fix #2831 again

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/ast/arith_decl_plugin.cpp

@@ -811,13 +811,24 @@ bool arith_util::is_considered_uninterpreted(func_decl* f, unsigned n, expr* con
         return true;
     }
     if (is_decl_of(f, m_afid, OP_POWER) && is_numeral(args[1], r) && r.is_zero() && is_numeral(args[0], r) && r.is_zero()) {
-        sort* rs[2] = { mk_real(), mk_real() };
+        f_out = is_int(args[0]) ? mk_ipower0() : mk_rpower0();
-        f_out = m_manager.mk_func_decl(m_afid, OP_POWER0, 0, nullptr, 2, rs, mk_real());
         return true;
     }
     return plugin().is_considered_uninterpreted(f);
 }
 
+func_decl* arith_util::mk_ipower0() {
+    sort* s = mk_int();
+    sort* rs[2] = { s, s };
+    return m_manager.mk_func_decl(m_afid, OP_POWER0, 0, nullptr, 2, rs, s);
+}
+
+func_decl* arith_util::mk_rpower0() {
+    sort* s = mk_real();
+    sort* rs[2] = { s, s };
+    return m_manager.mk_func_decl(m_afid, OP_POWER0, 0, nullptr, 2, rs, s);
+}
+
 func_decl* arith_util::mk_div0() {
     sort* rs[2] = { mk_real(), mk_real() };
     return m_manager.mk_func_decl(m_afid, OP_DIV0, 0, nullptr, 2, rs, mk_real());

src/ast/arith_decl_plugin.h

@@ -369,6 +369,8 @@ public:
 
     func_decl* mk_div0();
     func_decl* mk_idiv0();
+    func_decl* mk_ipower0();
+    func_decl* mk_rpower0();
 
 
     app * mk_numeral(rational const & val, bool is_int) const {

src/tactic/arith/purify_arith_tactic.cpp

@@ -194,6 +194,7 @@ struct purify_arith_proc {
         expr_ref_vector      m_new_cnstrs;
         proof_ref_vector     m_new_cnstr_prs;
         svector<div_def>     m_divs, m_idivs;
+        expr_ref             m_ipower0, m_rpower0;
         expr_ref             m_subst;
         proof_ref            m_subst_pr;
         expr_ref_vector      m_new_vars;
@@ -203,7 +204,9 @@ struct purify_arith_proc {
             m_pinned(o.m()),
             m_new_cnstrs(o.m()),
             m_new_cnstr_prs(o.m()),
-            m_subst(o.m()),
+            m_ipower0(o.m()),
+            m_rpower0(o.m()),
+            m_subst(o.m()),           
             m_subst_pr(o.m()),
             m_new_vars(o.m()) {
         }
@@ -407,11 +410,8 @@ struct purify_arith_proc {
             if (already_processed(t, result, result_pr))
                 return BR_DONE;
 
-            bool is_int = u().is_int(args[0]);
             expr * x = args[0];
-            rational xr;
+            bool is_int = u().is_int(x);
-            if (u().is_numeral(x, xr) && xr.is_zero())
-                return BR_FAILED;
 
             expr * k = mk_fresh_var(is_int);
             result = k;
@@ -421,10 +421,20 @@ struct purify_arith_proc {
             expr_ref zero(u().mk_numeral(rational(0), is_int), m());
             expr_ref one(u().mk_numeral(rational(1), is_int), m());
             if (y.is_zero()) {
+                expr* p0;
+                if (is_int) {
+                    if (!m_ipower0) m_ipower0 = mk_fresh_var(true);
+                    p0 = m_ipower0;
+                }
+                else {
+                    if (!m_rpower0) m_rpower0 = mk_fresh_var(false);
+                    p0 = m_rpower0;
+                }
+
                 // (^ x 0) --> k  |  x != 0 implies k = 1,   x = 0 implies k = 0^0 
                 push_cnstr(OR(EQ(x, zero), EQ(k, one)));
                 push_cnstr_pr(result_pr);
-                push_cnstr(OR(NOT(EQ(x, zero)), EQ(k, u().mk_power(zero, zero))));
+                push_cnstr(OR(NOT(EQ(x, zero)), EQ(k, p0)));
                 push_cnstr_pr(result_pr);
             }
             else if (!is_int) {
@@ -824,6 +834,12 @@ struct purify_arith_proc {
                 }
                 fmc->add(u().mk_idiv0(), body);
             }
+            if (r.cfg().m_ipower0) {
+                fmc->add(u().mk_ipower0(), r.cfg().m_ipower0);
+            }
+            if (r.cfg().m_rpower0) {
+                fmc->add(u().mk_rpower0(), r.cfg().m_rpower0);
+            }
         }
         if (produce_models && !m_sin_cos.empty()) {
             generic_model_converter* emc = alloc(generic_model_converter, m(), "purify_sin_cos");