From 34c70399625b1a258682e542622d3c26d3b3795a Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Mon, 1 Nov 2010 00:19:42 -0400 Subject: [PATCH] pattern matching: use standard OCaml conventions Signed-off-by: Jim Pryor --- towards_monads.mdwn | 42 ++++++++++++++++++++++++------------------ 1 file changed, 24 insertions(+), 18 deletions(-) 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)));;
--
2.11.0

```