# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1572195505 -32400
# Node ID 6d50a933bcb3d9c3a78849dda0d5fd0bb549957e
# Parent  64ea7d12894cc8a41ffc0b07bda4b0e2fb7c586b
add puzzle

diff -r 64ea7d12894c -r 6d50a933bcb3 agda/puzzle.agda
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/agda/puzzle.agda	Mon Oct 28 01:58:25 2019 +0900
@@ -0,0 +1,117 @@
+module puzzle where
+
+---- 仮定
+-- 猫か犬を飼っている人は山羊を飼ってない
+-- 猫を飼ってない人は、犬かウサギを飼っている
+-- 猫も山羊も飼っていない人は、ウサギを飼っている
+--
+---- 問題
+-- 山羊を飼っている人は、犬を飼っていない
+-- 山羊を飼っている人は、ウサギを飼っている
+-- ウサギを飼っていない人は、猫を飼っている
+
+module pet-research where
+  open import logic
+  open import Relation.Nullary
+  open import Data.Empty
+
+  postulate 
+     lem : (a : Set) → a ∨ ( ¬ a )
+
+  record PetResearch ( Cat Dog Goat Rabbit : Set ) : Set where
+     field
+        fact1 : ( Cat ∨ Dog ) → ¬ Goat
+        fact2 : ¬ Cat →  ( Dog ∨ Rabbit )
+        fact3 : ¬ ( Cat ∨ Goat ) →  Rabbit
+
+  module tmp ( Cat Dog Goat Rabbit : Set ) (p :  PetResearch  Cat Dog Goat Rabbit ) where
+
+    open PetResearch
+
+    problem0 : Cat ∨ Dog ∨ Goat ∨ Rabbit
+    problem0 with lem Cat | lem Goat
+    ... | case1 c | g = case1 c
+    ... | c | case1 g = case2 ( case2 ( case1 g ) )
+    ... | case2 ¬c | case2 ¬g  = case2 ( case2 ( case2 ( fact3 p lemma1 ))) where
+        lemma1 : ¬ ( Cat ∨ Goat )
+        lemma1 (case1 c) = ¬c c
+        lemma1 (case2 g) = ¬g g
+
+    problem1 : Goat → ¬ Dog
+    problem1 g d = ⊥-elim ( fact1 p (case2 d) g )
+  
+    problem2 : Goat → Rabbit
+    problem2 g with lem Cat | lem Dog
+    problem2 g | case1 c | d = ⊥-elim ( fact1 p (case1 c ) g )
+    problem2 g | case2 ¬c | case1 d = ⊥-elim ( fact1 p (case2 d ) g )
+    problem2 g | case2 ¬c | case2 ¬d with fact3 p | lem Rabbit
+    ... | _  | case1  r = r
+    ... | f3 | case2 ¬r = f3 lemma2 where
+        lemma2 : Cat ∨ Goat → ⊥
+        lemma2 (case1 c) = ¬c c
+        lemma2 (case2 g) with fact2 p ¬c
+        lemma2 (case2 g) | case1 d = ¬d d
+        lemma2 (case2 g) | case2 r = ¬r r
+  
+    problem3 : (¬ Rabbit ) → Cat
+    problem3 ¬r with lem Cat | lem Goat 
+    problem3 ¬r | case1 c | g = c
+    problem3 ¬r | case2 ¬c | g = ⊥-elim ( ¬r ( fact3 p lemma3 )) where
+       lemma3 :  ¬ ( Cat ∨ Goat )
+       lemma3 (case1 c) = ¬c c
+       lemma3 (case2 g) with fact2 p ¬c
+       lemma3 (case2 g) | case1 d = fact1 p (case2 d ) g
+       lemma3 (case2 g) | case2 r = ¬r r
+
+module pet-research1 ( Cat Dog Goat Rabbit : Set ) where
+
+  open import Data.Bool
+  open import Relation.Binary
+  open import Relation.Binary.PropositionalEquality 
+
+  _=>_ :  Bool → Bool → Bool
+  _ => true = true
+  false => _ = true
+  true => false = false
+
+  ¬_ : Bool → Bool
+  ¬ p = not p
+
+  problem0 :  ( Cat Dog Goat Rabbit : Bool ) →
+    ((( Cat ∨ Dog ) => (¬ Goat) ) ∧ ( (¬ Cat ) =>  ( Dog ∨ Rabbit ) ) ∧ ( ( ¬ ( Cat ∨ Goat ) ) =>  Rabbit ) )
+    => (Cat ∨ Dog ∨ Goat ∨ Rabbit) ≡ true
+  problem0 true d g r = refl
+  problem0 false true g r = refl
+  problem0 false false true r = refl
+  problem0 false false false true = refl
+  problem0 false false false false = refl
+
+  problem1 :  ( Cat Dog Goat Rabbit : Bool ) →
+    ((( Cat ∨ Dog ) => (¬ Goat) ) ∧ ( (¬ Cat ) =>  ( Dog ∨ Rabbit ) ) ∧ ( ( ¬ ( Cat ∨ Goat ) ) =>  Rabbit ) )
+    => ( Goat => ( ¬ Dog )) ≡ true
+  problem1 c false false r = refl
+  problem1 c true false r = refl
+  problem1 c false true r = refl
+  problem1 false true true r = refl
+  problem1 true true true r = refl
+
+  problem2 :  ( Cat Dog Goat Rabbit : Bool ) →
+    ((( Cat ∨ Dog ) => (¬ Goat) ) ∧ ( (¬ Cat ) =>  ( Dog ∨ Rabbit ) ) ∧ ( ( ¬ ( Cat ∨ Goat ) ) =>  Rabbit ) )
+    => ( Goat => Rabbit ) ≡ true
+  problem2 c d false false = refl
+  problem2 c d false true = refl
+  problem2 c d true true = refl
+  problem2 true d true false = refl
+  problem2 false false true false = refl
+  problem2 false true true false = refl
+
+  problem3 :  ( Cat Dog Goat Rabbit : Bool ) →
+    ((( Cat ∨ Dog ) => (¬ Goat) ) ∧ ( (¬ Cat ) =>  ( Dog ∨ Rabbit ) ) ∧ ( ( ¬ ( Cat ∨ Goat ) ) =>  Rabbit ) )
+    => ( (¬ Rabbit ) => Cat ) ≡ true
+  problem3 false d g true = refl 
+  problem3 true d g true = refl
+  problem3 true d g false = refl
+  problem3 false false false false = refl
+  problem3 false false true false = refl
+  problem3 false true false false = refl
+  problem3 false true true false = refl