Towards a theory for reflective programming languages.
		Anurag Mendhekar     Daniel P. Friedman,
		    Department of Computer Science
	                Indiana University
		       Bloomington IN 47405.

			
			   Abstract


	This paper attempts to develop a better theoretical
understanding of reflective systems. We begin by a developing a
reflective extension of the call-by-value lambda calculus  and define a 
simple operational semantics for it based on the infinite tower model
described by Smith in [1]. We then develop an equational logic from this
semantics. The resulting logic is shown to be weak because of reflective
properties. We establish properties about this logic and show that it
corresponds to the operational semantics. 

The infinite tower model described by Smith [1] can really
be described in much simpler operational terms. While the system we
have described here does not support first-class environments,
we believe that it captures the essence of reflective programming.
We point out that there are limitations to the reflective capability
of systems and that reflective systems depend crucially on a defining
system that cannot be reflected upon. 

Reflection is a very attractive solution for building extensible
systems. This paper shows that reasoning about such systems is much
harder. Language designers must take this into account when
introducing reflection into languages. We develop a calculus for
reasoning about programs in this system. The resulting calculus is
shown to be consistent, although extremely weak. This weakness is a
consequence of the reflective properties of the system. Equational
logics derive their power from behavioral equivalence between terms.
Since behavioral equivalence between terms is significantly reduced in
reflective systems, the corresponding equational logic has turned out to
be weak.  

Although weak, this logic is only a starting point for developing
theoretical models for reflective languages. The insight gained by
developing this logic will help us design reflective programming
languages that will be easier to reason about and implement.


Reference:

[1] Smith, B.C.,  Reflection and Semantics in a Procedural Language,
	          MIT-LCS-TR-272, MIT, (Cambridge, 1982).