SMT2 back-end: support empty compound types

Do not construct equalities over expressions the type of which has zero
bit width. Also, permit pointer arithmetic over objects of such type
(which was previously fixed in 6b09359 for the propositional back-end).

Fixes: diffblue#7185

regression/cbmc/empty_compound_type2/test.desc

@@ -1,4 +1,4 @@
-CORE broken-smt-backend
+CORE
 main.c
 --pointer-check
 ^EXIT=10$

regression/cbmc/empty_compound_type3/test.desc

@@ -1,4 +1,4 @@
-CORE broken-smt-backend
+CORE
 main.c
 
 ^EXIT=10$

regression/cbmc/empty_compound_type4/test.desc

@@ -1,4 +1,4 @@
-CORE broken-smt-backend
+CORE
 main.c
 --trace
 ^VERIFICATION FAILED$

src/solvers/smt2/smt2_conv.cpp

@@ -958,6 +958,23 @@ std::string smt2_convt::convert_identifier(const irep_idt &identifier)
   return result;
 }
 
+/// Returns true iff \p type has effective width of zero bits.
+static bool is_zero_width(const typet &type, const namespacet &ns)
+{
+  if(type.id() == ID_empty)
+    return true;
+  else if(type.id() == ID_struct_tag)
+    return is_zero_width(ns.follow_tag(to_struct_tag_type(type)), ns);
+  else if(type.id() == ID_struct)
+    return to_struct_type(type).components().empty();
+  else if(type.id() == ID_union_tag)
+    return is_zero_width(ns.follow_tag(to_union_tag_type(type)), ns);
+  else if(type.id() == ID_union)
+    return to_union_type(type).components().empty();
+  else
+    return false;
+}
+
 std::string smt2_convt::type2id(const typet &type) const
 {
   if(type.id()==ID_floatbv)
@@ -1365,11 +1382,18 @@ void smt2_convt::convert_expr(const exprt &expr)
       equal_expr.op0().type() == equal_expr.op1().type(),
       "operands of equal expression shall have same type");
 
-    out << "(= ";
-    convert_expr(equal_expr.op0());
-    out << " ";
-    convert_expr(equal_expr.op1());
-    out << ")";
+    if(is_zero_width(equal_expr.lhs().type(), ns))
+    {
+      convert_expr(true_exprt());
+    }
+    else
+    {
+      out << "(= ";
+      convert_expr(equal_expr.op0());
+      out << " ";
+      convert_expr(equal_expr.op1());
+      out << ")";
+    }
   }
   else if(expr.id() == ID_notequal)
   {
@@ -2369,10 +2393,6 @@ void smt2_convt::convert_expr(const exprt &expr)
   {
     convert_expr(simplify_expr(to_find_first_set_expr(expr).lower(), ns));
   }
-  else if(expr.id() == ID_empty_union)
-  {
-    out << "()";
-  }
   else if(expr.id() == ID_bitreverse)
   {
     convert_expr(simplify_expr(to_bitreverse_expr(expr).lower(), ns));
@@ -3597,7 +3617,7 @@ void smt2_convt::convert_plus(const plus_exprt &expr)
       else
       {
         auto element_size_opt = pointer_offset_size(base_type, ns);
-        CHECK_RETURN(element_size_opt.has_value() && *element_size_opt >= 1);
+        CHECK_RETURN(element_size_opt.has_value() && *element_size_opt >= 0);
         element_size = *element_size_opt;
       }
 
@@ -4701,9 +4721,7 @@ void smt2_convt::set_to(const exprt &expr, bool value)
   if(expr.id() == ID_equal && value)
   {
     const equal_exprt &equal_expr=to_equal_expr(expr);
-    if(
-      equal_expr.lhs().type().id() == ID_empty ||
-      equal_expr.rhs().id() == ID_empty_union)
+    if(is_zero_width(equal_expr.lhs().type(), ns))
     {
       // ignore equality checking over expressions with empty (void) type
       return;
@@ -4955,21 +4973,24 @@ void smt2_convt::find_symbols(const exprt &expr)
         convert_type(array_type);
         out << ")\n";
 
-        // use a quantifier-based initialization instead of lambda
-        out << "(assert (forall ((i ";
-        convert_type(array_type.index_type());
-        out << ")) (= (select " << id << " i) ";
-        if(array_type.element_type().id() == ID_bool && !use_array_of_bool)
+        if(!is_zero_width(array_type.element_type(), ns))
         {
-          out << "(ite ";
-          convert_expr(array_of.what());
-          out << " #b1 #b0)";
-        }
-        else
-        {
-          convert_expr(array_of.what());
+          // use a quantifier-based initialization instead of lambda
+          out << "(assert (forall ((i ";
+          convert_type(array_type.index_type());
+          out << ")) (= (select " << id << " i) ";
+          if(array_type.element_type().id() == ID_bool && !use_array_of_bool)
+          {
+            out << "(ite ";
+            convert_expr(array_of.what());
+            out << " #b1 #b0)";
+          }
+          else
+          {
+            convert_expr(array_of.what());
+          }
+          out << ")))\n";
         }
-        out << ")))\n";
 
         defined_expressions[expr] = id;
       }
@@ -5035,22 +5056,26 @@ void smt2_convt::find_symbols(const exprt &expr)
       convert_type(array_type);
       out << ")" << "\n";
 
-      for(std::size_t i=0; i<expr.operands().size(); i++)
+      if(!is_zero_width(array_type.element_type(), ns))
       {
-        out << "(assert (= (select " << id << " ";
-        convert_expr(from_integer(i, array_type.index_type()));
-        out << ") "; // select
-        if(array_type.element_type().id() == ID_bool && !use_array_of_bool)
-        {
-          out << "(ite ";
-          convert_expr(expr.operands()[i]);
-          out << " #b1 #b0)";
-        }
-        else
+        for(std::size_t i = 0; i < expr.operands().size(); i++)
         {
-          convert_expr(expr.operands()[i]);
+          out << "(assert (= (select " << id << " ";
+          convert_expr(from_integer(i, array_type.index_type()));
+          out << ") "; // select
+          if(array_type.element_type().id() == ID_bool && !use_array_of_bool)
+          {
+            out << "(ite ";
+            convert_expr(expr.operands()[i]);
+            out << " #b1 #b0)";
+          }
+          else
+          {
+            convert_expr(expr.operands()[i]);
+          }
+          out << "))"
+              << "\n"; // =, assert
         }
-        out << "))" << "\n"; // =, assert
       }
 
       defined_expressions[expr]=id;