16,082 research outputs found
Formulas as Programs
We provide here a computational interpretation of first-order logic based on
a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary
interpretation. In this approach the formulas themselves are programs. This
contrasts with the so-called formulas as types approach in which the proofs of
the formulas are typed terms that can be taken as programs. This view of
computing is inspired by logic programming and constraint logic programming but
differs from them in a number of crucial aspects.
Formulas as programs is argued to yield a realistic approach to programming
that has been realized in the implemented programming language ALMA-0 (Apt et
al.) that combines the advantages of imperative and logic programming. The work
here reported can also be used to reason about the correctness of non-recursive
ALMA-0 programs that do not include destructive assignment.Comment: 34 pages, appears in: The Logic Programming Paradigm: a 25 Years
Perspective, K.R. Apt, V. Marek, M. Truszczynski and D.S. Warren (eds),
Springer-Verlag, Artificial Intelligence Serie
Verifying Monadic Second-Order Properties of Graph Programs
The core challenge in a Hoare- or Dijkstra-style proof system for graph
programs is in defining a weakest liberal precondition construction with
respect to a rule and a postcondition. Previous work addressing this has
focused on assertion languages for first-order properties, which are unable to
express important global properties of graphs such as acyclicity,
connectedness, or existence of paths. In this paper, we extend the nested graph
conditions of Habel, Pennemann, and Rensink to make them equivalently
expressive to monadic second-order logic on graphs. We present a weakest
liberal precondition construction for these assertions, and demonstrate its use
in verifying non-local correctness specifications of graph programs in the
sense of Habel et al.Comment: Extended version of a paper to appear at ICGT 201
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