--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/whileTestGears.agda	Fri Dec 14 19:34:16 2018 +0900
@@ -0,0 +1,90 @@
+module whileTestGears where
+
+open import Function
+open import Data.Nat
+open import Data.Bool hiding ( _≟_ ; _∧_)
+open import Level renaming ( suc to succ ; zero to Zero )
+open import Relation.Nullary using (¬_; Dec; yes; no)
+open import Relation.Binary.PropositionalEquality
+
+
+record Env  : Set where
+  field
+    varn : ℕ
+    vari : ℕ
+open Env
+
+_-_ : ℕ -> ℕ -> ℕ 
+x - zero  = x
+zero - _  = zero
+(suc x) - (suc y)  = x - y
+
+record _∧_ {n : Level } (a : Set n) (b : Set n): Set n where
+  field
+    pi1 : a
+    pi2 : b
+
+lt : ℕ -> ℕ -> Bool
+lt x y with (suc x ) ≤? y
+lt x y | yes p = true
+lt x y | no ¬p = false
+
+Equal : ℕ -> ℕ -> Bool
+Equal x y with x ≟ y
+Equal x y | yes p = true
+Equal x y | no ¬p = false
+
+whileTest : {l : Level} {t : Set l} -> (Code : Env -> t) -> t
+whileTest next = next (record {varn = 10 ; vari = 0} )
+
+{-# TERMINATING #-}
+whileLoop : {l : Level} {t : Set l} -> Env -> (Code : Env -> t) -> t
+whileLoop env next with lt 0 (varn env)
+whileLoop env next | false = next env
+whileLoop env next | true =
+    whileLoop (record {varn = (varn env) - 1 ; vari = (vari env) + 1}) next
+
+test1 : Env
+test1 = whileTest (λ env → whileLoop env (λ env1 → env1 ))
+
+
+proof1 : whileTest (λ env → whileLoop env (λ e → (vari e) ≡ 10 ))
+proof1 = refl
+
+
+record EnvWithCond : Set (succ Zero) where
+  field
+    input : Env
+    condition : Set
+    proof : condition
+open EnvWithCond
+
+
+
+-- stmt2Cond : {l : Level} → EnvWithCond {l} → 
+-- stmt2Cond env = (Equal (varn' env) 10) ∧ (Equal (vari' env) 0)
+
+whileTest' :  {t : Set}  -> (Code : (env : Env)  -> ((vari env) ≡ 0) ∧ ((varn env) ≡ 10) -> t) -> t
+whileTest' next = next env proof2
+  where
+    env : Env
+    env = record {vari = 0 ; varn = 10}
+    proof2 : ((vari env) ≡ 0) ∧ ((varn env) ≡ 10)
+    proof2 = record {pi1 = refl ; pi2 = refl}
+    
+{-# TERMINATING #-}
+whileLoop' : {t : Set} -> (env : Env) -> ((vari env) + (vari env) ≡ 10) -> (Code : Env -> t) -> t
+whileLoop' env proof next with lt 0 (varn  env)
+whileLoop' env proof next | false = next env 
+whileLoop' env proof next | true = whileLoop' env1 proof3 next
+    where
+      env1 = record {varn = (varn  env) - 1 ; vari = (vari env) + 1}
+      proof3 : vari env1 + vari env1 ≡ 10
+      proof3 = {!!}
+
+conversion1 : {t : Set} → (env : Env) -> ((vari env) ≡ 0) ∧ ((varn env) ≡ 10)
+              -> (Code : (env1 : Env) -> (vari env1 + vari env1 ≡ 10) -> t) -> t
+conversion1 = {!!}
+
+-- proofGears : whileLoop' {!!} {!!} {!!}
+-- proofGears = {!!}

--- a/whileTestPrim.agda	Fri Dec 14 16:26:49 2018 +0900
+++ b/whileTestPrim.agda	Fri Dec 14 19:34:16 2018 +0900
@@ -5,8 +5,7 @@
 open import Data.Bool hiding ( _≟_ )
 open import Level renaming ( suc to succ ; zero to Zero )
 open import Relation.Nullary using (¬_; Dec; yes; no)
-open import Relation.Binary.Core 
-
+open import Relation.Binary.PropositionalEquality
 
 
 record Env : Set where