--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/paper/src/subtype.agda	Mon Feb 06 10:32:49 2017 +0900
@@ -0,0 +1,44 @@
+open import Level
+open import Relation.Binary.PropositionalEquality
+
+module subtype {l : Level} (Context : Set l) where
+
+
+record DataSegment {ll : Level} (A : Set ll) : Set (l ⊔ ll) where
+  field
+    get : Context -> A
+    set : Context -> A -> Context
+open DataSegment
+
+data CodeSegment {l1 l2 : Level} (A : Set l1) (B : Set l2) : Set (l ⊔ l1 ⊔ l2) where
+  cs : {{_ : DataSegment A}} {{_ : DataSegment B}} -> (A -> B) -> CodeSegment A B
+
+goto : {l1 l2 : Level} {I : Set l1} {O : Set l2} -> CodeSegment I O -> I -> O
+goto (cs b) i = b i
+
+exec : {l1 l2 : Level} {I : Set l1} {O : Set l2} {{_ : DataSegment I}} {{_ : DataSegment O}}
+     -> CodeSegment I O -> Context -> Context
+exec {l} {{i}} {{o}}  (cs b) c = set o c (b (get i c))
+
+
+comp : {con : Context} -> {l1 l2 l3 l4 : Level}
+       {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
+       {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
+       -> (C -> D) -> (A -> B) -> A -> D
+comp {con} {{i}} {{io}} {{oi}} {{o}} g f x = g (get oi (set io con (f x)))
+
+csComp : {con : Context} -> {l1 l2 l3 l4 : Level}
+        {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
+         {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
+       -> CodeSegment C D -> CodeSegment A B -> CodeSegment A D
+csComp {con} {A} {B} {C} {D} {{da}} {{db}} {{dc}} {{dd}} (cs g) (cs f)
+      = cs {{da}} {{dd}} (comp {con} {{da}} {{db}} {{dc}} {{dd}} g f)
+
+
+
+comp-associative : {A B C D E F : Set l} {con : Context}
+                   {{da : DataSegment A}} {{db : DataSegment B}} {{dc : DataSegment C}}
+                   {{dd : DataSegment D}} {{de : DataSegment E}} {{df : DataSegment F}}
+                   -> (a : CodeSegment A B) (b : CodeSegment C D) (c : CodeSegment E F)
+                   -> csComp {con} c (csComp {con} b a)  ≡ csComp {con} (csComp {con} c b) a
+comp-associative (cs _) (cs _) (cs _) = refl