From 472e280120834cc613fe8b7ff045a99e956636d3 Mon Sep 17 00:00:00 2001 From: Jim Pryor Date: Mon, 25 Oct 2010 20:33:30 -0400 Subject: [PATCH] decap OCAML Signed-off-by: Jim Pryor --- assignment5.mdwn | 20 ++++++++++---------- week6.mdwn | 24 ++++++++++++------------ 2 files changed, 22 insertions(+), 22 deletions(-) diff --git a/assignment5.mdwn b/assignment5.mdwn index 4a4e06d2..2078c1c0 100644 --- a/assignment5.mdwn +++ b/assignment5.mdwn @@ -1,10 +1,10 @@ Assignment 5 -Types and OCAML +Types and OCaml --------------- 0. Recall that the S combinator is given by \x y z. x z (y z). - Give two different typings for this function in OCAML. + Give two different typings for this function in OCaml. To get you started, here's one typing for K: # let k (y:'a) (n:'b) = y;; @@ -13,7 +13,7 @@ Types and OCAML - : int = 1 -1. Which of the following expressions is well-typed in OCAML? +1. Which of the following expressions is well-typed in OCaml? For those that are, give the type of the expression as a whole. For those that are not, why not? @@ -72,8 +72,8 @@ Types and OCAML The following expression is an attempt to make explicit the behavior of `if`-`then`-`else` explored in the previous question. The idea is to define an `if`-`then`-`else` expression using -other expression types. So assume that "yes" is any OCAML expression, -and "no" is any other OCAML expression (of the same type as "yes"!), +other expression types. So assume that "yes" is any OCaml expression, +and "no" is any other OCaml expression (of the same type as "yes"!), and that "bool" is any boolean. Then we can try the following: "if bool then yes else no" should be equivalent to @@ -143,12 +143,12 @@ Baby monads match x with None -> None | Some n -> f n;; -Booleans, Church numbers, and Church lists in OCAML +Booleans, Church numbers, and Church lists in OCaml --------------------------------------------------- These questions adapted from web materials written by some smart dude named Acar. The idea is to get booleans, Church numbers, "Church" lists, and -binary trees working in OCAML. +binary trees working in OCaml. Recall from class System F, or the polymorphic λ-calculus. @@ -180,8 +180,8 @@ binary trees working in OCAML. encoding above, the result of that iteration can be any type α, as long as you have a base element z : α and a function s : α → α. - **Excercise**: get booleans and Church numbers working in OCAML, - including OCAML versions of bool, true, false, zero, succ, add. + **Excercise**: get booleans and Church numbers working in OCaml, + including OCaml versions of bool, true, false, zero, succ, add. Consider the following list type: @@ -200,7 +200,7 @@ binary trees working in OCAML. map : (σ → τ ) → σ list → τ list := λf :σ → τ. λl:σ list. l [τ list] nilτ (λx:σ. λy:τ list. consτ (f x) y - **Excercise** convert this function to OCAML. Also write an `append` function. + **Excercise** convert this function to OCaml. Also write an `append` function. Test with simple lists. Consider the following simple binary tree type: diff --git a/week6.mdwn b/week6.mdwn index b97a09f3..25e52557 100644 --- a/week6.mdwn +++ b/week6.mdwn @@ -1,9 +1,9 @@ [[!toc]] -Types, OCAML +Types, OCaml ------------ -OCAML has type inference: the system can often infer what the type of +OCaml has type inference: the system can often infer what the type of an expression must be, based on the type of other known expressions. For instance, if we type @@ -32,7 +32,7 @@ element: # (3) = 3;; - : bool = true -though OCAML, like many systems, refuses to try to prove whether two +though OCaml, like many systems, refuses to try to prove whether two functional objects may be identical: # (f) = f;; @@ -41,11 +41,11 @@ functional objects may be identical: Oh well. -Booleans in OCAML, and simple pattern matching +Booleans in OCaml, and simple pattern matching ---------------------------------------------- Where we would write `true 1 2` in our pure lambda calculus and expect -it to evaluate to `1`, in OCAML boolean types are not functions +it to evaluate to `1`, in OCaml boolean types are not functions (equivalently, are functions that take zero arguments). Selection is accomplished as follows: @@ -73,7 +73,7 @@ Compare with Unit and thunks --------------- -All functions in OCAML take exactly one argument. Even this one: +All functions in OCaml take exactly one argument. Even this one: # let f x y = x + y;; # f 2 3;; @@ -87,7 +87,7 @@ Here's how to tell that `f` has been curry'd: After we've given our `f` one argument, it returns a function that is still waiting for another argument. -There is a special type in OCAML called `unit`. There is exactly one +There is a special type in OCaml called `unit`. There is exactly one object in this type, written `()`. So # ();; @@ -145,7 +145,7 @@ So we can try our usual tricks: # (fun x -> true) omega;; - : bool = true -OCAML declined to try to evaluate the argument before applying the +OCaml declined to try to evaluate the argument before applying the functor. But remember that `omega` is a function too, so we can reverse the order of the arguments: @@ -176,14 +176,14 @@ Towards Monads So the integer division operation presupposes that its second argument (the divisor) is not zero, upon pain of presupposition failure. -Here's what my OCAML interpreter says: +Here's what my OCaml interpreter says: # 12/0;; Exception: Division_by_zero. 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;; @@ -240,7 +240,7 @@ val div : int option -> int option -> int option = Beautiful, just what we need: now we can try to divide by anything we want, without fear that we're going to trigger any system errors. -I prefer to line up the `match` alternatives by using OCAML's +I prefer to line up the `match` alternatives by using OCaml's built-in tuple type: 
@@ -275,7 +275,7 @@ This works, but is somewhat disappointing: the `add` operation
 doesn't trigger any presupposition of its own, so it is a shame that
 it needs to be adjusted because someone else might make trouble.
 
-But we can automate the adjustment.  The standard way in OCAML,
+But we can automate the adjustment.  The standard way in OCaml,
 Haskell, etc., is to define a `bind` operator (the name `bind` is not
 well chosen to resonate with linguists, but what can you do):
 
-- 
2.11.0