add assume-eqs and extensionality

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

src/ast/finite_set_decl_plugin.cpp

@@ -70,6 +70,8 @@ void finite_set_decl_plugin::init() {
     m_sigs[OP_FINITE_SET_MAP]        = alloc(polymorphism::psig, m, "set.map",        2, 2, arrABsetA, setB);
     m_sigs[OP_FINITE_SET_SELECT]     = alloc(polymorphism::psig, m, "set.select",     1, 2, arrABoolsetA, setA);
     m_sigs[OP_FINITE_SET_RANGE]      = alloc(polymorphism::psig, m, "set.range",      0, 2, intintT, setInt);
+    m_sigs[OP_FINITE_SET_DIFF]       = alloc(polymorphism::psig, m, "set.diff", 1, 2, setAsetA, A);
+//    m_sigs[OP_FINITE_SET_MAP_INVERSE] = alloc(polymorphism::psig, m, "set.map_inverse", 2, 3, arrABsetBsetA, A);
 }
 
 sort * finite_set_decl_plugin::mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters) {
@@ -152,6 +154,7 @@ func_decl * finite_set_decl_plugin::mk_func_decl(decl_kind k, unsigned num_param
     case OP_FINITE_SET_MAP:
     case OP_FINITE_SET_SELECT:
     case OP_FINITE_SET_RANGE:
+    case OP_FINITE_SET_DIFF:
         return mk_finite_set_op(k, arity, domain, range);
     default:
         return nullptr;

src/ast/finite_set_decl_plugin.h

@@ -23,6 +23,7 @@ Operators:
     set.map : (S -> T) (FiniteSet S) -> (FiniteSet T)
     set.select : (S -> Bool) (FiniteSet S) -> (FiniteSet S)
     set.range : Int Int -> (FiniteSet Int)
+    set.diff : (FiniteSet S) (FiniteSet S) -> S
    
 --*/
 #pragma once
@@ -46,6 +47,8 @@ enum finite_set_op_kind {
     OP_FINITE_SET_MAP,
     OP_FINITE_SET_SELECT,
     OP_FINITE_SET_RANGE,
+    OP_FINITE_SET_DIFF,
+    OP_FINITE_SET_MAP_INVERSE,
     LAST_FINITE_SET_OP
 };
 

src/ast/rewriter/finite_set_axioms.cpp

@@ -298,4 +298,19 @@ void finite_set_axioms::subset_axiom(expr* a) {
     clause2.push_back(a);
     clause2.push_back(m.mk_not(eq));
     m_add_clause(clause2);
+}
+
+void finite_set_axioms::extensionality_axiom(expr *a, expr* b) {
+    // a != b => set.in (set.diff(a, b) a) != set.in (set.diff(a, b) b)
+    expr_ref diff_ab(u.mk_difference(a, b), m);
+
+    expr_ref a_eq_b(m.mk_eq(a, b), m);
+    expr_ref diff_in_a(u.mk_in(diff_ab, a), m);
+    expr_ref diff_in_b(u.mk_in(diff_ab, b), m);
+    
+    // (a != b) => (x in diff_ab != x in diff_ba)
+    expr_ref_vector clause(m);
+    clause.push_back(a_eq_b);
+    clause.push_back(m.mk_not(m.mk_iff(diff_in_a, diff_in_b)));
+    m_add_clause(clause);   
 }

src/ast/rewriter/finite_set_axioms.h

@@ -69,4 +69,7 @@ public:
     // set.size(a) = 1
     void size_singleton_axiom(expr *a);
 
+    // a != b => set.in (set.diff(a, b) a) != set.in (set.diff(a, b) b)
+    void extensionality_axiom(expr *a, expr *b);
+
 };