diff --git a/src/ast/CMakeLists.txt b/src/ast/CMakeLists.txt
index 0bcc4d84732..aad9e1826c1 100644
--- a/src/ast/CMakeLists.txt
+++ b/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
diff --git a/src/ast/value_generator.cpp b/src/ast/value_generator.cpp
new file mode 100644
index 00000000000..a132154b93e
--- /dev/null
+++ b/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);
+}
diff --git a/src/ast/value_generator.h b/src/ast/value_generator.h
new file mode 100644
index 00000000000..7b77b144ea7
--- /dev/null
+++ b/src/ast/value_generator.h
@@ -0,0 +1,39 @@
+/*++
+  Copyright (c) 2020 Microsoft Corporation
+
+  Module Name:
+
+   value_generatorr.h
+
+  Abstract:
+   
+    Generate mostly different values using index as seed.
+
+  Author:
+
+    Nikolaj Bjorner 2020-04-25
+  
+--*/
+
+#pragma once
+
+#include "util/scoped_ptr_vector.h"
+#include "ast/ast.h"
+
+
+class value_generator_core {
+ public:        
+    virtual ~value_generator_core() {}
+    virtual family_id get_fid() const = 0;
+    virtual expr_ref get_value(sort* s, unsigned index) = 0;
+};
+
+class value_generator {
+    ast_manager& m;
+    scoped_ptr_vector<value_generator_core> m_plugins;
+    void add_plugin(value_generator_core* g);
+    void init();
+ public:
+    value_generator(ast_manager& m);
+    expr_ref get_value(sort* s, unsigned index);    
+};
diff --git a/src/model/datatype_factory.cpp b/src/model/datatype_factory.cpp
index b181581ec09..41373b25b01 100644
--- a/src/model/datatype_factory.cpp
+++ b/src/model/datatype_factory.cpp
@@ -36,7 +36,7 @@ expr * datatype_factory::get_some_value(sort * s) {
     for (unsigned i = 0; i < num; i++) {
         args.push_back(m_model.get_some_value(c->get_domain(i)));
     }
-    expr * r = m_manager.mk_app(c, args.size(), args.c_ptr());
+    expr * r = m_manager.mk_app(c, args);
     register_value(r);
     TRACE("datatype", tout << mk_pp(r, m_util.get_manager()) << "\n";);
     return r;
@@ -115,7 +115,7 @@ expr * datatype_factory::get_almost_fresh_value(sort * s) {
             }
         }
         if (recursive || found_fresh_arg) {
-            app * new_value = m_manager.mk_app(constructor, args.size(), args.c_ptr());
+            app * new_value = m_manager.mk_app(constructor, args);
             SASSERT(!found_fresh_arg || !set->contains(new_value));
             register_value(new_value);
             if (m_util.is_recursive(s)) {
@@ -170,7 +170,7 @@ expr * datatype_factory::get_fresh_value(sort * s) {
             args.push_back(some_arg);
         }
         expr_ref new_value(m_manager);
-        new_value = m_manager.mk_app(constructor, args.size(), args.c_ptr());
+        new_value = m_manager.mk_app(constructor, args);
         CTRACE("datatype", found_fresh_arg && set->contains(new_value), tout << mk_pp(new_value, m_manager) << "\n";);
         SASSERT(!found_fresh_arg || !set->contains(new_value));
         if (!set->contains(new_value)) {
@@ -228,7 +228,7 @@ expr * datatype_factory::get_fresh_value(sort * s) {
                 }
                 if (found_sibling) {
                     expr_ref new_value(m_manager);
-                    new_value = m_manager.mk_app(constructor, args.size(), args.c_ptr());
+                    new_value = m_manager.mk_app(constructor, args);
                     TRACE("datatype", tout << "potential new value: " << mk_pp(new_value, m_manager) << "\n";);
                     m_last_fresh_value.insert(s, new_value);
                     if (!set->contains(new_value)) {
diff --git a/src/test/CMakeLists.txt b/src/test/CMakeLists.txt
index 9f44c6f0234..a9fb5aa6962 100644
--- a/src/test/CMakeLists.txt
+++ b/src/test/CMakeLists.txt
@@ -122,6 +122,7 @@ add_executable(test-z3
   udoc_relation.cpp
   uint_set.cpp
   upolynomial.cpp
+  value_generator.cpp
   var_subst.cpp
   vector.cpp
   lp/lp.cpp
diff --git a/src/test/main.cpp b/src/test/main.cpp
index 05723f63c9a..c8c16ba1828 100644
--- a/src/test/main.cpp
+++ b/src/test/main.cpp
@@ -217,6 +217,7 @@ int main(int argc, char ** argv) {
     if (test_all) return 0;
     TST(ext_numeral);
     TST(interval);
+    TST(value_generator);
     TST(vector);
     TST(f2n);
     TST(hwf);
diff --git a/src/test/value_generator.cpp b/src/test/value_generator.cpp
new file mode 100644
index 00000000000..ecde5885560
--- /dev/null
+++ b/src/test/value_generator.cpp
@@ -0,0 +1,59 @@
+#include "ast/value_generator.h"
+#include "ast/reg_decl_plugins.h"
+#include "ast/ast_pp.h"
+#include "ast/datatype_decl_plugin.h"
+#include "ast/seq_decl_plugin.h"
+#include "ast/array_decl_plugin.h"
+
+static void list(unsigned bound, ast_manager& m, sort* s) {
+    value_generator gen(m);
+    for (unsigned i = 0; i < bound; ++i) {
+        std::cout << gen.get_value(s, i) << "\n";
+    }
+}
+
+static void tst1_vg() {
+    ast_manager m;
+    reg_decl_plugins(m);
+    datatype_util dt(m);
+    arith_util a(m);
+    array_util ar(m);
+    seq_util seq(m);
+    sort_ref int_sort(a.mk_int(), m);
+    func_decl_ref cons(m), is_cons(m), head(m), tail(m), nil(m), is_nil(m);
+
+    sort_ref bool_seq(seq.str.mk_seq(m.mk_bool_sort()), m);
+    list(16, m, bool_seq);
+    return;
+
+    sort_ref ilist = dt.mk_list_datatype(int_sort, symbol("ilist"), 
+                                     cons, is_cons, head, tail, nil, is_nil);
+    list(100, m, ilist);
+
+    sort_ref blist = dt.mk_list_datatype(m.mk_bool_sort(), symbol("blist"), 
+                                     cons, is_cons, head, tail, nil, is_nil);
+    list(100, m, blist);
+    
+    sort_ref rlist = dt.mk_list_datatype(a.mk_real(), symbol("rlist"), 
+                                     cons, is_cons, head, tail, nil, is_nil);
+    list(100, m, rlist);
+
+    list(100, m, a.mk_real());
+    list(100, m, a.mk_int());
+
+    sort_ref int_seq(seq.str.mk_seq(a.mk_int()), m);
+    list(100, m, int_seq);
+
+    sort_ref as(m);
+    as = ar.mk_array_sort(a.mk_int(), a.mk_int());
+    list(100, m, as);
+    as = ar.mk_array_sort(m.mk_bool_sort(), a.mk_int());
+    list(100, m, as);
+    as = ar.mk_array_sort(m.mk_bool_sort(), m.mk_bool_sort());
+    list(10, m, as);
+
+}
+
+void tst_value_generator() {
+    tst1_vg();
+}
diff --git a/src/util/scoped_ptr_vector.h b/src/util/scoped_ptr_vector.h
index 9ec34d31355..fbdf9e9af0a 100644
--- a/src/util/scoped_ptr_vector.h
+++ b/src/util/scoped_ptr_vector.h
@@ -33,6 +33,7 @@ class scoped_ptr_vector {
     void pop_back() { SASSERT(!empty()); set(size()-1, nullptr); m_vector.pop_back(); }
     T * back() const { return m_vector.back(); }
     T * operator[](unsigned idx) const { return m_vector[idx]; }
+    T * get(unsigned idx, T* d = nullptr) const { return (0 <= idx && idx < m_vector.size()) ? (*this)[idx] : d; }
     void set(unsigned idx, T * ptr) { 
         if (m_vector[idx] == ptr) 
             return; 
@@ -52,6 +53,11 @@ class scoped_ptr_vector {
                 push_back(nullptr);
         }
     }
+    void reserve(unsigned sz) {
+        if (sz >= m_vector.size())
+            resize(sz);
+    }
+
     //!< swap last element with given pointer
     void swap_back(scoped_ptr<T> & ptr) {
         SASSERT(!empty());