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- W1531724428 abstract "This thesis presents two independent pieces of research.First, we consider the problem of automatically inferring properties of programs. Our approach is to explore the application of familiar inference principles to a type system sufficiently expressive that the typing problem is effectively the checking of program specifications. We present such a system, and use familiar syntax-directed inference rules to give a polynomial-time procedure for inferring theorems in this system. We discuss examples of simple functional programs and the specification information this procedure automatically infers. The enriched notion of allows the definition of any recursively enumerable set as a type, and includes argument-dependent output types for functions. The inference procedure is capable for example of automatically inferring that an insertion sort program always returns a sorted permutation of its input.We present both first-order and higher-order versions of our sample programming language and inference algorithms for both languages. We believe most of the interesting inferential challenges are already present in the first-order case.The second piece of research we present addresses the satisfiability of sets of formulas in a particular set constraints language. We consider set expressions built up from set constants by union, set complement, and taking the image of a set expression under a function or relation. Previous work in this area has neglected the Tarskian case where the functions and relations are allowed to take on arbitrary meanings, rather than only a standard Herbrand meaning. We prove that the satisfiability of a finite set of subset formulas between these Tarskian set expressions is in nondeterministic doubly exponential time. Our proof is by reduction to a new Diophantine inequation solvability problem, which we show to be in nondeterministic exponential time, but conjecture to be in NP. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)" @default.
- W1531724428 created "2016-06-24" @default.
- W1531724428 creator A5007751369 @default.
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- W1531724428 date "1996-01-01" @default.
- W1531724428 modified "2023-09-23" @default.
- W1531724428 title "Automatically inferring properties of computer programs" @default.
- W1531724428 hasPublicationYear "1996" @default.
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