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--- magistraleinformaticanetworking:spm:ocamlfs1 [23/03/2011 alle 15:59 (14 anni fa)] – Marco Danelutto
+++ magistraleinformaticanetworking:spm:ocamlfs1 [23/03/2011 alle 16:31 (14 anni fa)] (versione attuale) – Marco Danelutto
@@ Linea 3: / Linea 3: @@
 This is an summary of the lesson given on March 23rd.
-We represent the functional semantics of skeletons with higher order functions. We use [[http://caml.inria.fr/ocaml/|Ocaml]] for the examples.
+We represent the functional semantics of skeletons with higher order functions. We use [[http://caml.inria.fr/ocaml/|Ocaml]] for the examples (see the [[http://caml.inria.fr/pub/docs/manual-ocaml/index.html|Ocaml online manual]] for the syntax).
 Assuming that //data streams// are represented with Ocaml lists (just for the moment), a **farm** skeleton may be defined as follows:
@@ Linea 24: / Linea 24: @@
 # farm sq;;
 - : int list -> int list = <fun>
+#
+</code>
+and applying this function to a list of integers, we get the list of squares:
+<code>
+# (farm sq) [1;2;3;4;5];;
+- : int list = [1; 4; 9; 16; 25]
+#
+</code>
+Suppose we also use lists to represent arrays. The map skeleton can be modelled through the **List.map** function, available as primitive in Ocaml and having the obvious type:
+<code>
+# List.map;;
+- : ('a -> 'b) -> 'a list -> 'b list = <fun>
+#
+</code>
+Therefore we can look at the type of skeleton composition. As an example, a farm having a map worker computing sq on all the elements of the matrix (which is actually a vector represented as a list, in our simple assumption) has type:
+<code>
+# farm (List.map sq);;
+- : int list list -> int list list = <fun>
+#
+</code>
+and in fact, giving the composite skeleton a stream (a list, in our assumption) of arrays (vectors represented as a stream, in our assumptions), we get the correct result: all items of the stream are processed in such a way all the subitems of the arrays are squared.
+<code>
+# let array1 = [1;2];;
+val array1 : int list = [1; 2]
+# let array2 = [3;4];;
+val array2 : int list = [3; 4]
+# let stream = [array1;array2];;
+val stream : int list list = [[1; 2]; [3; 4]]
+# farm (List.map sq) stream;;
+- : int list list = [[1; 4]; [9; 16]]
+#
+</code>
+This is a little bit ambiguous due to the usage of lists to represent both streams and arrays.
+Ocaml provides arrays as primitive types actually. Arrays are denoted similarly to lists using particular brackets:
+<code>
+# [|1;2|];;
+- : int array = [|1; 2|]
+#
+</code>
+As for lists, a map working on arrays is pre-defined:
+<code>
+# Array.map;;
+- : ('a -> 'b) -> 'a array -> 'b array = <fun>
+#
+</code>
+Therefore we can re-write the //farm of map// example as follows:
+<code>
+# let rec farm f x =
+  match (x) with
+  [] -> []
+| listHead::listTail -> (f listHead)::(farm f listTail);;
+      val farm : ('a -> 'b) -> 'a list -> 'b list = <fun>
+# let sq x = x * x;;
+val sq : int -> int = <fun>
+# let worker = Array.map sq;;
+val worker : int array -> int array = <fun>
+# let main = farm worker;;
+val main : int array list -> int array list = <fun>
+# let array1 = [| 1 ; 2 |];;
+val array1 : int array = [|1; 2|]
+# let array2 = [| 3; 4 |];;
+val array2 : int array = [|3; 4|]
+# let stream = [ array1; array2 ];;
+val stream : int array list = [[|1; 2|]; [|3; 4|]]
+# main stream;;
+- : int array list = [[|1; 4|]; [|9; 16|]]
+#
+</code>
+Even better, we can define our data type **stream** using the Ocaml type definition syntax:
+<code>
+# type 'a stream = Empty | Stream of ('a * 'a stream);;
+type 'a stream = Empty | Stream of ('a * 'a stream)
+#
+</code>
+The farm functional semantics may therefore be defined by the function:
+<code>
+#
+  let rec farm f = function
+    Empty -> Empty
+  | Stream(x,y) -> Stream ((f x), (farm f y));;
+val farm : ('a -> 'b) -> 'a stream -> 'b stream = <fun>
+#
+</code>
+Therefore the type of our //farm of map// will be correctly inferred as:
+<code>
+# farm (Array.map sq);;
+- : int array stream -> int array stream = <fun>
 #
 </code>