🚀 go-pugleaf

In message <2006@dutiws.tudelft.nl>, dated 21 Aug 92 09:57:03 GMT,
klooster@dutiws.tudelft.nl (Marnix Klooster) writes:

> ...
>
>I have been thinking a bit about what I called "nondeterministic
>expressions", i.e. expressions that can have any number of values
>(zero, one, or more). A nondeterministic expression is entirely
>defined by the set of its possible values.
>
>It occurred to me that such expressions could be used to develop
>a "refinement calculus" for functional languages, by defining
>a relation  >>  (pronounced "refines to") like this:
>
>  E >> F == The set of values  F  can have is a subset of the set
>            of values  E  can have
>
>  ...

In our 1987 FPLCA paper, David Plaisted and I introduced the notation

   E contains F

with precisely the above semantics.  When there are multiple assertions of 
the form

   E contains F1	
   ...
   E contains Fk	

we defined the semantics of E as F1 U ... U Fk.   This paradigm may be
called subset-equational programming.   In our 1989 NACLP paper, we 
considered the possibility of conditional assertions as well, e.g.

   E contains F   :-  condition

where the condition can be stated in terms of relational (Prolog-like) 
clauses.  This paradigm may be called subset-relational progamming.  The 
following papers describe various aspects of these paradigms---semantics, 
application and implementation.  

1.Functional Programming with Sets, B.Jayaraman & D.A. Plaisted, Proc.
	Functional Programming Languages and Computer Architecture, 1987,
	Springer LNCS 274, pp. 194-210.
2.Subset-logic Programming: Application and Implementation, B.Jayaraman and
	 A. Nair, Proc. 5th Intl. Conf. on Logic Prog., pp. 843-858, 
	MIT Press, 1988.
3.Programming with Equations, Subsets and Relations, B.Jayaraman & D.A. 
	Plaisted, Proc. N. Amer. Conf.  on Logic Programming,  pp. 1051-1068, 
	MIT Press, 1989. 
4.Broader Forms of Logic Programming, B. Jayaraman, SUNY-Buffalo, TR 91-11.
5.Implementation of Subset-Equational Programs, B. Jayaraman, Journal of Logic
	Programming, vol. 12, pp. 299-324,  1992.
6. Set Construtors, Finite Sets, and Logical Semantics, D. Jana and 
	B. Jayaraman,  SUNY-Buffalo TR, 1992.