na

Signed-off-by: Nikolaj Bjorner <[email protected]>

Author: NikolajBjorner

src/ast/CMakeLists.txt

@@ -44,6 +44,7 @@ z3_add_component(ast
     special_relations_decl_plugin.cpp
     static_features.cpp
     used_vars.cpp
+    value_generator.cpp
     well_sorted.cpp
   COMPONENT_DEPENDENCIES
     polynomial

src/ast/value_generator.cpp

@@ -0,0 +1,386 @@
+/*++
+  Copyright (c) 2020 Microsoft Corporation
+
+  Module Name:
+
+   value_generatorr.cpp
+
+  Abstract:
+   
+    Generate mostly different values using index as seed.
+
+  Author:
+
+    Nikolaj Bjorner 2020-04-25
+
+--*/
+
+#include "ast/value_generator.h"
+#include "ast/datatype_decl_plugin.h"
+#include "ast/array_decl_plugin.h"
+#include "ast/arith_decl_plugin.h"
+#include "ast/bv_decl_plugin.h"
+#include "ast/seq_decl_plugin.h"
+#include <cmath>
+
+
+
+/*
+  \brief inverse of the Cantor function.
+  It converts an unsigned into a pair of unsigned numbers that are not
+  bigger (and only equal for values 0, 1).
+*/
+static void inverse_cantor(unsigned z, unsigned& x, unsigned& y) {
+    unsigned w = ((unsigned)sqrt(8*z + 1) - 1)/2;
+    unsigned t = (unsigned)(w*w + w)/2;
+    y = z - t;
+    x = w - y;
+}
+
+static bool is_small_size(sort_size const& sz) {
+    return sz.is_finite() && sz.size() < (UINT_MAX >> 12);
+}
+
+class datatype_value_generator : public value_generator_core {
+    ast_manager&     m;
+    value_generator& g;
+    datatype_util    dt;
+    sort_ref_vector  m_sorts;
+    obj_map<sort, expr_ref_vector*> m_values;
+    obj_map<func_decl, unsigned> m_constr2seen;
+    random_gen       m_rand;
+        
+    unsigned_vector inf;
+    void index2vector(unsigned z, func_decl* c, unsigned_vector& v) {
+        unsigned arity = c->get_arity();
+        v.resize(arity);
+        inf.reset();
+        for (unsigned i = 0; i < arity; ++i) {
+            sort* s = c->get_domain(i);
+            sort_size const& sz = s->get_num_elements();
+            if (is_small_size(sz)) {
+                v[i] = z % sz.size();
+                z = z/((unsigned)sz.size());
+            }
+            else {
+                inf.push_back(i);
+            }
+        }
+        // fill in values for large domains
+        for (unsigned i = 0; i + 1 < inf.size(); ++i) {
+            inverse_cantor(z, v[inf[i]], z);        
+        }
+        if (!inf.empty()) {
+            v[inf.back()] = z;   
+        } 
+    }
+
+    bool domain_size_exhausted(unsigned j, func_decl* c) {
+        unsigned arity = c->get_arity();
+        uint64_t dsz = 1;
+        for (unsigned i = 0; i < arity; ++i) {
+            sort* s = c->get_domain(i);
+            sort_size const& sz = s->get_num_elements();
+            if (is_small_size(sz)) {
+                dsz *= sz.size();
+            }
+            else {
+                return false;
+            }
+            if (dsz > j) {
+                return false;
+            }
+        }
+        return j >= dsz;
+    }
+
+
+public:
+    datatype_value_generator(value_generator& g, ast_manager& m):
+        m(m), g(g), dt(m), m_sorts(m) {}
+   
+    ~datatype_value_generator() {
+        for (auto& kv : m_values) dealloc(kv.m_value);
+    }
+
+    family_id get_fid() const override { 
+        return dt.get_family_id(); 
+    }
+
+    /*
+      In the off chance that a recursive datatype constructor is left recursive and has no base case on its own
+      we iterate over constructors in a random order to make sure to hit the base cases eventually.
+      In such cases m_constr2seen might not get updated accurately and we admit repetitions. 
+      
+     */
+    unsigned_vector indices;
+    expr_ref get_value(sort* s, unsigned index) override {
+        expr_ref_vector* vp = nullptr;
+        if (!m_values.find(s, vp)) {
+            vp = alloc(expr_ref_vector, m);
+            for (auto* c : *dt.get_datatype_constructors(s)) {
+                if (c->get_arity() == 0)
+                    vp->push_back(m.mk_const(c));
+            }
+            m_values.insert(s, vp);
+            m_sorts.push_back(s);
+        }
+        auto& v = *vp;
+        expr_ref_vector args(m);
+        bool some_valid = true;
+        while (v.size() <= index && some_valid) {
+            some_valid = false;
+            auto const& decls = *dt.get_datatype_constructors(s);
+            int start = m_rand();
+            for (unsigned i = 0; i < decls.size(); ++i) { 
+                func_decl* c = decls[(i + start) % decls.size()];
+                unsigned arity = c->get_arity();
+                if (arity == 0)
+                    continue;
+                args.resize(c->get_arity());
+                unsigned j = 0;
+                m_constr2seen.find(c, j);
+                if (domain_size_exhausted(j, c))
+                    continue;
+                m_constr2seen.insert(c, j + 1);
+                index2vector(j, c, indices);
+                bool valid = true;
+                for (unsigned i = 0; valid && i < args.size(); ++i) {
+                    args[i] = g.get_value(c->get_domain(i), indices[i]);
+                    valid &= args.get(i) != nullptr;
+                }
+                if (valid) {
+                    v.push_back(m.mk_app(c, args));
+                    some_valid = true;
+                }
+            }
+        }
+        return expr_ref(v.get(index, nullptr), m);
+    }
+};
+
+
+class arith_value_generator : public value_generator_core {
+    ast_manager&     m;
+    arith_util       a;
+    int u2i(unsigned u) {
+        if (0 == (u % 2))
+            return u/2;
+        else
+            return -(int)((u+1)/2);
+    }
+
+    void calkin_wilf(unsigned i, unsigned& x, unsigned& y) {
+        while (i > 1) {
+            if (i % 2 == 0) {
+                x += y;                
+            }
+            else {
+                y += x;
+            }
+            i /= 2;
+        }
+    }
+
+public:
+    arith_value_generator(ast_manager& m): m(m), a(m) {}
+
+    family_id get_fid() const override { 
+        return a.get_family_id(); 
+    }
+
+    expr_ref get_value(sort* s, unsigned index) override {
+        if (a.is_int(s)) {
+            return expr_ref(a.mk_int(u2i(index)), m);
+        }
+        if (index == 0) 
+            return expr_ref(a.mk_real(rational(0)), m);
+        unsigned x = 1, y = 1;
+        calkin_wilf((index/2) + 1, x, y);
+        if ((index % 2) == 0) x = -(int)x;
+        return expr_ref(a.mk_real(rational(x, y)), m);
+    }    
+};
+
+class seq_value_generator : public value_generator_core {
+    ast_manager&  m;
+    value_generator& g;
+    seq_util      seq;
+public:
+    seq_value_generator(value_generator& g, ast_manager& m): g(g), m(m), seq(m) {}
+
+    family_id get_fid() const override { 
+        return seq.get_family_id(); 
+    }
+
+    expr_ref get_value(sort* s, unsigned index) override {
+        sort* elem_sort = nullptr;
+        if (!seq.is_seq(s, elem_sort)) {
+            return expr_ref(m.mk_fresh_const("re", s), m);
+        }
+        if (index == 0) {
+            return expr_ref(seq.str.mk_empty(s), m);
+        }
+        --index;
+        sort_size const& sz = elem_sort->get_num_elements();
+        expr_ref_vector es(m);
+        unsigned idx = 0;
+        if (is_small_size(sz)) {
+            // TBD: could also use a Gray-code version
+            // TBD: could also prefer longer sequences
+            unsigned esz = (unsigned)sz.size();
+            index += esz;
+            do {
+                idx = index % esz; 
+                expr_ref elem = g.get_value(elem_sort, idx);
+                es.push_back(seq.str.mk_unit(elem));
+                index /= esz;
+            }
+            while (index >= esz);
+        }
+        else {
+            do {
+                inverse_cantor(index, idx, index);
+                expr_ref elem = g.get_value(elem_sort, idx);
+                es.push_back(seq.str.mk_unit(elem));
+            }
+            while (index > 0);
+        }
+        return expr_ref(seq.str.mk_concat(es, s), m);
+    }    
+};
+
+
+class array_value_generator : public value_generator_core {
+    ast_manager&     m;
+    value_generator& g;
+    array_util       a;
+public:
+    array_value_generator(value_generator& g, ast_manager& m): g(g), m(m), a(m) {}
+
+    family_id get_fid() const override { 
+        return a.get_family_id(); 
+    }
+
+    // if both domain and range are finite, this will create repetitions.
+    // overall, finite domain arrays can be handled separately
+    // repetitions also happen when the same set of indices are updated twice
+
+    expr_ref get_value(sort* s, unsigned index) override {
+        unsigned arity = get_array_arity(s);
+        sort* r = get_array_range(s);
+        sort_size const& sz = r->get_num_elements();
+        if (sz.is_finite() && sz.size() == 1) {
+            return expr_ref(a.mk_const_array(s, g.get_value(r, 0)), m);           
+        }
+        
+        unsigned z = 0;
+        if (is_small_size(sz)) {
+            z = index % sz.size();
+            index = index / (unsigned)sz.size();
+        }
+        else {
+            inverse_cantor(index, z, index);
+        }
+        expr_ref result(a.mk_const_array(s, g.get_value(r, z)), m);
+        unsigned default_index = z;
+        expr_ref_vector args(m);
+        unsigned_vector inf;
+        args.resize(arity+2);
+        while (index > 0) {            
+            args[0] = result;
+            for (unsigned i = 0; i < arity; ++i) {
+                sort* d = get_array_domain(s, i);
+                sort_size const& dsz = d->get_num_elements();
+                if (is_small_size(dsz)) {
+                    args[1 + i] = g.get_value(d, index % dsz.size());
+                    index = index / ((unsigned)dsz.size());
+                }
+                else {
+                    inf.push_back(i);
+                }
+            }
+            for (unsigned i : inf) {
+                inverse_cantor(index, z, index);
+                args[1 + i] = g.get_value(get_array_domain(s, i), z);
+            }
+
+            // ensure z is different from default_index.
+            if (is_small_size(sz)) {
+                z = index % (sz.size() - 1);
+                index = index / (unsigned)sz.size();
+            }
+            else {
+                inverse_cantor(index, z, index);
+            }
+            if (z >= default_index) z++;
+            args[arity+1] = g.get_value(r, z);
+            result = a.mk_store(args);
+        }
+        
+        return result;
+    }    
+};
+
+class bv_value_generator : public value_generator_core {
+    ast_manager& m;
+    bv_util bv;
+public:
+    bv_value_generator(ast_manager& m): m(m), bv(m) {}
+
+    family_id get_fid() const override { 
+        return bv.get_family_id(); 
+    }
+
+    expr_ref get_value(sort* s, unsigned index) override {
+        index %= bv.get_bv_size(s);
+        return expr_ref(bv.mk_numeral(rational(index), s), m);
+    }
+};
+
+class bool_value_generator : public value_generator_core {
+    ast_manager& m;
+public:
+    bool_value_generator(ast_manager& m): m(m) {}
+
+    family_id get_fid() const override { 
+        return m.get_basic_family_id(); 
+    }
+
+    expr_ref get_value(sort* s, unsigned index) override {
+        if (!m.is_bool(s))
+            return expr_ref(m.mk_fresh_const("basic", s), m);
+        if (index % 2 == 0)
+            return expr_ref(m.mk_false(), m);
+        return expr_ref(m.mk_true(), m);
+    }
+};
+
+    
+value_generator::value_generator(ast_manager& m): m(m) {
+}
+
+void value_generator::init() {
+    if (!m_plugins.empty())
+        return;
+    add_plugin(alloc(datatype_value_generator, *this, m));
+    add_plugin(alloc(arith_value_generator, m));
+    add_plugin(alloc(bv_value_generator, m));
+    add_plugin(alloc(bool_value_generator, m));
+    add_plugin(alloc(seq_value_generator, *this, m));
+    add_plugin(alloc(array_value_generator, *this, m));
+    // fp_value_generator
+    // uninterp_sort_value_generator
+}
+
+void value_generator::add_plugin(value_generator_core* v) {
+    m_plugins.reserve(v->get_fid() + 1);
+    m_plugins.set(v->get_fid(), v);
+}
+
+expr_ref value_generator::get_value(sort* s, unsigned index) {
+    init();
+    auto fid = s->get_family_id();
+    auto* p = m_plugins.get(fid, nullptr);
+    return p ? p->get_value(s, index) : expr_ref(m.mk_fresh_const(s->get_name(), s), m);
+}