refactor(library/data/{nat,int,rat}/{basic.lean,order.lean}: make algebra instance declarations local

library/data/int/basic.lean

@@ -1,8 +1,6 @@
 /-
 Copyright (c) 2014 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-
-Module: data.int.basic
 Authors: Floris van Doorn, Jeremy Avigad
 
 The integers, with addition, multiplication, and subtraction. The representation of the integers is
@@ -609,10 +607,10 @@ or_of_or_of_imp_of_imp H3
   (assume H : (nat_abs a) = nat.zero, nat_abs_eq_zero H)
   (assume H : (nat_abs b) = nat.zero, nat_abs_eq_zero H)
 
-section
+section migrate_algebra
   open [classes] algebra
 
-  protected definition integral_domain [instance] [reducible] : algebra.integral_domain int :=
+  protected definition integral_domain [reducible] : algebra.integral_domain int :=
   ⦃algebra.integral_domain,
     add            := add,
     add_assoc      := add.assoc,
@@ -632,6 +630,7 @@ section
     mul_comm       := mul.comm,
     eq_zero_or_eq_zero_of_mul_eq_zero := @eq_zero_or_eq_zero_of_mul_eq_zero⦄
 
+  local attribute int.integral_domain [instance]
   definition sub (a b : ℤ) : ℤ := algebra.sub a b
   infix - := int.sub
   definition dvd (a b : ℤ) : Prop := algebra.dvd a b
@@ -639,7 +638,7 @@ section
 
   migrate from algebra with int
   replacing sub → sub, dvd → dvd
-end
+end migrate_algebra
 
 /- additional properties -/
 

library/data/int/order.lean

@@ -1,8 +1,6 @@
 /-
 Copyright (c) 2014 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-
-Module: data.int.order
 Authors: Floris van Doorn, Jeremy Avigad
 
 The order relation on the integers. We show that int is an instance of linear_comm_ordered_ring
@@ -218,10 +216,10 @@ lt.intro
         ... = of_nat (succ (succ n * m + n))   : nat.add_succ
         ... = 0 + succ (succ n * m + n)        : zero_add))
 
-section
+section migrate_algebra
   open [classes] algebra
 
-  protected definition linear_ordered_comm_ring [instance] [reducible] :
+  protected definition linear_ordered_comm_ring [reducible] :
     algebra.linear_ordered_comm_ring int :=
   ⦃algebra.linear_ordered_comm_ring, int.integral_domain,
     le               := le,
@@ -237,12 +235,16 @@ section
     le_total         := le.total,
     zero_ne_one      := zero_ne_one⦄
 
-  protected definition decidable_linear_ordered_comm_ring [instance] [reducible] :
+  protected definition decidable_linear_ordered_comm_ring [reducible] :
     algebra.decidable_linear_ordered_comm_ring int :=
   ⦃algebra.decidable_linear_ordered_comm_ring,
     int.linear_ordered_comm_ring,
     decidable_lt := decidable_lt⦄
 
+  local attribute int.integral_domain [instance]
+  local attribute int.linear_ordered_comm_ring [instance]
+  local attribute int.decidable_linear_ordered_comm_ring [instance]
+
   definition ge [reducible] (a b : ℤ) := algebra.has_le.ge a b
   definition gt [reducible] (a b : ℤ) := algebra.has_lt.gt a b
   infix >= := int.ge
@@ -257,7 +259,7 @@ section
 
   migrate from algebra with int
   replacing has_le.ge → ge, has_lt.gt → gt, sign → sign, abs → abs, dvd → dvd, sub → sub
-end
+end migrate_algebra
 
 /- more facts specific to int -/
 

library/data/nat/basic.lean

@@ -290,7 +290,7 @@ nat.cases_on n
 section
   open [classes] algebra
 
-  protected definition comm_semiring [instance] [reducible] : algebra.comm_semiring nat :=
+  protected definition comm_semiring [reducible] : algebra.comm_semiring nat :=
   ⦃algebra.comm_semiring,
     add            := add,
     add_assoc      := add.assoc,
@@ -312,6 +312,7 @@ end
 
 section port_algebra
   open [classes] algebra
+  local attribute comm_semiring [instance]
   theorem mul.left_comm : ∀a b c : ℕ, a * (b * c) = b * (a * c) := algebra.mul.left_comm
   theorem mul.right_comm : ∀a b c : ℕ, (a * b) * c = (a * c) * b := algebra.mul.right_comm
 

library/data/nat/order.lean

@@ -143,8 +143,9 @@ le.intro !zero_add
 
 section
   open [classes] algebra
+  local attribute nat.comm_semiring [instance]
 
-  protected definition linear_ordered_semiring [instance] [reducible] :
+  protected definition linear_ordered_semiring [reducible] :
     algebra.linear_ordered_semiring nat :=
   ⦃ algebra.linear_ordered_semiring, nat.comm_semiring,
     add_left_cancel            := @add.cancel_left,
@@ -164,6 +165,11 @@ section
     mul_le_mul_of_nonneg_right := (take a b c H1 H2, mul_le_mul_right H1 c),
     mul_lt_mul_of_pos_left     := @mul_lt_mul_of_pos_left,
     mul_lt_mul_of_pos_right    := @mul_lt_mul_of_pos_right ⦄
+end
+
+section
+  open [classes] algebra
+  local attribute nat.linear_ordered_semiring [instance]
 
   migrate from algebra with nat
     replacing has_le.ge → ge, has_lt.gt → gt
@@ -172,6 +178,7 @@ end
 
 section port_algebra
   open [classes] algebra
+  local attribute nat.linear_ordered_semiring [instance]
   theorem add_pos_left : ∀{a : ℕ}, 0 < a → ∀b : ℕ, 0 < a + b :=
     take a H b, @algebra.add_pos_of_pos_of_nonneg _ _ a b H !zero_le
   theorem add_pos_right : ∀{a : ℕ}, 0 < a → ∀b : ℕ, 0 < b + a :=

library/data/rat/basic.lean

@@ -365,10 +365,10 @@ take a b, quot.rec_on_subsingleton₂ a b
 theorem inv_zero : inv 0 = 0 :=
 quot.sound (prerat.inv_zero' ▸ !prerat.equiv.refl)
 
-section
+section migrate_algebra
   open [classes] algebra
 
-  protected definition discrete_field [instance] [reducible] : algebra.discrete_field rat :=
+  protected definition discrete_field [reducible] : algebra.discrete_field rat :=
   ⦃algebra.discrete_field,
     add              := add,
     add_assoc        := add.assoc,
@@ -392,10 +392,12 @@ section
     inv_zero         := inv_zero,
     has_decidable_eq := has_decidable_eq⦄
 
+  local attribute rat.discrete_field [instance]
   definition divide (a b : rat) := algebra.divide a b
   definition dvd (a b : rat) := algebra.dvd a b
 
   migrate from algebra with rat
     replacing sub → rat.sub, divide → divide, dvd → dvd
-end
+
+end migrate_algebra
 end rat

library/data/rat/order.lean

@@ -202,10 +202,10 @@ have H : pos (a * b), from pos_mul (!sub_zero ▸ H1) (!sub_zero ▸ H2),
 definition decidable_lt [instance] : decidable_rel rat.lt :=
 take a b, decidable_pos (b - a)
 
-section
+section migrate_algebra
   open [classes] algebra
 
-  protected definition discrete_linear_ordered_field [instance] [reducible] :
+  protected definition discrete_linear_ordered_field [reducible] :
     algebra.discrete_linear_ordered_field rat :=
   ⦃algebra.discrete_linear_ordered_field,
     rat.discrete_field,
@@ -220,10 +220,12 @@ section
     mul_pos          := @mul_pos,
     decidable_lt     := @decidable_lt⦄
 
+  local attribute rat.discrete_field [instance]
+  local attribute rat.discrete_linear_ordered_field [instance]
   definition abs (n : rat) : rat := algebra.abs n
   definition sign (n : rat) : rat := algebra.sign n
 
   migrate from algebra with rat
-  replacing has_le.ge → ge, has_lt.gt → gt, sub → sub, abs → abs, sign → sign, dvd → dvd, divide → divide
+    replacing has_le.ge → ge, has_lt.gt → gt, sub → sub, abs → abs, sign → sign, dvd → dvd, divide → divide
-end
+end migrate_algebra
 end rat