# HG changeset patch
# User Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
# Date 1425016195 -32400
# Node ID b93e4b2aea9edece126b470827c0f42cfd2885dd
# Parent  575de2e3838563002d997ba7a429b20139264e04
Add prototype Delta for modification with type changes

diff -r 575de2e38385 -r b93e4b2aea9e modificationWithType/delta.agda
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/modificationWithType/delta.agda	Fri Feb 27 14:49:55 2015 +0900
@@ -0,0 +1,25 @@
+open import Function
+open import Level
+
+module delta where
+
+data Delta {l : Level} (A : Set l) {B : Set l} : Set l where
+  delta : A -> B -> Delta A {B}
+
+fst : {l : Level} {A B : Set l} -> Delta A {B} -> A
+fst (delta x _) = x
+
+eta : {l : Level} {A B : Set l} -> A -> {x' : B} -> Delta A {B}
+eta x {x'} = delta x x'
+
+
+bind : {l : Level} {A A' B B' X : Set l} -> {f' : A' -> B'}
+  -> Delta A {A'} -> (A -> Delta B {X}) -> Delta B {B'}
+bind {f' = f'} (delta x x') f = delta (fst (f x))  (f' x')
+
+mu : {l : Level} {A A' : Set l} -> Delta (Delta A {A'}) {A'} -> Delta A
+mu d = bind {f' = id} d id
+
+program : {l : Level} {A A' B B' C C' X : Set l} -> (x : Delta A {A'}) 
+  (f : A -> Delta B {X} ) -> {f' : A' -> B'} ->  (g : B -> Delta C {X}) -> {g' : B' -> C'} -> Delta C {C'}
+program x f {f'} g {g'} = bind {f' = g'} (bind {f' = f'} x f) g
\ No newline at end of file