diff --git a/src/kernel/environment.cpp b/src/kernel/environment.cpp
index 7757a90a55..57e0a0358e 100644
--- a/src/kernel/environment.cpp
+++ b/src/kernel/environment.cpp
@@ -9,6 +9,7 @@ Author: Leonardo de Moura
 #include <limits>
 #include "runtime/sstream.h"
 #include "runtime/thread.h"
+#include "runtime/sharecommon.h"
 #include "util/map_foreach.h"
 #include "util/io.h"
 #include "kernel/environment.h"
@@ -220,12 +221,15 @@ environment environment::add_theorem(declaration const & d, bool check) const {
     theorem_val const & v = d.to_theorem_val();
     if (check) {
         type_checker checker(*this, diag.get());
-        if (!checker.is_prop(v.get_type()))
-            throw theorem_type_is_not_prop(*this, v.get_name(), v.get_type());
+        sharecommon_persistent_fn share;
+        expr val(share(v.get_value().raw()));
+        expr type(share(v.get_type().raw()));
+        if (!checker.is_prop(type))
+            throw theorem_type_is_not_prop(*this, v.get_name(), type);
         check_constant_val(*this, v.to_constant_val(), checker);
-        check_no_metavar_no_fvar(*this, v.get_name(), v.get_value());
-        expr val_type = checker.check(v.get_value(), v.get_lparams());
-        if (!checker.is_def_eq(val_type, v.get_type()))
+        check_no_metavar_no_fvar(*this, v.get_name(), val);
+        expr val_type = checker.check(val, v.get_lparams());
+        if (!checker.is_def_eq(val_type, type))
             throw definition_type_mismatch_exception(*this, d, val_type);
     }
     return diag.update(add(constant_info(d)));
diff --git a/src/kernel/expr_eq_fn.cpp b/src/kernel/expr_eq_fn.cpp
index 647bbec2d3..875b4e2dc1 100644
--- a/src/kernel/expr_eq_fn.cpp
+++ b/src/kernel/expr_eq_fn.cpp
@@ -11,65 +11,49 @@ Author: Leonardo de Moura
 #include "kernel/expr.h"
 #include "kernel/expr_sets.h"
 
-#ifndef LEAN_EQ_CACHE_CAPACITY
-#define LEAN_EQ_CACHE_CAPACITY 1024*8
-#endif
-
 namespace lean {
-struct eq_cache {
-    struct entry {
-        object * m_a;
-        object * m_b;
-        entry():m_a(nullptr), m_b(nullptr) {}
-    };
-    unsigned              m_capacity;
-    std::vector<entry>    m_cache;
-    std::vector<unsigned> m_used;
-    eq_cache():m_capacity(LEAN_EQ_CACHE_CAPACITY), m_cache(LEAN_EQ_CACHE_CAPACITY) {}
+/**
+\brief Functional object for comparing expressions.
 
-    bool check(expr const & a, expr const & b) {
-        if (!is_shared(a) || !is_shared(b))
-            return false;
-        unsigned i = hash(hash(a), hash(b)) % m_capacity;
-        if (m_cache[i].m_a == a.raw() && m_cache[i].m_b == b.raw()) {
-            return true;
-        } else {
-            if (m_cache[i].m_a == nullptr)
-                m_used.push_back(i);
-            m_cache[i].m_a = a.raw();
-            m_cache[i].m_b = b.raw();
-            return false;
-        }
-    }
-
-    void clear() {
-        for (unsigned i : m_used)
-            m_cache[i].m_a = nullptr;
-        m_used.clear();
-    }
-};
-
-/* CACHE_RESET: No */
-MK_THREAD_LOCAL_GET_DEF(eq_cache, get_eq_cache);
-
-/** \brief Functional object for comparing expressions.
-
-    Remark if CompareBinderInfo is true, then functional object will also compare
-    binder information attached to lambda and Pi expressions */
+Remark if CompareBinderInfo is true, then functional object will also compare
+binder information attached to lambda and Pi expressions
+*/
 template<bool CompareBinderInfo>
 class expr_eq_fn {
-    eq_cache & m_cache;
-
+    struct key_hasher {
+        std::size_t operator()(std::pair<lean_object *, lean_object *> const & p) const {
+            return hash((size_t)p.first >> 3, (size_t)p.first >> 3);
+        }
+    };
+    typedef std::unordered_set<std::pair<lean_object *, lean_object *>, key_hasher> cache;
+    cache * m_cache = nullptr;
+    bool check_cache(expr const & a, expr const & b) {
+        if (!is_shared(a) || !is_shared(b))
+            return false;
+        if (!m_cache)
+            m_cache = new cache();
+        std::pair<lean_object *, lean_object *> key(a.raw(), b.raw());
+        if (m_cache->find(key) != m_cache->end())
+            return true;
+        m_cache->insert(key);
+        return false;
+    }
     static void check_system() {
         ::lean::check_system("expression equality test");
     }
-
-    bool apply(expr const & a, expr const & b) {
+    bool apply(expr const & a, expr const & b, bool root = false) {
         if (is_eqp(a, b))          return true;
         if (hash(a) != hash(b))    return false;
         if (a.kind() != b.kind())  return false;
-        if (is_bvar(a))            return bvar_idx(a) == bvar_idx(b);
-        if (m_cache.check(a, b))
+        switch (a.kind()) {
+        case expr_kind::BVar: return bvar_idx(a) == bvar_idx(b);
+        case expr_kind::Lit:  return lit_value(a) == lit_value(b);
+        case expr_kind::MVar: return mvar_name(a) == mvar_name(b);
+        case expr_kind::FVar: return fvar_name(a) == fvar_name(b);
+        case expr_kind::Sort: return sort_level(a) == sort_level(b);
+        default: break;
+        }
+        if (!root && check_cache(a, b))
             return true;
         /*
            We increase the number of heartbeats here because some code (e.g., `simp`) may spend a lot of time comparing
@@ -78,6 +62,10 @@ class expr_eq_fn {
         lean_inc_heartbeat();
         switch (a.kind()) {
         case expr_kind::BVar:
+        case expr_kind::Lit:
+        case expr_kind::MVar:
+        case expr_kind::FVar:
+        case expr_kind::Sort:
             lean_unreachable(); // LCOV_EXCL_LINE
         case expr_kind::MData:
             return
@@ -88,16 +76,10 @@ class expr_eq_fn {
                 apply(proj_expr(a), proj_expr(b)) &&
                 proj_sname(a) == proj_sname(b) &&
                 proj_idx(a) == proj_idx(b);
-        case expr_kind::Lit:
-            return lit_value(a) == lit_value(b);
         case expr_kind::Const:
             return
                 const_name(a) == const_name(b) &&
                 compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
-        case expr_kind::MVar:
-            return mvar_name(a) == mvar_name(b);
-        case expr_kind::FVar:
-            return fvar_name(a) == fvar_name(b);
         case expr_kind::App:
             check_system();
             return
@@ -117,15 +99,13 @@ class expr_eq_fn {
                 apply(let_value(a), let_value(b)) &&
                 apply(let_body(a), let_body(b)) &&
                 (!CompareBinderInfo || let_name(a) == let_name(b));
-        case expr_kind::Sort:
-            return sort_level(a) == sort_level(b);
         }
         lean_unreachable(); // LCOV_EXCL_LINE
     }
 public:
-    expr_eq_fn():m_cache(get_eq_cache()) {}
-    ~expr_eq_fn() { m_cache.clear(); }
-    bool operator()(expr const & a, expr const & b) { return apply(a, b); }
+    expr_eq_fn() {}
+    ~expr_eq_fn() { if (m_cache) delete m_cache; }
+    bool operator()(expr const & a, expr const & b) { return apply(a, b, true); }
 };
 
 bool is_equal(expr const & a, expr const & b) {
diff --git a/src/kernel/replace_fn.cpp b/src/kernel/replace_fn.cpp
index 65b9a07dc2..0dde49600e 100644
--- a/src/kernel/replace_fn.cpp
+++ b/src/kernel/replace_fn.cpp
@@ -14,7 +14,7 @@ namespace lean {
 class replace_rec_fn {
     struct key_hasher {
         std::size_t operator()(std::pair<lean_object *, unsigned> const & p) const {
-            return hash((size_t)p.first, p.second);
+            return hash((size_t)p.first >> 3, p.second);
         }
     };
     std::unordered_map<std::pair<lean_object *, unsigned>, expr, key_hasher> m_cache;
diff --git a/src/runtime/sharecommon.cpp b/src/runtime/sharecommon.cpp
index 47a3b80f41..53305df97d 100644
--- a/src/runtime/sharecommon.cpp
+++ b/src/runtime/sharecommon.cpp
@@ -4,10 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 
 Author: Leonardo de Moura
 */
-#include <vector>
 #include <cstring>
-#include <unordered_map>
-#include <unordered_set>
 #include "runtime/sharecommon.h"
 #include "runtime/hash.h"
 
@@ -294,6 +291,15 @@ lean_object * sharecommon_quick_fn::check_cache(lean_object * a) {
             it->second->m_rc++;
             return it->second;
         }
+        if (m_check_set) {
+            auto it = m_set.find(a);
+            if (it != m_set.end()) {
+                lean_object * result = *it;
+                lean_assert(lean_is_st(result));
+                result->m_rc++;
+                return result;
+            }
+        }
     }
     return nullptr;
 }
@@ -416,4 +422,14 @@ lean_object * sharecommon_quick_fn::visit(lean_object * a) {
 extern "C" LEAN_EXPORT obj_res lean_sharecommon_quick(obj_arg a) {
     return sharecommon_quick_fn()(a);
 }
+
+lean_object * sharecommon_persistent_fn::operator()(lean_object * e) {
+    lean_object * r = check_cache(e);
+    if (r != nullptr)
+        return r;
+    m_saved.push_back(object_ref(e, true));
+    r = visit(e);
+    m_saved.push_back(object_ref(r, true));
+    return r;
+}
 };
diff --git a/src/runtime/sharecommon.h b/src/runtime/sharecommon.h
index 1ac304182e..c88d632c9a 100644
--- a/src/runtime/sharecommon.h
+++ b/src/runtime/sharecommon.h
@@ -5,7 +5,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #pragma once
-#include "runtime/object.h"
+#include <vector>
+#include <unordered_map>
+#include <unordered_set>
+#include "runtime/object_ref.h"
 
 namespace lean {
 extern "C" LEAN_EXPORT uint8 lean_sharecommon_eq(b_obj_arg o1, b_obj_arg o2);
@@ -17,6 +20,7 @@ It optimizes the number of RC operations, the strategy for caching results,
 and uses C++ hashmap.
 */
 class sharecommon_quick_fn {
+protected:
     struct set_hash {
         std::size_t operator()(lean_object * o) const { return lean_sharecommon_hash(o); }
     };
@@ -31,6 +35,12 @@ class sharecommon_quick_fn {
     std::unordered_map<lean_object *, lean_object *> m_cache;
     /* Set of maximally shared terms. AKA hash-consing table. */
     std::unordered_set<lean_object *, set_hash, set_eq> m_set;
+    /*
+    If `true`, `check_cache` will also check `m_set`.
+    This is useful when the input term may contain terms that have already
+    been hashconsed.
+    */
+    bool m_check_set;
 
     lean_object * check_cache(lean_object * a);
     lean_object * save(lean_object * a, lean_object * new_a);
@@ -39,8 +49,23 @@ class sharecommon_quick_fn {
     lean_object * visit_ctor(lean_object * a);
     lean_object * visit(lean_object * a);
 public:
+    sharecommon_quick_fn(bool s = false):m_check_set(s) {}
+    void set_check_set(bool f) { m_check_set = f; }
     lean_object * operator()(lean_object * a) {
         return visit(a);
     }
 };
+
+/*
+Similar to `sharecommon_quick_fn`, but we save the entry points and result values to ensure
+they are not deleted.
+*/
+class sharecommon_persistent_fn : private sharecommon_quick_fn {
+    std::vector<object_ref> m_saved;
+public:
+    sharecommon_persistent_fn(bool s = false):sharecommon_quick_fn(s) {}
+    void set_check_set(bool f) { m_check_set = f; }
+    lean_object * operator()(lean_object * e);
+};
+
 };