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diff --git a/Gentle_introduction_Inpla.md b/Gentle_introduction_Inpla.md index 0903a6f..e2617d1 100644 --- a/Gentle_introduction_Inpla.md +++ b/Gentle_introduction_Inpla.md @@ -688,31 +688,31 @@ it merges two lists into one. Merger agent has two principal ports that can take ``` ### Map and reduce functions -* **Lambda and Application like computation**: We can leave an interaction later by using a couple of Tuple2 agents. For instance, an destructor agent `foo` whose arity is 1 can be abstracted as `(r, foo(r))`, and we can give a constructor `s` later: +* **Lambda-application-like computation**: We can leave an interaction later by using a couple of Tuple2 agents. For instance, an destructor agent `foo` whose arity is 1 can be abstracted as `(r, foo(r))`, and we can give a constructor `s` later: ``` (r, foo(r)) >< (result, s) -->* foo(result)~s. // where the following rule has been defined as a built-in: // (a1,a2) ><> (b1,b2) => a1~b1, a2~b2. ``` - So, the map function can be realised: +* **Map function operation**: So, the map function operation can be realised by a built-in `Map` agent with the following already defined rules: ``` - map(result, f) >< [] => result~[], Eraser~f; - map(result, f) >< x:xs => Dup(f1,f2)~f, + Map(result, f) >< [] => result~[], Eraser~f; + Map(result, f) >< x:xs => Dup(f1,f2)~f, result~w:ws, - f1 ~ (w, x), map(ws, f2)~xs; + f1 ~ (w, x), Map(ws, f2)~xs; ``` Actually, by using the incrementor `inc` we can add one to each list element: ``` inc(r)><(int i) => r~(i+1); - map( result, (r,inc(r)) ) ~ [10,20,30] - --> Dup(f1,f2)~(r,inc(r)), result~w:ws, f1~(w,10), map(ws,f2)~[20,30] - -->* result~w:ws, (r1,inc(r1))~(w,10), map( ws, (r2,inc(r2)) )~[20,30] - -->* result~w:ws, inc(w)~10, map( ws, (r2,inc(r2)) )~[20,30] - --> result~w:ws, w~11, map(ws, (r2,inc(r2)) )~[20,30] - --> result~11:ws, map(ws, (r2,inc(r2)) )~[20,30] - -->* result~11:21:ws, map(ws, (r3,inc(r3)) )~[30] - -->* result~11:21:31:ws, map(ws, (r4,inc(r4)) )~[] + Map( result, (r,inc(r)) ) ~ [10,20,30] + --> Dup(f1,f2)~(r,inc(r)), result~w:ws, f1~(w,10), Map(ws,f2)~[20,30] + -->* result~w:ws, (r1,inc(r1))~(w,10), Map( ws, (r2,inc(r2)) )~[20,30] + -->* result~w:ws, inc(w)~10, Map( ws, (r2,inc(r2)) )~[20,30] + --> result~w:ws, w~11, Map(ws, (r2,inc(r2)) )~[20,30] + --> result~11:ws, Map(ws, (r2,inc(r2)) )~[20,30] + -->* result~11:21:ws, Map(ws, (r3,inc(r3)) )~[30] + -->* result~11:21:31:ws, Map(ws, (r4,inc(r4)) )~[] -->* result~[11,21,31]; ``` The Tuple2 agent seems a little complicated, so we prepare an abbreviation `%`. In the following, `foo1`, `foo2`, `foo3`, ... are any agents whose arity is 1, 2, 3, ..., respectively. @@ -731,14 +731,14 @@ it merges two lists into one. Merger agent has two principal ports that can take ``` This is quite useful for the map application. The `inc` application is written simply as follows: ``` - >>> map(result, %inc) ~ [1,2,3]; + >>> Map(result, %inc) ~ [1,2,3]; >>> result; [2,3,4] >>> ``` Wonderful! - The same as the map operation, we can define foldr and foldl as follows (Do not worry if it looks complicated. It is OK if we can just use these!): +* **Reduce function operation**: The same as the map operation, we can define foldr and foldl as follows (Do not worry if it looks complicated. It is OK if we can just use these!): ``` // -------------------------------------------------------------------- // foldr f v [x0, x1, ..., xn] = f(x0, f(x1, ... f(xn-1, f(xn, v))...)) |