Mercurial > hg > Members > atton > agda-proofs

diff systemT/boolean.agda @ 1:fe247f476ecb

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Migrate systemT from atton/agda/systemT (13:5a81867278af)
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Sun, 02 Nov 2014 09:40:54 +0900
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/systemT/boolean.agda	Sun Nov 02 09:40:54 2014 +0900
@@ -0,0 +1,22 @@
+open import systemT
+open import Relation.Binary.PropositionalEquality
+
+module boolean where
+
+_and_ : Bool -> Bool -> Bool
+T and b = b
+F and _ = F
+
+_or_ : Bool -> Bool -> Bool
+T or _ = T
+F or b = b
+
+not : Bool -> Bool
+not T = F
+not F = T
+
+De-Morgan's-laws : (a b : Bool) -> (not a) and (not b) ≡ not (a or b)
+De-Morgan's-laws T T = refl
+De-Morgan's-laws T F = refl
+De-Morgan's-laws F T = refl
+De-Morgan's-laws F F = refl