fix(library/init/{prod,sigma},library/data/sum): move notation in/out of namespaces

library/data/sum.lean

@@ -11,9 +11,9 @@ import logic.connectives
 open inhabited eq.ops
 
 notation A ⊎ B := sum A B
-notation A + B := sum A B
 
 namespace sum
+  notation A + B := sum A B
   namespace low_precedence_plus
     reserve infixr `+`:25  -- conflicts with notation for addition
     infixr `+` := sum

library/init/datatypes.lean

@@ -69,6 +69,9 @@ or.inl Ha
 definition or.intro_right (a : Prop) {b : Prop} (Hb : b) : or a b :=
 or.inr Hb
 
+structure sigma {A : Type} (B : A → Type) :=
+mk :: (pr1 : A) (pr2 : B pr1)
+
 -- pos_num and num are two auxiliary datatypes used when parsing numerals such as 13, 0, 26.
 -- The parser will generate the terms (pos (bit1 (bit1 (bit0 one)))), zero, and (pos (bit0 (bit1 (bit1 one)))).
 -- This representation can be coerced in whatever we want (e.g., naturals, integers, reals, etc).

library/init/prod.lean

@@ -9,21 +9,21 @@ prelude
 import init.num init.wf
 
 definition pair := @prod.mk
+notation A × B := prod A B
+-- notation for n-ary tuples
+notation `(` h `,` t:(foldl `,` (e r, prod.mk r e) h) `)` := t
 
 namespace prod
   notation A * B := prod A B
-  notation A × B := prod A B
+  notation A × B := prod A B  -- repeat, so this takes precedence
   namespace low_precedence_times
-    reserve infixr `*`:30  -- conflicts with notation for multiplication
+    reserve infixr `*`:30     -- conflicts with notation for multiplication
     infixr `*` := prod
   end low_precedence_times
 
   notation `pr₁` := pr1
   notation `pr₂` := pr2
 
-  -- notation for n-ary tuples
-  notation `(` h `,` t:(foldl `,` (e r, prod.mk r e) h) `)` := t
-
   namespace ops
   postfix `.1`:(max+1) := pr1
   postfix `.2`:(max+1) := pr2

library/init/sigma.lean

@@ -6,21 +6,16 @@ Module: init.sigma
 Author: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
 -/
 prelude
-import init.num init.wf init.logic init.tactic
-
-structure sigma {A : Type} (B : A → Type) :=
-mk :: (pr1 : A) (pr2 : B pr1)
+import init.datatypes init.num init.wf init.logic init.tactic
 
 definition dpair := @sigma.mk
-definition dpr1 := @sigma.pr1
-definition dpr2 := @sigma.pr2
-
 notation `Σ` binders `,` r:(scoped P, sigma P) := r
+-- notation for n-ary tuples; input ⟨ ⟩ as \< \>
+notation `⟨`:max t:(foldr `,` (e r, sigma.mk e r)) `⟩`:0 := t
 
 namespace sigma
   notation `pr₁`  := pr1
   notation `pr₂`  := pr2
-  notation `⟨`:max t:(foldr `,` (e r, mk e r)) `⟩`:0 := t --input ⟨ ⟩ as \< \>
 
   namespace ops
   postfix `.1`:(max+1) := pr1