Source

z3 / src / tactic / core / reduce_args_tactic.cpp

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
/*++
Copyright (c) 2012 Microsoft Corporation

Module Name:

    reduce_args_tactic.cpp

Abstract:

    Reduce the number of arguments in function applications.

Author:

    Leonardo (leonardo) 2012-02-19

Notes:

--*/
#include"tactical.h"
#include"cooperate.h"
#include"ast_smt2_pp.h"
#include"map.h"
#include"rewriter_def.h"
#include"extension_model_converter.h"
#include"filter_model_converter.h"

/**
   \brief Reduce the number of arguments in function applications.

   Example, suppose we have a function f with 2 arguments. 
   There are 1000 applications of this function, but the first argument is always "a", "b" or "c".
   Thus, we replace the f(t1, t2)
   with 
      f_a(t2)   if   t1 = a
      f_b(t2)   if   t2 = b
      f_c(t2)   if   t2 = c

   Since f_a, f_b, f_c are new symbols, satisfiability is preserved.
   
   This transformation is very similar in spirit to the Ackermman's reduction. 

   This transformation should work in the following way:

   1- Create a mapping decl2arg_map from declarations to tuples of booleans, an entry [f -> (true, false, true)]
       means that f is a declaration with 3 arguments where the first and third arguments are always values.
   2- Traverse the formula and populate the mapping. 
        For each function application f(t1, ..., tn) do
          a) Create a boolean tuple (is_value(t1), ..., is_value(tn)) and do
             the logical-and with the tuple that is already in the mapping. If there is no such tuple
             in the mapping, we just add a new entry.

   If all entries are false-tuples, then there is nothing to be done. The transformation is not applicable.

   Now, we create a mapping decl2new_decl from (decl, val_1, ..., val_n) to decls. Note that, n may be different for each entry,
   but it is the same for the same declaration.
   For example, suppose we have [f -> (true, false, true)] in decl2arg_map, and applications f(1, a, 2), f(1, b, 2), f(1, b, 3), f(2, b, 3), f(2, c, 3) in the formula.
   Then, decl2arg_map would contain
        (f, 1, 2) -> f_1_2
        (f, 1, 3) -> f_1_3
        (f, 2, 3) -> f_2_3
   where f_1_2, f_1_3 and f_2_3 are new function symbols.
   Using the new map, we can replace the occurrences of f.
*/
class reduce_args_tactic : public tactic {
    struct     imp;
    imp *      m_imp;
public:
    reduce_args_tactic(ast_manager & m);

    virtual tactic * translate(ast_manager & m) {
        return alloc(reduce_args_tactic, m);
    }

    virtual ~reduce_args_tactic();
    
    virtual void operator()(goal_ref const & g, goal_ref_buffer & result, model_converter_ref & mc, proof_converter_ref & pc, expr_dependency_ref & core);
    virtual void cleanup();
    virtual void set_cancel(bool f);
};

tactic * mk_reduce_args_tactic(ast_manager & m, params_ref const & p) {
    return clean(alloc(reduce_args_tactic, m));
}

struct reduce_args_tactic::imp {
    ast_manager &            m_manager;
    bool                     m_produce_models;
    volatile bool            m_cancel;

    ast_manager & m() const { return m_manager; }
    
    imp(ast_manager & m):
        m_manager(m) {
        m_cancel = false;
    }

    void set_cancel(bool f) {
        m_cancel = f;
    }

    void checkpoint() { 
        if (m_cancel)
            throw tactic_exception(TACTIC_CANCELED_MSG);
        cooperate("reduce-args");
    }
    
    struct find_non_candidates_proc {
        ast_manager &              m_manager;
        obj_hashtable<func_decl> & m_non_cadidates;
        
        find_non_candidates_proc(ast_manager & m, obj_hashtable<func_decl> & non_cadidates):
            m_manager(m),
            m_non_cadidates(non_cadidates) {
        }
        
        void operator()(var * n) {}
        
        void operator()(quantifier * n) {}
        
        void operator()(app * n) {
            if (n->get_num_args() == 0)
                return; // ignore constants
            func_decl * d = n->get_decl();
            if (d->get_family_id() != null_family_id)
                return; // ignore interpreted symbols
            if (m_non_cadidates.contains(d))
                return; // it is already in the set.
            unsigned j    = n->get_num_args();        
            while (j > 0) {
                --j;
                if (m_manager.is_value(n->get_arg(j)))
                    return;
            }  
            m_non_cadidates.insert(d);
        }
    };

    /**
       \brief Populate the table non_cadidates with function declarations \c f
       such that there is a function application (f t1 ... tn) where t1 ... tn are not values.
    */
    void find_non_candidates(goal const & g, obj_hashtable<func_decl> & non_candidates) {
        non_candidates.reset();
        find_non_candidates_proc proc(m_manager, non_candidates);
        expr_fast_mark1 visited;
        unsigned sz = g.size();
        for (unsigned i = 0; i < sz; i++) {
            checkpoint();
            quick_for_each_expr(proc, visited, g.form(i));
        }
        
        TRACE("reduce_args", tout << "non_candidates:\n";
              obj_hashtable<func_decl>::iterator it  = non_candidates.begin();
              obj_hashtable<func_decl>::iterator end = non_candidates.end();
              for (; it != end; ++it) {
                  func_decl * d = *it;
                  tout << d->get_name() << "\n";
              });
    }

    struct populate_decl2args_proc {
        ast_manager &                     m_manager;
        obj_hashtable<func_decl> &        m_non_cadidates;
        obj_map<func_decl, bit_vector> &  m_decl2args;    
        
        populate_decl2args_proc(ast_manager & m, obj_hashtable<func_decl> & nc, obj_map<func_decl, bit_vector> & d):
            m_manager(m), m_non_cadidates(nc), m_decl2args(d) {}
        
        void operator()(var * n) {}
        void operator()(quantifier * n) {}
        void operator()(app * n) {
            if (n->get_num_args() == 0)
                return; // ignore constants
            func_decl * d = n->get_decl();
            if (d->get_family_id() != null_family_id)
                return; // ignore interpreted symbols
            if (m_non_cadidates.contains(d))
                return; // declaration is not a candidate
            unsigned j = n->get_num_args();
            obj_map<func_decl, bit_vector>::iterator it = m_decl2args.find_iterator(d);
            if (it == m_decl2args.end()) {
                m_decl2args.insert(d, bit_vector());
                it = m_decl2args.find_iterator(d);
                SASSERT(it != m_decl2args.end());
                it->m_value.reserve(j);
                while (j > 0) {
                    --j;
                    it->m_value.set(j, m_manager.is_value(n->get_arg(j)));
                }
            } else {
                SASSERT(j == it->m_value.size());                        
                while (j > 0) {
                    --j;
                    it->m_value.set(j, it->m_value.get(j) && m_manager.is_value(n->get_arg(j)));
                }
            }
        }
    };

    void populate_decl2args(goal const & g, 
                            obj_hashtable<func_decl> & non_candidates, 
                            obj_map<func_decl, bit_vector> & decl2args) {
        expr_fast_mark1 visited;
        decl2args.reset();
        populate_decl2args_proc proc(m_manager, non_candidates, decl2args);
        unsigned sz = g.size();
        for (unsigned i = 0; i < sz; i++) {
            checkpoint();
            quick_for_each_expr(proc, visited, g.form(i));
        }
        
        // Remove all cases where the simplification is not applicable.
        ptr_buffer<func_decl> bad_decls;
        obj_map<func_decl, bit_vector>::iterator it  = decl2args.begin();
        obj_map<func_decl, bit_vector>::iterator end = decl2args.end();
        for (; it != end; it++) {
            bool is_zero = true;
            for (unsigned i = 0; i < it->m_value.size() && is_zero ; i++) {
                if (it->m_value.get(i)) 
                    is_zero = false;
            }
            if (is_zero) 
                bad_decls.push_back(it->m_key);
        }
    
        ptr_buffer<func_decl>::iterator it2  = bad_decls.begin();
        ptr_buffer<func_decl>::iterator end2 = bad_decls.end();
        for (; it2 != end2; ++it2)
            decl2args.erase(*it2);

        TRACE("reduce_args", tout << "decl2args:" << std::endl;
              for (obj_map<func_decl, bit_vector>::iterator it = decl2args.begin() ; it != decl2args.end() ; it++) {
                  tout << it->m_key->get_name() << ": ";
                  for (unsigned i = 0 ; i < it->m_value.size() ; i++)
                      tout << (it->m_value.get(i) ? "1" : "0");                            
                  tout << std::endl;
              });
    }

    struct arg2func_hash_proc {
        bit_vector const & m_bv;
        
        arg2func_hash_proc(bit_vector const & bv):m_bv(bv) {}
        unsigned operator()(app const * n) const {
            // compute the hash-code using only the arguments where m_bv is true.
            unsigned a = 0x9e3779b9;
            unsigned num_args = n->get_num_args();
            for (unsigned i = 0; i < num_args; i++) {
                if (!m_bv.get(i)) 
                    continue; // ignore argument
                a = hash_u_u(a, n->get_arg(i)->get_id());
            }
            return a;
        }
    };
     
    struct arg2func_eq_proc {
        bit_vector const & m_bv;
     
        arg2func_eq_proc(bit_vector const & bv):m_bv(bv) {}
        bool operator()(app const * n1, app const * n2) const {
            // compare only the arguments where m_bv is true
            SASSERT(n1->get_num_args() == n2->get_num_args());
            unsigned num_args = n1->get_num_args();
            for (unsigned i = 0; i < num_args; i++) {
                if (!m_bv.get(i)) 
                    continue; // ignore argument
                if (n1->get_arg(i) != n2->get_arg(i))
                    return false;
            }
            return true;
        }
    };

    typedef map<app *, func_decl *, arg2func_hash_proc, arg2func_eq_proc> arg2func;
    typedef obj_map<func_decl, arg2func *> decl2arg2func_map;

    struct reduce_args_ctx { 
        ast_manager &           m_manager;
        decl2arg2func_map       m_decl2arg2funcs;

        reduce_args_ctx(ast_manager & m): m_manager(m) {
        }
        
        ~reduce_args_ctx() {
            obj_map<func_decl, arg2func *>::iterator it  = m_decl2arg2funcs.begin();
            obj_map<func_decl, arg2func *>::iterator end = m_decl2arg2funcs.end();
            for (; it != end; ++it) {
                arg2func * map = it->m_value;
                arg2func::iterator it2  = map->begin();
                arg2func::iterator end2 = map->end();
                for (; it2 != end2; ++it2) {
                    m_manager.dec_ref(it2->m_key);
                    m_manager.dec_ref(it2->m_value);
                }
                dealloc(map);
            }
        }
    };

    struct populate_decl2arg_set_proc {
        ast_manager &                          m_manager;
        obj_map<func_decl, bit_vector> &       m_decl2args;
        decl2arg2func_map &                    m_decl2arg2funcs;
    
        populate_decl2arg_set_proc(ast_manager & m, 
                                   obj_map<func_decl, bit_vector> & d,
                                   decl2arg2func_map & ds):
            m_manager(m), m_decl2args(d), m_decl2arg2funcs(ds) {}

        void operator()(var * n) {}
        void operator()(quantifier * n) {}

        void operator()(app * n) {
            if (n->get_num_args() == 0)
                return; // ignore constants
            func_decl * d = n->get_decl();
            if (d->get_family_id() != null_family_id)
                return; // ignore interpreted symbols
            obj_map<func_decl, bit_vector>::iterator it = m_decl2args.find_iterator(d);
            if (it == m_decl2args.end())
                return; // not reducing the arguments of this declaration
            bit_vector & bv = it->m_value;
            arg2func * map = 0;
            decl2arg2func_map::iterator it2 = m_decl2arg2funcs.find_iterator(d);
            if (it2 == m_decl2arg2funcs.end()) {
                map = alloc(arg2func, arg2func_hash_proc(bv), arg2func_eq_proc(bv));
                m_decl2arg2funcs.insert(d, map);
            }
            else {
                map = it2->m_value;
            }
            if (!map->contains(n)) {
                // create fresh symbol...
                ptr_buffer<sort> domain;
                unsigned arity = d->get_arity();
                for (unsigned i = 0; i < arity; i++) {
                    if (!bv.get(i))
                        domain.push_back(d->get_domain(i));
                }
                func_decl * new_d = m_manager.mk_fresh_func_decl(d->get_name(), symbol::null, domain.size(), domain.c_ptr(), d->get_range());
                map->insert(n, new_d);
                m_manager.inc_ref(n);
                m_manager.inc_ref(new_d);
            }
        }    
    };
    
    void populate_decl2arg_set(goal const & g, 
                               obj_map<func_decl, bit_vector> & decl2args,
                               decl2arg2func_map & decl2arg2funcs) {
        expr_fast_mark1 visited;
    
        populate_decl2arg_set_proc proc(m_manager, decl2args, decl2arg2funcs);
        unsigned sz = g.size();
        for (unsigned i = 0; i < sz; i++) {
            checkpoint();
            quick_for_each_expr(proc, visited, g.form(i));
        }
    }
    
    struct reduce_args_rw_cfg : public default_rewriter_cfg {
        ast_manager &                    m;
        imp &                            m_owner;
        obj_map<func_decl, bit_vector> & m_decl2args;
        decl2arg2func_map &              m_decl2arg2funcs;
        
        reduce_args_rw_cfg(imp & owner, obj_map<func_decl, bit_vector> & decl2args, decl2arg2func_map & decl2arg2funcs):
            m(owner.m_manager),
            m_owner(owner),
            m_decl2args(decl2args),
            m_decl2arg2funcs(decl2arg2funcs) {
        }

        bool max_steps_exceeded(unsigned num_steps) const { 
            m_owner.checkpoint();
            return false;
        }
        
        br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, proof_ref & result_pr) {
            result_pr = 0;
            if (f->get_arity() == 0)
                return BR_FAILED; // ignore constants
            if (f->get_family_id() != null_family_id)
                return BR_FAILED; // ignore interpreted symbols
            decl2arg2func_map::iterator it  = m_decl2arg2funcs.find_iterator(f);
            if (it == m_decl2arg2funcs.end())
                return BR_FAILED;
            SASSERT(m_decl2args.contains(f));
            bit_vector & bv = m_decl2args.find(f);
            arg2func * map  = it->m_value;
            app_ref tmp(m);
            tmp = m.mk_app(f, num, args);
            CTRACE("reduce_args", !map->contains(tmp),
                   tout << "map does not contain tmp f: " << f->get_name() << "\n";
                   tout << mk_ismt2_pp(tmp, m) << "\n";
                   arg2func::iterator it  = map->begin();
                   arg2func::iterator end = map->end();
                   for (; it != end; ++it) {
                       tout << mk_ismt2_pp(it->m_key, m) << "\n---> " << it->m_value->get_name() << "\n";
                   });
            SASSERT(map->contains(tmp));
            func_decl * new_f = map->find(tmp);
            ptr_buffer<expr> new_args;
            for (unsigned i = 0; i < num; i++) {
                if (!bv.get(i))
                    new_args.push_back(args[i]);
            }
            result = m.mk_app(new_f, new_args.size(), new_args.c_ptr());
            return BR_DONE;
        }
    };

    struct reduce_args_rw : rewriter_tpl<reduce_args_rw_cfg> {
        reduce_args_rw_cfg m_cfg;
    public:
        reduce_args_rw(imp & owner, obj_map<func_decl, bit_vector> & decl2args, decl2arg2func_map & decl2arg2funcs):
            rewriter_tpl<reduce_args_rw_cfg>(owner.m_manager, false, m_cfg),
            m_cfg(owner, decl2args, decl2arg2funcs) {
        }
    };

    model_converter * mk_mc(obj_map<func_decl, bit_vector> & decl2args, decl2arg2func_map & decl2arg2funcs) {
        ptr_buffer<expr> new_args;
        var_ref_vector   new_vars(m_manager);
        ptr_buffer<expr> new_eqs;
        extension_model_converter * e_mc = alloc(extension_model_converter, m_manager);
        filter_model_converter * f_mc    = alloc(filter_model_converter, m_manager);
        decl2arg2func_map::iterator it   = decl2arg2funcs.begin();
        decl2arg2func_map::iterator end  = decl2arg2funcs.end();
        for (; it != end; ++it) {
            func_decl * f  = it->m_key;
            arg2func * map = it->m_value;
            expr * def     = 0;
            SASSERT(decl2args.contains(f));
            bit_vector & bv = decl2args.find(f);
            new_vars.reset();
            new_args.reset();
            for (unsigned i = 0; i < f->get_arity(); i++) {
                new_vars.push_back(m_manager.mk_var(i, f->get_domain(i)));
                if (!bv.get(i))
                    new_args.push_back(new_vars.back());
            }
            arg2func::iterator it2  = map->begin();
            arg2func::iterator end2 = map->end();
            for (; it2 != end2; ++it2) {
                app * t = it2->m_key;
                func_decl * new_def = it2->m_value;
                f_mc->insert(new_def);
                SASSERT(new_def->get_arity() == new_args.size());
                app * new_t = m_manager.mk_app(new_def, new_args.size(), new_args.c_ptr());
                if (def == 0) {
                    def = new_t;
                }
                else {
                    new_eqs.reset();
                    for (unsigned i = 0; i < f->get_arity(); i++) {
                        if (bv.get(i))
                            new_eqs.push_back(m_manager.mk_eq(new_vars.get(i), t->get_arg(i)));
                    }
                    SASSERT(new_eqs.size() > 0);
                    expr * cond;
                    if (new_eqs.size() == 1)
                        cond = new_eqs[0];
                    else
                        cond = m_manager.mk_and(new_eqs.size(), new_eqs.c_ptr());
                    def = m_manager.mk_ite(cond, new_t, def);
                }
            }
            SASSERT(def);
            e_mc->insert(f, def);
        }
        return concat(f_mc, e_mc);
    }

    void operator()(goal & g, model_converter_ref & mc) {
        if (g.inconsistent())
            return;
        m_produce_models = g.models_enabled();
        TRACE("reduce_args", g.display(tout););
        tactic_report report("reduce-args", g);
        obj_hashtable<func_decl> non_candidates;
        obj_map<func_decl, bit_vector> decl2args;
        find_non_candidates(g, non_candidates);
        populate_decl2args(g, non_candidates, decl2args);
        
        if (decl2args.empty())
            return;
        
        ptr_vector<arg2func> arg2funcs;
        reduce_args_ctx ctx(m_manager);
        populate_decl2arg_set(g, decl2args, ctx.m_decl2arg2funcs);
    
        reduce_args_rw rw(*this, decl2args, ctx.m_decl2arg2funcs);
        
        unsigned sz = g.size();
        for (unsigned i = 0; i < sz; i++) {
            if (g.inconsistent())
                break;
            expr * f = g.form(i);
            expr_ref new_f(m_manager);
            rw(f, new_f);
            g.update(i, new_f);
        }

        report_tactic_progress(":reduced-funcs", decl2args.size());

        if (m_produce_models)
            mc = mk_mc(decl2args, ctx.m_decl2arg2funcs);

        TRACE("reduce_args", g.display(tout); if (mc) mc->display(tout););
    }
};

reduce_args_tactic::reduce_args_tactic(ast_manager & m) {
    m_imp = alloc(imp, m);
}

reduce_args_tactic::~reduce_args_tactic() {
    dealloc(m_imp);
}

void reduce_args_tactic::operator()(goal_ref const & g, 
                                    goal_ref_buffer & result, 
                                    model_converter_ref & mc, 
                                    proof_converter_ref & pc,
                                    expr_dependency_ref & core) {
    SASSERT(g->is_well_sorted());
    fail_if_proof_generation("reduce-args", g);
    fail_if_unsat_core_generation("reduce-args", g);
    mc = 0; pc = 0; core = 0; result.reset();
    m_imp->operator()(*(g.get()), mc);
    g->inc_depth();
    result.push_back(g.get());
    SASSERT(g->is_well_sorted());
}

void reduce_args_tactic::set_cancel(bool f) {
    if (m_imp)
        m_imp->set_cancel(f);
}

void reduce_args_tactic::cleanup() {
    ast_manager & m   = m_imp->m();
    imp * d = m_imp;
    #pragma omp critical (tactic_cancel)
    {
        m_imp = 0;
    }
    dealloc(d);
    d = alloc(imp, m);
    #pragma omp critical (tactic_cancel)
    {
        m_imp = d;
    }
}