Cynthia Kop

Term Rewriting with Logical Constraints

In recent works on program analysis, transformations of various programming languages to term rewriting are used. In this setting, constraints appear naturally. Several definitions which combine rewriting with logical constraints, or with separate rules for integer functions, have been proposed. This paper seeks to unify and generalise these proposals.

Automatic Constrained Rewriting Induction towards Verifying Procedural Programs

This paper aims at developing a verification method for procedural programs via a transformation into logically constrained term rewriting systems (LCTRSs). To this end, we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can handle realistic functions, involving, e.g., integers and arrays. An implementation is provided.

Polynomial Interpretations for Higher-Order Rewriting

The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative formalism of algebraic functional systems, where the simply-typed lambda-calculus is combined with algebraic reduction. Using this theory, we define higher-order polynomial interpretations, and show how the implementation challenges of this technique can be tackled. A full implementation is provided in the termination tool Wanda.

Higher Order Dependency Pairs for Algebraic Functional Systems

We extend the termination method using dynamic dependency pairs to higher order rewriting systems with beta as a rewrite step, also called Algebraic Functional Systems (AFSs). We introduce a variation of usable rules, and use monotone algebras to solve the constraints generated by dependency pairs. This approach differs in several respects from those dealing with higher order rewriting modulo beta (e.g. HRSs).

Verifying Procedural Programs via Constrained Rewriting Induction

This article aims to develop a verification method for procedural programs via a transformation into logically constrained term rewriting systems (LCTRSs). To this end, we extend transformation methods based on integer term rewriting systems to handle arbitrary data types, global variables, function calls, and arrays, and to encode safety checks. Then we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can automatically verify memory safety and prove correctness of realistic functions. Our approach proves equivalence between two implementations; thus, in contrast to other works, we do not require an explicit specification in a separate specification language.

Simplifying algebraic functional systems

A popular formalism of higher order rewriting, especially in the light of termination research, are the Algebraic Functional Systems (AFSs) defined by Jouannaud and Okada. However, the formalism is very permissive, which makes it hard to obtain results; consequently, techniques are often restricted to a subclass. In this paper we study termination-preserving transformations to make AFS-programs adhere to a number of standard properties. This makes it significantly easier to obtain general termination results.

Complexity Hierarchies and Higher-order Cons-free Term Rewriting

Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of constructor terms in the left-hand side; the computational intuition is that rules cannot build new data structures. It is well-known that cons-free programming languages can be used to characterize computational complexity classes, and that cons-free first-order term rewriting can be used to characterize the set of polynomial-time decidable sets. We investigate cons-free higher-order term rewriting systems, the complexity classes they characterize, and how these depend on the order of the types used in the systems. We prove that, for every k

Dynamic Dependency Pairs for Algebraic Functional Systems

\geq

Harnessing first order termination provers using higher order dependency pairs

1, left-linear cons-free systems with type order k characterize E

A Higher-Order Iterative Path Ordering

^k