# HG changeset patch
# User Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
# Date 1424352148 -32400
# Node ID 8d1325911030e6b2310a78f59eb6e12552005392
# Parent  65fdfe9c3997d99a178ec9c79bebdd204a6902a8
Mini fixes

diff -r 65fdfe9c3997 -r 8d1325911030 english_presentation/slide.md
--- a/english_presentation/slide.md	Thu Feb 19 20:24:16 2015 +0900
+++ b/english_presentation/slide.md	Thu Feb 19 22:22:28 2015 +0900
@@ -12,14 +12,14 @@
 # Formalization using Monad
 * Monad is a notion of Category theory
 * Monad represents meta computations in functional programming languages
-* We proposed delta monad representation of program modifications
+* We proposed Delta Monad representation of program modifications
 * We give definitions and the proof
-* Delta monad can be used with other monads
+* Delta Monad can be used with other monads
 
 # Merits of formalizing program modifications
 * Formal methods give verification of program based on mathematics and logics
 * Such as lambda calculus and corresponding proofs
-* Moggi[1990] , introduce Monad as notion of meta computation in program
+* Moggi[1989] , introduce Monad as notion of meta computation in program
 * A meta computation represented as a Monad has one to one mapping
 * We define program modification as meta computation which includes all modifications
 
@@ -50,8 +50,8 @@
 
 * ``data`` is a data type definition in Haskell
 * `` a `` is a type variable
-* `` Mono a`` has a type `` Delta a``
-* `` Delta a (Delta a) `` has a type ``Delta a``
+* `` Mono a`` and `` Delta a (Delta a) `` has a type `` Delta a``
+* Delta can be stores all modification like list structure
 
 # How to define meta computation in Haskell
 * original function : f  :: a -> b
@@ -80,7 +80,7 @@
 * Gives Delta Monad representation of the versions
 * Various computation can be possible in the Delta
 
-# numberCount (Version 1)
+# An Example Program: numberCount (Version 1)
 
 ```
 generator x     = [1..x]
@@ -90,7 +90,7 @@
 numberCount x = count (numberFilter (generator x))
 ```
 
-# numberCount (Version 2)
+# An Example Program: numberCount (Version 2)
 
 ```
 generator x     = [1..x]
@@ -110,10 +110,22 @@
 numberCount x = count =<< numberFilter =<< generator x
 ```
 
-# Combine Delta Monad and other Monads
-* TODO
+# Execution Program includes two version
+* result
+    * Version 1 : 168
+    * Version 2 : 500
 
-# Example
+```
+*Main> numberCount 1000
+Delta 500 (Mono 168)
+```
+
+# Combine Delta Monad with other Monads
+* Delta Monad can be used with other monads
+* Meta computations can be added function to Delta
+    * Exception, Logging , I/O
+
+# An Example Delta Monad with Traces
 ```
 *Main> numberCountM 10
 DeltaM (Delta (Writer (4, ["[1,2,3,4,5,6,7,8,9,10]",