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From: db@lfcs.ed.ac.uk (Dave Berry)
Newsgroups: sci.math,comp.lang.misc
Subject: Re: "Semiabstract" datatypes
Message-ID: <774@etive.ed.ac.uk>
Date: 13 Sep 88 13:32:50 GMT
References: <896@tragicomix.liu.se>
Sender: news@etive.ed.ac.uk
Reply-To: db@lfcs.ed.ac.uk (Dave Berry)
Organization: Laboratory for the Foundations of Computer Science, Edinburgh U
Lines: 46

In article <896@tragicomix.liu.se> JWC@IDA.LiU.SE (Jonas Wallgren) writes:
>Assume the following declaration (in ML) of an abstract tree type:
>
>	abstype tree=leaf of int|branch of tree*tree
>	with val tend=leaf
>	     fun tfork l1 l2=branch(l1,l2)
>	end;
>
>Everytime a tree is created one is forced to write e.g.
>
>	tfork(tend 1)(tend 2);
>
>My idea is [...]
>Then the example above becomes
>
>	tfork 1 2;

I'm not sure what you're asking.  You can write this in ML as follows:

       abstype tree=leaf of int|branch of tree*tree
       with val tend=leaf
            fun tfork l1 l2=branch(tend l1,tend l2)
       end;

but then you can't write "tfork(tend 1)(tend 2);" anymore.

Do you want to be able to write either
       tfork(tend 1)(tend 2); 	or	tfork 1 2;
with the same definition of tfork?  I agree this would be useful.  I've
sometimes wanted it to abbreviate large ML patterns.

>	Are there any programming languages supporting such a construction?

The nearest I know of is C++, which has the feature that if a function
expects an argmuent of type A and receives one of type B, it will convert
the argument to type A if it knows how to do so.  It can do this iff there
is a constructor (C++ usage of the word) for type A that takes an argument
of type B.

Any other offers?

>	Is there any algebraic concept or other mathematical structure
>	suitable for describing such a phenomenon?
-----------------------------------------------------------------------------
 Dave Berry.		 db@lfcs.ed.ac.uk