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From: guido@cwi.nl (Guido van Rossum)
Newsgroups: comp.object,comp.lang.misc,comp.lang.eiffel
Subject: Re: A Hard Problem for Static Type Systems
Message-ID: <3378@charon.cwi.nl>
Date: 21 Apr 91 17:13:43 GMT
References: <1991Apr20.010347.28984@leland.Stanford.EDU>
Sender: news@cwi.nl
Followup-To: comp.object
Lines: 66

craig@leland.Stanford.EDU (Craig Chambers) writes:

>Consider the general min function (written in a dynamically-typed
>C-like language):
>[...]
>Here's the problem: we'd like to describe the type of the min
>function, so that this one piece of source code can be used to compute
>the minimum of two numbers or of two collections of numbers or of two
>collections of collections of numbers, etc.

This can be done in ABC, a statically typed interpreted language
developed at CWI [1].  ABC knows a single type "number" which can hold
a float or arbitrary-precision rational, and "lists" that are
sorted collections of values with the same type; list items may be
lists if their types are the same, etc.; lists are sorted
lexicographically.  If you don't want the items sorted there is a
"table" type that lets you determine the order; tables are really
associative arrays.

The function you describe is written in ABC as follows:

	HOW TO RETURN min(x, y):
	    IF x < y: RETURN x
	    RETURN y

and now you will have min(3.14, 1) = 1, min({1;2;3}, {1;2}) = {1;2}, etc.,
and min(3.14, {}) will not type-check.  [2]

--Guido van Rossum, CWI, Amsterdam <guido@cwi.nl>
Founder of the Royal Society for Prevention of Cruelty to Amoebae

[1]
%T ABC Programmer's Handbook
%A Leo Geurts
%A Lambert Meertens
%A Steven Pemberton
%I Prentice-Hall
%C London
%D 1990
%O ISBN 0-13-000027-2

[2]
ABC is implemented; I typed the example in and here's the session log:

piring& abc

ABC Release 1.02.01.
Copyright (c) Stichting Mathematisch Centrum, Amsterdam, 1989.
Type '?' for help.
>first
>>> HOW TO RETURN min(x, y):
HOW TO RETURN min(x, y):
   IF x < y: RETURN x
   RETURN y

>>> WRITE min(3.14, 1)
1
>>> WRITE min({1; 2; 3}, {1; 2})
{1; 2}
>>> WRITE min(1, {})
*** Cannot reconcile the types in your command
    WRITE min(1, {})
*** The problem is: I found type EG (0, list or table)
where I expected (?, ?)
>>> QUIT
piring&