Program logics for homogeneous meta-programming.

A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself. Meta-programming has been used extensively since macros were introduced to Lisp, yet we have little idea how formally to reason about metaprograms. This paper provides the first program logics for homogeneous metaprogramming – using a variant of MiniMLe by Davies and Pfenning as underlying meta-programming language.We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics

Reachability analysis of first-order definable pushdown systems

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1

What's Decidable About Sequences?

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the quantifier-free fragment, based on an encoding into the first-order theory of concatenation; the procedure has PSPACE complexity. The quantifier-free fragment of the theory of sequences can express properties such as sortedness and injectivity, as well as Boolean combinations of periodic and arithmetic facts relating the elements of the sequence and their positions (e.g., "for all even i's, the element at position i has value i+3 or 2i"). The resulting expressive power is orthogonal to that of the most expressive decidable logics for arrays. Some examples demonstrate that the fragment is also suitable to reason about sequence-manipulating programs within the standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl