diff --git a/src/sat/smt/polysat_egraph.cpp b/src/sat/smt/polysat_egraph.cpp
index 5c14aa752..56246c97b 100644
--- a/src/sat/smt/polysat_egraph.cpp
+++ b/src/sat/smt/polysat_egraph.cpp
@@ -114,13 +114,13 @@ namespace polysat {
         m_bv_plugin->super_slices(b, consume_slice);
     }
     
-    void solver::explain_slice(pvar pv, pvar pw, unsigned offset, std::function<void(euf::enode*, euf::enode*)>& consume_eq) {
+    void solver::explain_slice(pvar pv, pvar pw, unsigned offset, std::function<void(euf::enode*, euf::enode*)> const& consume_eq) {
         euf::theory_var v = m_pddvar2var[pv];
         euf::theory_var w = m_pddvar2var[pw];
         m_bv_plugin->explain_slice(var2enode(v), offset, var2enode(w), consume_eq);
     }
 
-    void solver::explain_fixed(pvar pv, fixed_slice const& slice, std::function<void(euf::enode*, euf::enode*)>& consume_eq) {
+    void solver::explain_fixed(pvar pv, fixed_slice const& slice, std::function<void(euf::enode*, euf::enode*)> const& consume_eq) {
         euf::theory_var v = m_pddvar2var[pv];
         expr_ref val(bv.mk_numeral(slice.value, slice.length), m);
         euf::enode* b = ctx.get_egraph().find(val);
diff --git a/src/sat/smt/polysat_solver.h b/src/sat/smt/polysat_solver.h
index 3f42381c6..c70a89989 100644
--- a/src/sat/smt/polysat_solver.h
+++ b/src/sat/smt/polysat_solver.h
@@ -111,8 +111,8 @@ namespace polysat {
 
         sat::check_result intblast();
 
-        void explain_slice(pvar v, pvar w, unsigned offset, std::function<void(euf::enode*, euf::enode*)>& consume);
-        void explain_fixed(pvar v, fixed_slice const& s, std::function<void(euf::enode*, euf::enode*)>& consume_eq);
+        void explain_slice(pvar v, pvar w, unsigned offset, std::function<void(euf::enode*, euf::enode*)> const& consume);
+        void explain_fixed(pvar v, fixed_slice const& s, std::function<void(euf::enode*, euf::enode*)> const& consume_eq);
 
         // internalize
         bool visit(expr* e) override;