static bool has_free_var_in_domain(expr const & b, unsigned vidx, bool strict) { if (is_pi(b)) { return (has_free_var(binding_domain(b), vidx) && is_explicit(binding_info(b))) || has_free_var_in_domain(binding_body(b), vidx+1, strict); } else if (!strict) { return has_free_var(b, vidx); } else { return false; } }
bool is_arrow(expr const & t) { optional<bool> r = t.raw()->is_arrow(); if (r) { return *r; } else { bool res = is_pi(t) && !has_free_var(binding_body(t), 0); t.raw()->set_is_arrow(res); return res; } }
bool is_arrow(expr const & t) { return is_pi(t) && !has_free_var(abst_body(t), 0); }
/** \brief Create a "choice" constraint that postpones the resolution of a calc proof step. By delaying it, we can perform quick fixes such as: - adding symmetry - adding ! - adding subst */ constraint mk_calc_proof_cnstr(environment const & env, options const & opts, old_local_context const & _ctx, expr const & m, expr const & _e, constraint_seq const & cs, unifier_config const & cfg, info_manager * im, update_type_info_fn const & fn) { justification j = mk_failed_to_synthesize_jst(env, m); auto choice_fn = [=](expr const & meta, expr const & _meta_type, substitution const & _s) { old_local_context ctx = _ctx; expr e = _e; substitution s = _s; expr meta_type = _meta_type; type_checker_ptr tc = mk_type_checker(env); constraint_seq new_cs = cs; expr e_type = tc->infer(e, new_cs); e_type = s.instantiate(e_type); tag g = e.get_tag(); bool calc_assistant = get_elaborator_calc_assistant(opts); if (calc_assistant) { // add '!' is needed while (is_norm_pi(*tc, e_type, new_cs)) { binder_info bi = binding_info(e_type); if (!bi.is_implicit() && !bi.is_inst_implicit()) { if (!has_free_var(binding_body(e_type), 0)) { // if the rest of the type does not reference argument, // then we also stop consuming arguments break; } } expr imp_arg = ctx.mk_meta(some_expr(binding_domain(e_type)), g); e = mk_app(e, imp_arg, g); e_type = instantiate(binding_body(e_type), imp_arg); } if (im) fn(e); } e_type = head_beta_reduce(e_type); expr const & meta_type_fn = get_app_fn(meta_type); expr const & e_type_fn = get_app_fn(e_type); if (is_constant(meta_type_fn) && (!is_constant(e_type_fn) || const_name(e_type_fn) != const_name(meta_type_fn))) { // try to make sure meta_type and e_type have the same head symbol if (!try_normalize_to_head(env, const_name(meta_type_fn), e_type, new_cs) && is_constant(e_type_fn)) { try_normalize_to_head(env, const_name(e_type_fn), meta_type, new_cs); } } auto try_alternative = [&](expr const & e, expr const & e_type, constraint_seq fcs, bool conservative) { justification new_j = mk_type_mismatch_jst(e, e_type, meta_type); if (!tc->is_def_eq(e_type, meta_type, new_j, fcs)) throw unifier_exception(new_j, s); buffer<constraint> cs_buffer; fcs.linearize(cs_buffer); metavar_closure cls(meta); cls.add(meta_type); cls.mk_constraints(s, j, cs_buffer); unifier_config new_cfg(cfg); new_cfg.m_discard = false; new_cfg.m_kind = conservative ? unifier_kind::Conservative : unifier_kind::Liberal; unify_result_seq seq = unify(env, cs_buffer.size(), cs_buffer.data(), substitution(), new_cfg); auto p = seq.pull(); lean_assert(p); substitution new_s = p->first.first; constraints postponed = map(p->first.second, [&](constraint const & c) { // we erase internal justifications return update_justification(c, j); }); expr new_e = new_s.instantiate(e); if (conservative && has_expr_metavar_relaxed(new_s.instantiate_all(e))) throw_elaborator_exception("solution contains metavariables", e); if (im) im->instantiate(new_s); constraints r = cls.mk_constraints(new_s, j); buffer<expr> locals; expr mvar = get_app_args(meta, locals); expr val = Fun(locals, new_e); r = cons(mk_eq_cnstr(mvar, val, j), r); return append(r, postponed); }; if (!get_elaborator_calc_assistant(opts)) { bool conservative = false; return try_alternative(e, e_type, new_cs, conservative); } else { // TODO(Leo): after we have the simplifier and rewriter tactic, we should revise // this code. It is "abusing" the higher-order unifier. { // Try the following possible intrepretations using a "conservative" unification procedure. // That is, we only unfold definitions marked as reducible. // Assume pr is the proof provided. // 1. pr bool conservative = true; try { return try_alternative(e, e_type, new_cs, conservative); } catch (exception & ex) {} // 2. eq.symm pr constraint_seq symm_cs = new_cs; auto symm = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g); if (symm) { try { return try_alternative(symm->first, symm->second, symm_cs, conservative); } catch (exception &) {} } // 3. subst pr (eq.refl lhs) constraint_seq subst_cs = new_cs; if (auto subst = apply_subst(env, ctx, tc, e, e_type, meta_type, subst_cs, g)) { try { return try_alternative(subst->first, subst->second, subst_cs, conservative); } catch (exception&) {} } // 4. subst (eq.symm pr) (eq.refl lhs) if (symm) { constraint_seq subst_cs = symm_cs; if (auto subst = apply_subst(env, ctx, tc, symm->first, symm->second, meta_type, subst_cs, g)) { try { return try_alternative(subst->first, subst->second, subst_cs, conservative); } catch (exception&) {} } } } { // Try the following possible insterpretations using the default unification procedure. // 1. pr bool conservative = false; std::unique_ptr<throwable> saved_ex; try { return try_alternative(e, e_type, new_cs, conservative); } catch (exception & ex) { saved_ex.reset(ex.clone()); } // 2. eq.symm pr constraint_seq symm_cs = new_cs; auto symm = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g); if (symm) { try { return try_alternative(symm->first, symm->second, symm_cs, conservative); } catch (exception &) {} } // We use the exception for the first alternative as the error message saved_ex->rethrow(); lean_unreachable(); } } }; bool owner = false; return mk_choice_cnstr(m, choice_fn, to_delay_factor(cnstr_group::Epilogue), owner, j); }