fix(frontends/lean/structure_cmd): modify coercion generation

The previous coercion was more efficient, but the computation was
getting stuck when processing algebraic structures

src/frontends/lean/structure_cmd.cpp

@@ -628,16 +628,13 @@ struct structure_cmd_fn {
                 bi = mk_inst_implicit_binder_info();
             expr st                        = mk_local(m_ngen.next(), "s", st_type, bi);
             expr coercion_type             = infer_implicit(Pi(m_params, Pi(st, parent)), m_params.size(), true);;
-            levels rec_ls                  = levels(parent_rlvl, st_ls);
-            expr rec                       = mk_app(mk_constant(inductive::get_elim_name(m_name), rec_ls), m_params);
-            expr type_former               = Fun(st, parent);
-            rec                            = mk_app(rec, type_former);
-            expr minor_premise             = parent_intro;
-            for (unsigned idx : fmap)
-                minor_premise = mk_app(minor_premise, m_fields[idx]);
-            minor_premise                  = Fun(m_fields, minor_premise);
-            rec                            = mk_app(rec, minor_premise, st);
-            expr coercion_value            = Fun(m_params, Fun(st, rec));
+            expr coercion_value            = parent_intro;
+            for (unsigned idx : fmap) {
+                expr const & field = m_fields[idx];
+                expr proj          = mk_app(mk_app(mk_constant(m_name + mlocal_name(field), st_ls), m_params), st);
+                coercion_value     = mk_app(coercion_value, proj);
+            }
+            coercion_value                 = Fun(m_params, Fun(st, coercion_value));
             name coercion_name             = m_name + parent_name.append_before("to_");
 
             bool opaque                    = false;

tests/lean/run/group4.lean

@@ -0,0 +1,184 @@
+-- Copyright (c) 2014 Jeremy Avigad. All rights reserved.
+-- Released under Apache 2.0 license as described in the file LICENSE.
+-- Authors: Jeremy Avigad, Leonardo de Moura
+
+-- algebra.group
+-- =============
+
+-- Various structures with 1, *, inv, including groups.
+
+import logic.eq logic.connectives
+import data.unit data.sigma data.prod
+import algebra.function algebra.binary
+
+open eq
+
+namespace algebra
+
+structure has_mul [class] (A : Type) :=
+mk :: (mul : A → A → A)
+
+structure has_one [class] (A : Type) :=
+mk :: (one : A)
+
+structure has_inv [class] (A : Type) :=
+mk :: (inv : A → A)
+
+infixl `*`   := has_mul.mul
+postfix `⁻¹` := has_inv.inv
+notation 1   := has_one.one
+
+structure semigroup [class] (A : Type) extends has_mul A :=
+mk :: (assoc : ∀ a b c, mul (mul a b) c = mul a (mul b c))
+
+set_option pp.notation false
+-- set_option pp.implicit true
+-- set_option pp.coercions true
+print instances has_mul
+
+section
+  variables {A : Type} [s : semigroup A]
+  include s
+  variables a b : A
+
+  example : a * b = semigroup.mul a b :=
+  rfl
+
+  theorem mul_assoc (a b c : A) : a * b * c = a * (b * c) :=
+    semigroup.assoc a b c
+end
+
+structure comm_semigroup [class] (A : Type) extends semigroup A :=
+mk :: (comm : ∀a b, mul a b = mul b a)
+
+namespace comm_semigroup
+  variables {A : Type} [s : comm_semigroup A]
+  include s
+  variables a b c : A
+  theorem mul_comm : a * b = b * a := !comm_semigroup.comm
+
+  theorem mul_left_comm : a * (b * c) = b * (a * c) :=
+    binary.left_comm mul_comm mul_assoc a b c
+end comm_semigroup
+
+structure monoid [class] (A : Type) extends semigroup A, has_one A:=
+mk :: (right_id : ∀a, mul a one = a) (left_id : ∀a, mul one a = a)
+
+section
+  variables {A : Type} [s : monoid A]
+  variable a : A
+  include s
+
+  theorem mul_right_id : a * 1 = a := !monoid.right_id
+  theorem mul_left_id  : 1 * a = a := !monoid.left_id
+end
+
+exit
+structure comm_monoid [class] (A : Type) extends monoid A, comm_semigroup A :=
+mk ::
+
+exit
+
+namespace comm_monoid
+  section
+  variables {A : Type} [s : comm_monoid A]
+  variables a b c : A
+  definition mul := comm_monoid.rec (λmul one assoc right_id left_id comm, mul) s a b
+  definition one := comm_monoid.rec (λmul one assoc right_id left_id comm, one) s
+  definition assoc : mul (mul a b) c = mul a (mul b c) :=
+    comm_monoid.rec (λmul one assoc right_id left_id comm, assoc) s a b c
+  definition right_id : mul a one = a :=
+    comm_monoid.rec (λmul one assoc right_id left_id comm, right_id) s a
+  definition left_id : mul one a = a :=
+    comm_monoid.rec (λmul one assoc right_id left_id comm, left_id) s a
+  definition comm : mul a b = mul b a :=
+    comm_monoid.rec (λmul one assoc right_id left_id comm, comm) s a b
+  end
+end comm_monoid
+
+section
+  variables {A : Type} [s : comm_monoid A]
+  include s
+  definition comm_monoid_monoid [instance] : monoid A :=
+    monoid.mk comm_monoid.mul comm_monoid.one comm_monoid.assoc
+              comm_monoid.right_id comm_monoid.left_id
+  definition comm_monoid_comm_semigroup [instance] : comm_semigroup A :=
+    comm_semigroup.mk comm_monoid.mul comm_monoid.assoc comm_monoid.comm
+end
+
+-- bundled structures
+-- ------------------
+
+inductive Semigroup [class] : Type := mk : Π carrier : Type, semigroup carrier → Semigroup
+section
+  variable S : Semigroup
+  definition Semigroup.carrier [coercion] : Type := Semigroup.rec (λc s, c) S
+  definition Semigroup.struc   [instance] : semigroup S := Semigroup.rec (λc s, s) S
+end
+
+inductive CommSemigroup [class] : Type :=
+  mk : Π carrier : Type, comm_semigroup carrier → CommSemigroup
+section
+  variable S : CommSemigroup
+  definition CommSemigroup.carrier [coercion] : Type := CommSemigroup.rec (λc s, c) S
+  definition CommSemigroup.struc [instance] : comm_semigroup S := CommSemigroup.rec (λc s, s) S
+end
+
+inductive Monoid [class] : Type := mk : Π carrier : Type, monoid carrier → Monoid
+section
+  variable S : Monoid
+  definition Monoid.carrier [coercion] : Type := Monoid.rec (λc s, c) S
+  definition Monoid.struc [instance] : monoid S := Monoid.rec (λc s, s) S
+end
+
+inductive CommMonoid : Type := mk : Π carrier : Type, comm_monoid carrier → CommMonoid
+section
+  variable S : CommMonoid
+  definition CommMonoid.carrier [coercion] : Type := CommMonoid.rec (λc s, c) S
+  definition CommMonoid.struc [instance] : comm_monoid S := CommMonoid.rec (λc s, s) S
+end
+end algebra
+
+open algebra
+
+section examples
+
+theorem test1 {S : Semigroup} (a b c d : S) : a * (b * c) * d = a * b * (c * d) :=
+calc
+  a * (b * c) * d = a * b * c * d   : {symm !mul_assoc}
+              ... = a * b * (c * d) : !mul_assoc
+
+theorem test2 {M : CommSemigroup} (a b : M) : a * b = a * b := rfl
+
+theorem test3 {M : Monoid} (a b c d : M) : a * (b * c) * d = a * b * (c * d) :=
+calc
+  a * (b * c) * d = a * b * c * d   : {symm !mul_assoc}
+              ... = a * b * (c * d) : !mul_assoc
+
+-- for test4b to work, we need instances at the level of the bundled structures as well
+definition Monoid_Semigroup [instance] (M : Monoid) : Semigroup :=
+Semigroup.mk (Monoid.carrier M) _
+
+theorem test4 {M : Monoid} (a b c d : M) : a * (b * c) * d = a * b * (c * d) :=
+test1 a b c d
+
+theorem test5 {M : Monoid} (a b c : M) : a * 1 * b * c = a * (b * c) :=
+calc
+  a * 1 * b * c = a * b * c   : {!mul_right_id}
+            ... = a * (b * c) : !mul_assoc
+
+theorem test5a {M : Monoid} (a b c : M) : a * 1 * b * c = a * (b * c) :=
+calc
+  a * 1 * b * c = a * b * c   : {!mul_right_id}
+            ... = a * (b * c) : !mul_assoc
+
+theorem test5b {A : Type} {M : monoid A} (a b c : A) : a * 1 * b * c = a * (b * c) :=
+calc
+  a * 1 * b * c = a * b * c   : {!mul_right_id}
+            ... = a * (b * c) : !mul_assoc
+
+theorem test6 {M : CommMonoid} (a b c : M) : a * 1 * b * c = a * (b * c) :=
+calc
+  a * 1 * b * c = a * b * c   : {!mul_right_id}
+            ... = a * (b * c) : !mul_assoc
+end examples