_args;
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// check that var order is standard
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SASSERT(vars.size() == 0 || vars[vars.size()-1]->get_idx() == 0);
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expr_ref lhs(u().mk_fun_defined(d, args), m());
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// substitute `e.args` into the RHS of this particular case
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expr_ref rhs = apply_args(vars, args, e.m_cdef->get_rhs());
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// substitute `e.args` into the guard of this particular case, to make
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// the `condition` part of the clause `conds => lhs=rhs`
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expr_ref_vector guards(m());
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for (auto & g : e.m_cdef->get_guards()) {
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expr_ref new_guard = apply_args(vars, args, g);
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guards.push_back(new_guard);
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}
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// now build the axiom `conds => lhs = rhs`
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ctx.internalize(rhs, false);
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for (auto& g : guards) ctx.internalize(g, false);
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// add unit clause `conds => lhs=rhs`
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literal_vector clause;
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for (auto& g : guards) {
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ctx.internalize(g, false);
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literal l = ~ ctx.get_literal(g);
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ctx.mark_as_relevant(l);
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clause.push_back(l);
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}
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literal l(mk_eq(lhs, rhs, true));
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ctx.mark_as_relevant(l);
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clause.push_back(l);
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DEBUG("assert_body_axiom " << pp_lits(ctx, clause.size(), clause.c_ptr()));
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ctx.mk_th_axiom(get_id(), clause.size(), clause.c_ptr());
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}
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final_check_status theory_recfun::final_check_eh() {
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return FC_DONE;
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}
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void theory_recfun::add_theory_assumptions(expr_ref_vector & assumptions) {
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app_ref dlimit = m_util.mk_depth_limit_pred(get_max_depth());
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DEBUG("add_theory_assumption " << mk_pp(dlimit.get(), m()));
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assumptions.push_back(dlimit);
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}
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// if `dlimit` occurs in unsat core, return "unknown"
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lbool theory_recfun::validate_unsat_core(expr_ref_vector & unsat_core) {
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for (auto & e : unsat_core) {
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if (is_app(e) && m_util.is_depth_limit(to_app(e)))
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return l_undef;
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}
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return l_false;
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}
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void theory_recfun::display(std::ostream & out) const {
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out << "recfun{}";
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}
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void theory_recfun::collect_statistics(::statistics & st) const {
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st.update("recfun macro expansion", m_stats.m_macro_expansions);
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st.update("recfun case expansion", m_stats.m_case_expansions);
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st.update("recfun body expansion", m_stats.m_body_expansions);
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}
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#ifdef Z3DEBUG
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std::ostream& operator<<(std::ostream & out, theory_recfun::pp_case_expansion const & e) {
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return out << "case_exp(" << mk_pp(e.e.m_lhs, e.m) << ")";
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}
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std::ostream& operator<<(std::ostream & out, theory_recfun::pp_body_expansion const & e) {
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out << "body_exp(" << e.e.m_cdef->get_name();
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for (auto* t : e.e.m_args) {
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out << " " << mk_pp(t,e.m);
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}
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return out << ")";
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}
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#endif
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}
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