feat(library/definitional/projection): use strict implicit inference, closes #344

library/algebra/group.lean

@@ -42,8 +42,8 @@ infixl `*`   := has_mul.mul
 infixl `+`   := has_add.add
 postfix `⁻¹` := has_inv.inv
 prefix `-`   := has_neg.neg
-notation 1   := has_one.one
-notation 0   := has_zero.zero
+notation 1   := !has_one.one
+notation 0   := !has_zero.zero
 
 
 /- semigroup -/

library/algebra/ordered_group.lean

@@ -161,7 +161,7 @@ structure ordered_comm_group [class] (A : Type) extends add_comm_group A, order_
 
 definition ordered_comm_group.to_ordered_cancel_comm_monoid [instance] (A : Type)
     [s : ordered_comm_group A] : ordered_cancel_comm_monoid A :=
-ordered_cancel_comm_monoid.mk has_add.add add_assoc has_zero.zero add_left_id add_right_id add_comm
+ordered_cancel_comm_monoid.mk has_add.add add_assoc !has_zero.zero add_left_id add_right_id add_comm
 (@add_left_cancel _ _) (@add_right_cancel _ _) has_le.le le_refl (@le_trans _ _) (@le_antisym _ _)
 has_lt.lt (@lt_iff_le_ne _ _) ordered_comm_group.add_le_left
 proof

library/algebra/ring.lean

@@ -38,8 +38,7 @@ theorem mul_zero_right [s : mul_zero A] (a : A) : a * 0 = 0 := !mul_zero.mul_zer
 structure zero_ne_one_class [class] (A : Type) extends has_zero A, has_one A :=
 (zero_ne_one : zero ≠ one)
 
-theorem zero_ne_one [s: zero_ne_one_class A] : 0 ≠ 1 := zero_ne_one_class.zero_ne_one
-
+theorem zero_ne_one [s: zero_ne_one_class A] : 0 ≠ 1 := !zero_ne_one_class.zero_ne_one
 
 /- semiring -/
 structure semiring [class] (A : Type) extends add_comm_monoid A, monoid A, distrib A, mul_zero A,
@@ -150,9 +149,9 @@ end comm_semiring_dvd
 structure ring [class] (A : Type) extends add_comm_group A, monoid A, distrib A, zero_ne_one_class A
 
 definition ring.to_semiring [instance] [s : ring A] : semiring A :=
-semiring.mk ring.add ring.add_assoc ring.zero ring.add_left_id
+semiring.mk ring.add ring.add_assoc !ring.zero ring.add_left_id
   add_right_id   -- note: we've shown that add_right_id follows from add_left_id in add_comm_group
-  ring.add_comm ring.mul ring.mul_assoc ring.one ring.mul_left_id ring.mul_right_id
+  ring.add_comm ring.mul ring.mul_assoc !ring.one ring.mul_left_id ring.mul_right_id
   ring.distrib_left ring.distrib_right
   (take a,
     have H : 0 * a  + 0 = 0 * a + 0 * a, from
@@ -168,7 +167,7 @@ semiring.mk ring.add ring.add_assoc ring.zero ring.add_left_id
           ... = a * (0 + 0) : add_right_id
           ... = a * 0 + a * 0 : ring.distrib_left,
     show a * 0 = 0, from  (add_left_cancel H)⁻¹)
-  ring.zero_ne_one
+  !ring.zero_ne_one
 
 section
 
@@ -224,8 +223,8 @@ end
 structure comm_ring [class] (A : Type) extends ring A, comm_semigroup A
 
 definition comm_ring.to_comm_semiring [instance] [s : comm_ring A] : comm_semiring A :=
-comm_semiring.mk has_add.add add_assoc has_zero.zero add_left_id add_right_id add_comm
-  has_mul.mul mul_assoc has_one.one mul_left_id mul_right_id distrib_left distrib_right
+comm_semiring.mk has_add.add add_assoc !has_zero.zero add_left_id add_right_id add_comm
+  has_mul.mul mul_assoc !has_one.one mul_left_id mul_right_id distrib_left distrib_right
   mul_zero_left mul_zero_right zero_ne_one mul_comm
 
 section
@@ -244,8 +243,8 @@ end
 structure comm_ring_dvd [class] (A : Type) extends comm_ring A, has_dvd A
 
 definition comm_ring_dvd.to_comm_semiring_dvd [instance] [s : comm_ring_dvd A] : comm_semiring_dvd A :=
-comm_semiring_dvd.mk has_add.add add_assoc has_zero.zero add_left_id add_right_id add_comm
-  has_mul.mul mul_assoc has_one.one mul_left_id mul_right_id distrib_left distrib_right
+comm_semiring_dvd.mk has_add.add add_assoc !has_zero.zero add_left_id add_right_id add_comm
+  has_mul.mul mul_assoc !has_one.one mul_left_id mul_right_id distrib_left distrib_right
   mul_zero_left mul_zero_right zero_ne_one mul_comm dvd (@dvd_intro A s) (@dvd_imp_exists A s)
 
 section

library/hott/trunc.lean

@@ -81,11 +81,11 @@ namespace truncation
   -- maybe rename to is_trunc_succ.mk
   definition is_trunc_succ (A : Type) {n : trunc_index} [H : ∀x y : A, is_trunc n (x ≈ y)]
     : is_trunc n.+1 A :=
-  is_trunc.mk (λ x y, is_trunc.to_internal)
+  is_trunc.mk (λ x y, !is_trunc.to_internal)
 
   -- maybe rename to is_trunc_succ.elim
   definition succ_is_trunc {n : trunc_index} [H : is_trunc (n.+1) A] (x y : A) : is_trunc n (x ≈ y) :=
-  is_trunc.mk (is_trunc.to_internal x y)
+  is_trunc.mk (!is_trunc.to_internal x y)
 
   /- contractibility -/
 
@@ -93,10 +93,10 @@ namespace truncation
   is_trunc.mk (contr_internal.mk center contr)
 
   definition center (A : Type) [H : is_contr A] : A :=
-  @contr_internal.center A is_trunc.to_internal
+  @contr_internal.center A !is_trunc.to_internal
 
   definition contr [H : is_contr A] (a : A) : !center ≈ a :=
-  @contr_internal.contr A is_trunc.to_internal a
+  @contr_internal.contr A !is_trunc.to_internal a
 
   definition path_contr [H : is_contr A] (x y : A) : x ≈ y :=
   contr x⁻¹ ⬝ (contr y)

src/library/definitional/projection.cpp

@@ -107,7 +107,7 @@ environment mk_projections(environment const & env, name const & n, buffer<name>
         rec_args.push_back(major_premise);
         expr rec_app      = mk_app(rec, rec_args);
         expr proj_type    = Pi(proj_args, result_type);
-        bool strict       = false;
+        bool strict       = true;
         proj_type         = infer_implicit(proj_type, nparams, strict);
         expr proj_val     = Fun(proj_args, rec_app);
         bool opaque       = false;

tests/lean/run/group4.lean

@@ -26,7 +26,7 @@ mk :: (inv : A → A)
 
 infixl `*`   := has_mul.mul
 postfix `⁻¹` := has_inv.inv
-notation 1   := has_one.one
+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))

tests/lean/run/group5.lean

@@ -26,7 +26,7 @@ structure has_inv [class] (A : Type) :=
 
 infixl `*`   := has_mul.mul
 postfix `⁻¹` := has_inv.inv
-notation 1   := has_one.one
+notation 1   := !has_one.one
 
 structure semigroup [class] (A : Type) extends has_mul A :=
 (assoc : ∀ a b c, mul (mul a b) c = mul a (mul b c))