Subterms Theory (#8115)

* somewhaat failed attempt at declaring subterm predicate

I can't really figure out how to link the smt parser to the rest of the
machinenery, so I will stop here and try from the other side. I'll start
implmenting the logic and see if it brings me back to the parser.

* initial logic implmentation

Very primitive, but I don't like have that much work uncommitted.

* parser implementation

* more theory

* Working base

* subterm reflexivity

* a few optimization

Skip adding obvious equalities or disequality

* removed some optimisations

* better handling of backtracking

* stupid segfault

Add m_subterm to the trail

* Update src/smt/theory_datatype.h

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Update src/ast/rewriter/datatype_rewriter.cpp

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Update src/smt/theory_datatype.cpp

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Update src/smt/theory_datatype.cpp

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Update src/smt/theory_datatype.cpp

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* review

* forgot to update `iterate_subterm`'s signature

* fix iterator segfault

* Remove duplicate include statement

Removed duplicate include of 'theory_datatype.h'.

* Replace 'optional' with 'std::option' in datatype_decl_plugin.h

* Add is_subterm_predicate matcher to datatype_decl_plugin

* Change std::option to std::optional for m_subterm

* Update pdecl.h

* Change has_subterm to use has_value method

* Update pdecl.cpp

---------

Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

src/cmd_context/cmd_context.cpp

@@ -2546,6 +2546,9 @@ void cmd_context::dt_eh::operator()(sort * dt, pdecl* pd) {
             m_owner.insert(a);
         }
     }
+    if (func_decl * sub = m_dt_util.get_datatype_subterm(dt)) {
+        m_owner.insert(sub);
+    }
     if (!m_owner.m_scopes.empty() && !m_owner.m_global_decls) {
         m_owner.pm().inc_ref(pd);
         m_owner.m_psort_inst_stack.push_back(pd);

src/cmd_context/pdecl.cpp

@@ -541,6 +541,12 @@ void pconstructor_decl::display(std::ostream & out, pdatatype_decl const * const
     out << ")";
 }
 
+// ~~~~~~~~~~~~ psubterm_decl ~~~~~~~~~~~~ //
+std::ostream&  psubterm_decl::display(std::ostream & out) const {
+    return out << ":subterm " << m_name;
+}
+
+
 pdatatype_decl::pdatatype_decl(unsigned id, unsigned num_params, pdecl_manager & m,
                                symbol const & n, unsigned num_constructors, pconstructor_decl * const * constructors):
     psort_decl(id, num_params, m, n),
@@ -589,7 +595,11 @@ datatype_decl * pdatatype_decl::instantiate_decl(pdecl_manager & m, unsigned n,
     for (auto c : m_constructors) 
         cs.push_back(c->instantiate_decl(m, n, s));
     datatype_util util(m.m());
-    return mk_datatype_decl(util, m_name, m_num_params, s, cs.size(), cs.data());
+    symbol subterm_name = symbol::null;
+    if (m_subterm.has_value()) {
+        subterm_name = m_subterm->get_name();
+    }
+    return mk_datatype_decl(util, m_name, m_num_params, s, cs.size(), cs.data(), subterm_name);
 }
 
 struct datatype_decl_buffer {
@@ -647,6 +657,9 @@ std::ostream& pdatatype_decl::display(std::ostream & out) const {
         }
         first = false;
     }
+    if (m_subterm.has_value()) {
+        m_subterm->display(out);
+    }
     return out << ")";
 }
 

src/cmd_context/pdecl.h

@@ -229,11 +229,23 @@ public:
     void display(std::ostream & out, pdatatype_decl const * const * dts) const;
 };
 
+class psubterm_decl: public pdecl {
+    friend class pdecl_manager;
+    friend class pdatatype_decl;
+    symbol                     m_name;
+    ptype    m_type;
+    symbol const & get_name() const { return m_name; }
+public:
+    psubterm_decl(symbol const& n) : pdecl(0, 0), m_name(n) {}
+    std::ostream& display(std::ostream & out) const override;
+};
+
 class pdatatype_decl : public psort_decl {
     friend class pdecl_manager;
     friend class pdatatypes_decl;
     ptr_vector<pconstructor_decl> m_constructors;
     pdatatypes_decl *             m_parent;
+    std::optional<psubterm_decl>         m_subterm;
     pdatatype_decl(unsigned id, unsigned num_params, pdecl_manager & m, symbol const & n,
                    unsigned num_constructors, pconstructor_decl * const * constructors);
     void finalize(pdecl_manager & m) override;
@@ -246,6 +258,7 @@ public:
     bool has_missing_refs(symbol & missing) const;
     bool has_duplicate_accessors(symbol & repeated) const;
     bool commit(pdecl_manager& m);
+    void set_subterm(symbol const& n) { m_subterm = psubterm_decl(n); }
 };
 
 /**