Xref: utzoo sci.math:4472 comp.lang.misc:1816
Path: utzoo!yunexus!geac!syntron!jtsv16!uunet!mcvax!enea!kth!draken!liuida!JWC
From: JWC@IDA.LiU.SE (Jonas Wallgren)
Newsgroups: sci.math,comp.lang.misc
Subject: "Semiabstract" datatypes
Message-ID: <896@tragicomix.liu.se>
Date: 6 Sep 88 16:24:48 GMT
Article-I.D.: tragicom.896
Sender: jonwa@tragicomix.liu.se
Lines: 45
Organisation: CIS Dept, Univ of Linkoping, Sweden

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 fork l1 l2=branch(l1,l2)
	end;

Everytime a tree is created one is forced to write e.g.

	tfork(tend 1,tend 2);

I.e. every integer must be prefixed with 'tend'.
This implementation not only hides the representation of the tree structure
(tree*tree) but also hides the representation of the leaves.

My idea is that the declaration could look like

	semiabstype tree=int|branch of tree*tree
	with fun tfork l1 l2=branch(l1,l2)
	end;

Then the example above becomes

	tfork 1 2;

in the original abstract type the top is visible and the rest below is hidden.
In the second example there is something visible at the top and something
visible in the bottom, and the middle part is hidden - that's why I call the
type 'semiabstract'.


My questions are:

	Are there any programming languages supporting such a construction?

	Is there any algebraic concept or other mathematical structure
	suitable for describing such a fenomenon?

-------------------------------------------------------------------------------
Jonas Wallgren                                   |               JWC@IDA.LiU.SE
Department of Computer and Information Science   |
Linkoping University                             |-----------------------------
SE-581 83  Linkoping                             |
Sweden                                           |   The Argument Eater: YKx=YK
-------------------------------------------------------------------------------