From 21c41f50ea0db5bd91e4821e5a8b539f14fbee7c Mon Sep 17 00:00:00 2001
From: Leonardo de Moura <leonardo@microsoft.com>
Date: Mon, 17 Aug 2015 14:54:05 -0700
Subject: [PATCH] fix(frontends/lean/elaborator): fixes #803

---
 src/frontends/lean/elaborator.cpp | 40 +++++++++++++++++++++----------
 src/frontends/lean/elaborator.h   |  2 +-
 tests/lean/run/803.lean           | 25 +++++++++++++++++++
 3 files changed, 54 insertions(+), 13 deletions(-)
 create mode 100644 tests/lean/run/803.lean

diff --git a/src/frontends/lean/elaborator.cpp b/src/frontends/lean/elaborator.cpp
index 23c12126e..73229c5d9 100644
--- a/src/frontends/lean/elaborator.cpp
+++ b/src/frontends/lean/elaborator.cpp
@@ -544,32 +544,47 @@ bool elaborator::has_coercions_to(expr d_type) {
     }
 }
 
-expr elaborator::apply_coercion(expr const & a, expr a_type, expr d_type) {
+pair<expr, constraint_seq> elaborator::apply_coercion(expr const & a, expr a_type, expr d_type, justification const & j) {
     a_type = m_coercion_from_tc->whnf(a_type).first;
     d_type = m_coercion_to_tc->whnf(d_type).first;
     constraint_seq aux_cs;
     list<expr> coes = get_coercions_from_to(*m_coercion_from_tc, *m_coercion_to_tc, a_type, d_type, aux_cs, m_ctx.m_lift_coercions);
     if (is_nil(coes)) {
         erase_coercion_info(a);
-        return a;
+        return to_ecs(a);
     } else if (is_nil(tail(coes))) {
         expr r = mk_coercion_app(head(coes), a);
         save_coercion_info(a, r);
-        return r;
+        return to_ecs(r);
     } else {
+        optional<expr> r;
         for (expr const & coe : coes) {
-            expr r = mk_coercion_app(coe, a);
-            expr r_type = infer_type(r).first;
+            expr new_r = mk_coercion_app(coe, a);
+            expr new_r_type = infer_type(new_r).first;
             try {
-                if (m_tc->is_def_eq(r_type, d_type).first) {
-                    save_coercion_info(a, r);
-                    return r;
+                if (m_tc->is_def_eq(new_r_type, d_type).first) {
+                    if (!r) {
+                        r = new_r;
+                    } else {
+                        // More than one coercion seems to be applicable.
+                        // This can happen when the types new_r_type and d_type contain
+                        // metavariables. That is, we don't have sufficient information
+                        // to decide which one should be used.
+                        // So, we switch to the delayed_coercions approach.
+                        // See issue #803
+                        return mk_delayed_coercion(a, a_type, d_type, j);
+                    }
                 }
             } catch (exception&) {
             }
         }
-        erase_coercion_info(a);
-        return a;
+        if (r) {
+            save_coercion_info(a, *r);
+            return to_ecs(*r);
+        } else {
+            erase_coercion_info(a);
+            return to_ecs(a);
+        }
     }
 }
 
@@ -603,8 +618,9 @@ pair<expr, constraint_seq> elaborator::ensure_has_type_core(
         if (dcs.first) {
             return to_ecs(a, dcs.second);
         } else {
-            expr new_a = apply_coercion(a, a_type, expected_type);
-            constraint_seq cs;
+            auto new_a_cs = apply_coercion(a, a_type, expected_type, j);
+            expr new_a    = new_a_cs.first;
+            constraint_seq cs = new_a_cs.second;
             bool coercion_worked = false;
             if (!is_eqp(a, new_a)) {
                 expr new_a_type = infer_type(new_a, cs);
diff --git a/src/frontends/lean/elaborator.h b/src/frontends/lean/elaborator.h
index e16aa86c2..7b08b5a81 100644
--- a/src/frontends/lean/elaborator.h
+++ b/src/frontends/lean/elaborator.h
@@ -124,7 +124,7 @@ class elaborator : public coercion_info_manager {
     pair<expr, expr> ensure_fun(expr f, constraint_seq & cs);
     bool has_coercions_from(expr const & a_type, bool & lifted_coe);
     bool has_coercions_to(expr d_type);
-    expr apply_coercion(expr const & a, expr a_type, expr d_type);
+    pair<expr, constraint_seq> apply_coercion(expr const & a, expr a_type, expr d_type, justification const & j);
     pair<expr, constraint_seq> mk_delayed_coercion(expr const & a, expr const & a_type, expr const & expected_type,
                                                    justification const & j);
     pair<expr, constraint_seq> ensure_has_type_core(expr const & a, expr const & a_type, expr const & expected_type,
diff --git a/tests/lean/run/803.lean b/tests/lean/run/803.lean
new file mode 100644
index 000000000..a2b65dc65
--- /dev/null
+++ b/tests/lean/run/803.lean
@@ -0,0 +1,25 @@
+import data.matrix
+open algebra fin nat
+
+namespace matrix
+
+definition vector [reducible] (A : Type) (n : nat) := fin n → A
+
+definition to_cvec [reducible] [coercion] {A : Type} {n : nat} (v : vector A n)
+: matrix A n 1 := λ i o, v i
+
+definition to_rvec [reducible] [coercion] {A : Type} {n : nat} (v : vector A n)
+: matrix A 1 n := λ o i, v i
+
+variables (A : Type) (n : nat)
+variable [r : comm_ring A]
+include r
+variables (M : matrix A n n) (v : vector A n)
+
+print "----------------"
+
+check matrix.mul M v
+check (λ f, f v) (matrix.mul M)
+check (λ v, matrix.mul M v) v
+
+end matrix