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Add special_relations_simplifier: new simplifier and tactic registration

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Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
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copilot-swe-agent[bot] 2026-03-12 04:39:05 +00:00
parent 7a00cb4e01
commit fb31b689ea
3 changed files with 209 additions and 0 deletions
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1
src/ast/simplifiers/CMakeLists.txt
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@ -43,4 +43,5 @@ z3_add_component(simplifiers
randomizer.h
refine_inj_axiom.h
rewriter_simplifier.h
special_relations_simplifier.h
)

198
src/ast/simplifiers/special_relations_simplifier.h Normal file
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@ -0,0 +1,198 @@
/*++
Copyright (c) 2019 Microsoft Corporation
Module Name:
special_relations_simplifier.h
Abstract:
Detect special relations in an axiomatization,
rewrite goal using special relations.
Author:
Nikolaj Bjorner (nbjorner) 2019-03-28
Notes:
--*/
#pragma once
#include "ast/simplifiers/dependent_expr_state.h"
#include "ast/special_relations_decl_plugin.h"
#include "ast/pattern/expr_pattern_match.h"
#include "ast/rewriter/func_decl_replace.h"
#include "ast/ast_util.h"
class special_relations_simplifier : public dependent_expr_simplifier {
expr_pattern_match m_pm;
svector<sr_property> m_properties;
struct sp_axioms {
unsigned_vector m_formula_indices;
sr_property m_sp_features;
sp_axioms() : m_sp_features(sr_none) {}
};
obj_map<func_decl, sp_axioms> m_detected_relations;
void initialize() {
if (!m_properties.empty()) return;
sort_ref A(m.mk_uninterpreted_sort(symbol("A")), m);
func_decl_ref R(m.mk_func_decl(symbol("?R"), A, A, m.mk_bool_sort()), m);
var_ref x(m.mk_var(0, A), m);
var_ref y(m.mk_var(1, A), m);
var_ref z(m.mk_var(2, A), m);
expr* _x = x, *_y = y, *_z = z;
expr_ref Rxy(m.mk_app(R, _x, _y), m);
expr_ref Ryz(m.mk_app(R, _y, _z), m);
expr_ref Rxz(m.mk_app(R, _x, _z), m);
expr_ref Rxx(m.mk_app(R, _x, _x), m);
expr_ref Ryx(m.mk_app(R, _y, _x), m);
expr_ref Rzy(m.mk_app(R, _z, _y), m);
expr_ref Rzx(m.mk_app(R, _z, _x), m);
expr_ref nRxy(m.mk_not(Rxy), m);
expr_ref nRyx(m.mk_not(Ryx), m);
expr_ref nRzx(m.mk_not(Rzx), m);
expr_ref nRxz(m.mk_not(Rxz), m);
sort* As[3] = { A, A, A };
symbol xyz[3] = { symbol("x"), symbol("y"), symbol("z") };
expr_ref fml(m);
quantifier_ref q(m);
expr_ref pat(m.mk_pattern(to_app(Rxy)), m);
expr_ref pat0(m.mk_pattern(to_app(Rxx)), m);
expr* pats[1] = { pat };
expr* pats0[1] = { pat0 };
fml = m.mk_or(m.mk_not(Rxy), m.mk_not(Ryz), Rxz);
q = m.mk_forall(3, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_transitive);
fml = m.mk_or(mk_not(Rxy & Ryz), Rxz);
q = m.mk_forall(3, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_transitive);
fml = Rxx;
q = m.mk_forall(1, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats0);
register_pattern(m_pm.initialize(q), sr_reflexive);
fml = m.mk_or(nRxy, nRyx, m.mk_eq(x, y));
q = m.mk_forall(2, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_antisymmetric);
fml = m.mk_or(mk_not(Rxy & Ryx), m.mk_eq(x, y));
q = m.mk_forall(2, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_antisymmetric);
fml = m.mk_or(nRyx, nRzx, Ryz, Rzy);
q = m.mk_forall(3, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_lefttree);
fml = m.mk_or(mk_not(Ryx & Rzx), Ryz, Rzy);
q = m.mk_forall(3, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_lefttree);
fml = m.mk_or(nRxy, nRxz, Ryz, Rzy);
q = m.mk_forall(3, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_righttree);
fml = m.mk_or(mk_not(Rxy & Rxz), Ryz, Rzy);
q = m.mk_forall(3, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_righttree);
fml = m.mk_or(Rxy, Ryx);
q = m.mk_forall(2, As, xyz, fml, 0, symbol::null, symbol::null, 1, pats);
register_pattern(m_pm.initialize(q), sr_total);
TRACE(special_relations, m_pm.display(tout););
}
void register_pattern(unsigned index, sr_property p) {
SASSERT(index == m_properties.size());
m_properties.push_back(p);
}
void insert(func_decl* f, unsigned idx, sr_property p) {
sp_axioms ax;
m_detected_relations.find(f, ax);
ax.m_formula_indices.push_back(idx);
ax.m_sp_features = (sr_property)(p | ax.m_sp_features);
m_detected_relations.insert(f, ax);
}
void collect_feature(unsigned idx, expr* f) {
if (!is_quantifier(f)) return;
unsigned index = 0;
app_ref_vector patterns(m);
bool is_match = m_pm.match_quantifier_index(to_quantifier(f), patterns, index);
TRACE(special_relations, tout << "check " << is_match << " " << mk_pp(f, m) << "\n";
if (is_match) tout << patterns << " " << index << "\n";);
if (is_match) {
func_decl* p = to_app(patterns.get(0)->get_arg(0))->get_decl();
insert(p, idx, m_properties[index]);
}
}
public:
special_relations_simplifier(ast_manager& m, params_ref const& p, dependent_expr_state& s)
: dependent_expr_simplifier(m, s), m_pm(m) {}
char const* name() const override { return "special-relations"; }
void reduce() override {
initialize();
m_detected_relations.reset();
// Phase 1: scan all formulas to detect special relation axioms
for (unsigned idx : indices())
collect_feature(idx, m_fmls[idx].fml());
if (m_detected_relations.empty())
return;
// Phase 2: for each detected relation, create a special relation declaration
special_relations_util u(m);
func_decl_replace replace(m);
unsigned_vector to_delete;
for (auto const& kv : m_detected_relations) {
sr_property feature = kv.m_value.m_sp_features;
switch (feature) {
case sr_po:
replace.insert(kv.m_key, u.mk_po_decl(kv.m_key));
to_delete.append(kv.m_value.m_formula_indices);
break;
case sr_to:
replace.insert(kv.m_key, u.mk_to_decl(kv.m_key));
to_delete.append(kv.m_value.m_formula_indices);
break;
case sr_plo:
replace.insert(kv.m_key, u.mk_plo_decl(kv.m_key));
to_delete.append(kv.m_value.m_formula_indices);
break;
case sr_lo:
replace.insert(kv.m_key, u.mk_lo_decl(kv.m_key));
to_delete.append(kv.m_value.m_formula_indices);
break;
default:
TRACE(special_relations, tout << "unprocessed feature " << feature << "\n";);
break;
}
}
if (replace.empty())
return;
// Phase 3: replace function declarations across all formulas
for (unsigned idx : indices()) {
auto const& d = m_fmls[idx];
if (to_delete.contains(idx)) {
m_fmls.update(idx, dependent_expr(m, m.mk_true(), nullptr, d.dep()));
}
else {
expr_ref new_fml = replace(d.fml());
if (new_fml != d.fml())
m_fmls.update(idx, dependent_expr(m, new_fml, nullptr, d.dep()));
}
}
}
};

10
src/tactic/core/special_relations_tactic.h
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@ -21,8 +21,10 @@ Notes:
#include "tactic/tactic.h"
#include "tactic/tactical.h"
#include "tactic/dependent_expr_state_tactic.h"
#include "ast/special_relations_decl_plugin.h"
#include "ast/pattern/expr_pattern_match.h"
#include "ast/simplifiers/special_relations_simplifier.h"
class special_relations_tactic : public tactic {
ast_manager& m;
@ -63,8 +65,16 @@ public:
tactic * mk_special_relations_tactic(ast_manager & m, params_ref const & p = params_ref());
inline tactic* mk_special_relations2_tactic(ast_manager& m, params_ref const& p = params_ref()) {
return alloc(dependent_expr_state_tactic, m, p,
[](auto& m, auto& p, auto& s) -> dependent_expr_simplifier* {
return alloc(special_relations_simplifier, m, p, s);
});
}
/*
ADD_TACTIC("special-relations", "detect and replace by special relations.", "mk_special_relations_tactic(m, p)")
ADD_TACTIC("special-relations2", "detect and replace by special relations.", "mk_special_relations2_tactic(m, p)")
ADD_SIMPLIFIER("special-relations", "detect and replace by special relations.", "alloc(special_relations_simplifier, m, p, s)")
*/