explain comments

[lambda.git] / topics / _week8_using_monads.mdwn

diff --git a/topics/_week8_using_monads.mdwn b/topics/_week8_using_monads.mdwn
index 561ce7c..f23ef50 100644 (file)
--- a/topics/_week8_using_monads.mdwn
+++ b/topics/_week8_using_monads.mdwn
@@ -30,7 +30,7 @@ let safe_div (x:int) (y:int) =
     | 0 -> None
     | _ -> Some (x / y);;
 
-(*
+(* an Ocaml session could continue with OCaml's response:
 val safe_div : int -> int -> int option = fun
 # safe_div 12 2;;
 - : int option = Some 6
@@ -57,7 +57,7 @@ let safe_div2 (u:int option) (v:int option) =
       | Some 0 -> None
       | Some y -> Some (x / y));;
 
-(*
+(* an Ocaml session could continue with OCaml's response:
 val safe_div2 : int option -> int option -> int option = <fun>
 # safe_div2 (Some 12) (Some 2);;
 - : int option = Some 6
@@ -95,7 +95,7 @@ let safe_add (u:int option) (v:int option) =
     | (_, None) -> None
     | (Some x, Some y) -> Some (x + y);;
 
-(*
+(* an Ocaml session could continue with OCaml's response:
 val safe_add : int option -> int option -> int option = <fun>
 # safe_add (Some 12) (Some 4);;
 - : int option = Some 16
@@ -142,7 +142,7 @@ Haskell has an even more user-friendly notation for defining `safe_div3`, namely
 Let's see our new functions in action:
 
 <pre>
-(*
+(* an Ocaml session could continue with OCaml's response:
 # safe_div3 (safe_div3 (Some 12) (Some 2)) (Some 3);;
 - : int option = Some 2
 #  safe_div3 (safe_div3 (Some 12) (Some 0)) (Some 3);;
@@ -180,3 +180,18 @@ material that otherwise would trigger a presupposition violation; but,
 not surprisingly, these refinements will require some more
 sophisticated techniques than the super-simple Option/Maybe monad.)
 
+
+## Scratch, more... ##
+
+We've just seen a way to separate thinking about error conditions
+(such as trying to divide by zero) from thinking about normal
+arithmetic computations.  We did this by making use of the `option`
+type: in each place where we had something of type `int`, we put
+instead something of type `int option`, which is a sum type consisting
+either of one choice with an `int` payload, or else a `None` choice
+which we interpret as signaling that something has gone wrong.
+
+The goal was to make normal computing as convenient as possible: when
+we're adding or multiplying, we don't have to worry about generating
+any new errors, so we would rather not think about the difference
+between `int`s and `int option`s.