feat(library/standard): add pairs

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

library/standard/pair.lean

@@ -0,0 +1,31 @@
+-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+-- Released under Apache 2.0 license as described in the file LICENSE.
+-- Author: Leonardo de Moura
+import logic
+
+inductive pair (A : Type) (B : Type) : Type :=
+| mk_pair : A → B → pair A B
+
+section
+  parameter {A : Type}
+  parameter {B : Type}
+
+  definition fst [inline] (p : pair A B) := pair_rec (λ x y, x) p
+  definition snd [inline] (p : pair A B) := pair_rec (λ x y, y) p
+
+  theorem pair_inhabited (H1 : inhabited A) (H2 : inhabited B) : inhabited (pair A B)
+  := inhabited_elim H1 (λ a, inhabited_elim H2 (λ b, inhabited_intro (mk_pair a b)))
+
+  theorem fst_mk_pair (a : A) (b : B) : fst (mk_pair a b) = a
+  := refl a
+
+  theorem snd_mk_pair (a : A) (b : B) : snd (mk_pair a b) = b
+  := refl b
+
+  theorem pair_ext (p : pair A B) : mk_pair (fst p) (snd p) = p
+  := pair_rec (λ x y, refl (mk_pair x y)) p
+end
+
+-- notation for n-ary tuples
+notation `(` h `,` t:(foldl `,` (e r, mk_pair r e) h) `)` := t
+

library/standard/standard.lean

@@ -1,2 +1,2 @@
-import logic tactic num string
+import logic tactic num string pair
 

tests/lean/run/ptst.lean

@@ -0,0 +1,4 @@
+import standard
+
+-- Test tuple notation
+check (3, false, 1, true)