Section: New Results
A Two-level Approach to Reasoning about Computation
Participant : Dale Miller.
In a paper that appeared in the J. of Automated Reasoning, Gacek,
Miller, and Nadathur [12] described the foundations and
architecture of a new interactive theorem prover capable of reasoning
with rich collections of inductive and coinductive relations. This
prover, called Abella, also contains the “generic” quantifier
A novel aspect of Abella is that it can define provability in various
simple logics and can also reason about provability in such logics.
The current system includes a specification logic that is a
(restricted) intuitionistic logic programming language (a sublanguage
of
This approach to reasoning about computation has interesting applications. For example, the reasoning logic is aware of the fact that the cut and substitution rules can be eliminated in the specification logic. As a consequence, the notoriously difficult "substitution lemmas" that occur repeated in the study of operational semantics are proved essentially for free (that is, they are an immediate consequence of cut-elimination).
In [17] , Accattoli showed that when one reasons about
the untyped