---
diff --git a/towards_monads.mdwn b/towards_monads.mdwn
index 223c592b..3671d273 100644
--- a/towards_monads.mdwn
+++ b/towards_monads.mdwn
@@ -1,7 +1,7 @@
Dividing by zero
----------------
-Integer division operation presupposes that its second argument
+Integer division presupposes that its second argument
(the divisor) is not zero, upon pain of presupposition failure.
Here's what my OCaml interpreter says:
@@ -10,7 +10,7 @@ Here's what my OCaml interpreter says:
So we want to explicitly allow for the possibility that
division will return something other than a number.
-We'll use OCaml's option type, which works like this:
+We'll use OCaml's `option` type, which works like this:
# type 'a option = None | Some of 'a;;
# None;;
@@ -19,12 +19,13 @@ We'll use OCaml's option type, which works like this:
- : int option = Some 3
So if a division is normal, we return some number, but if the divisor is
-zero, we return None. As a mnemonic aid, we'll append a `'` to the end of our new divide function.
+zero, we return `None`. As a mnemonic aid, we'll append a `'` to the end of our new divide function.
let div' (x:int) (y:int) =
- match y with 0 -> None |
- _ -> Some (x / y);;
+ match y with
+ 0 -> None
+ | _ -> Some (x / y);;
(*
val div' : int -> int -> int option = fun
@@ -48,10 +49,12 @@ operations. So we have to jack up the types of the inputs:
let div' (x:int option) (y:int option) =
- match y with None -> None |
- Some 0 -> None |
- Some n -> (match x with None -> None |
- Some m -> Some (m / n));;
+ match y with
+ None -> None
+ | Some 0 -> None
+ | Some n -> (match x with
+ None -> None
+ | Some m -> Some (m / n));;
(*
val div' : int option -> int option -> int option =
@@ -72,10 +75,11 @@ built-in tuple type:
let div' (x:int option) (y:int option) =
- match (x, y) with (None, _) -> None |
- (_, None) -> None |
- (_, Some 0) -> None |
- (Some m, Some n) -> Some (m / n);;
+ match (x, y) with
+ (None, _) -> None
+ | (_, None) -> None
+ | (_, Some 0) -> None
+ | (Some m, Some n) -> Some (m / n);;

So far so good. But what if we want to combine division with
@@ -85,9 +89,10 @@ presupposition failure:
let add' (x:int option) (y:int option) =
- match (x, y) with (None, _) -> None |
- (_, None) -> None |
- (Some m, Some n) -> Some (m + n);;
+ match (x, y) with
+ (None, _) -> None
+ | (_, None) -> None
+ | (Some m, Some n) -> Some (m + n);;
(*
val add' : int option -> int option -> int option =
@@ -108,8 +113,9 @@ well chosen to resonate with linguists, but what can you do). To continue our mn
let bind' (x: int option) (f: int -> (int option)) =
- match x with None -> None |
- Some n -> f n;;
+ match x with
+ None -> None
+ | Some n -> f n;;
let add' (x: int option) (y: int option) =
bind' x (fun x -> bind' y (fun y -> Some (x + y)));;