Abstract. This paper presents an elegant algorithm for existential quantifier elimination using incremental SAT solving. This approach contrasts with existing techniques in that it is based solely on manipulating the SAT instance rather than requiring any reengineering of the SAT solver or needing an auxiliary data-structure such as a BDD. The algorithm combines model enumeration with the generation of shortest prime implicants so as to converge onto a quantifier-free formula presented in CNF. We apply the technique to a number of hardware circuits and transfer functions to demonstrate the effectiveness of the method.
This paper revisits the problem of determinacy inference addressing the problem of how to uniformly handle cut. To this end a new semantics is introduced for cut, which is abstracted to systematically derive a backward analysis that derives conditions sufficient for a goal to succeed at most once. The method is conceptionally simpler and easier to implement than existing techniques, whilst improving the latter's handling of cut. Formal arguments substantiate correctness and experimental work, and a tool called 'RedAlert' demonstrates the method's generality and applicability.
We present a syntactic abstraction method to reason about first-order modal logics by using theorem provers for standard first-order logic and for propositional modal logic.
Abstract. The question of what constraints must hold for a predicate to behave as a (partial) function, is key to understanding the behaviour of a logic program. It has been shown how this question can be answered by combining backward analysis, a form of analysis that propagates determinacy requirements against the control flow, with a component for deriving so-called mutual exclusion conditions. The latter infers conditions sufficient to ensure that if one clause yields an answer then another cannot. This paper addresses the challenge of how to compute these conditions by showing that this problem can be reformulated as that of vertex enumeration. Whilst directly applicable in logic programming, the method might well also find application in reasoning about type classes.
Basing program analyses on formal semantics has a long and successful tradition in the logic programming paradigm. These analyses rely on results about the relative correctness of mathematically sophisticated semantics, and authors of such analyses often invest considerable effort into establishing these results. The development of interactive theorem provers such as Coq and their recent successes both in the field of program verification as well as in mathematics, poses the question whether these tools can be usefully deployed in logic programming. This paper presents formalisations in Coq of several general results about the correctness of semantics in different styles; forward and backward, top-down and bottom-up. The results chosen are paradigmatic of the kind of correctness theorems that semantic analyses rely on and are therefore well-suited to explore the possibilities afforded by the application of interactive theorem provers to this task, as well as the difficulties likely to be encountered in the endeavour. It turns out that the advantages offered by moving to a functional setting, including the possibility to apply higher-order abstract syntax, are considerable.
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