Term rewriting with traversal functions

Term Rewriting with Type-safe Traversal Functions

Term Rewriting with Type-safe Traversal Functions

Term rewriting is an appealing technique for performing program analysis and program transformation. Tree (term) traversal is frequently used but is not supported by standard term rewriting. In this paper, many-sorted rst-order term rewriting is extended with automatic tree traversal by adding two primitive tree traversal strategies and complementing them with three types of traversals. These s...

Typed generic traversal with term rewriting strategies

A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S γ . The calculus employs a many-sorted type system extended by designated generic strategy types γ. We consider two generic strategy types, namely the types of type-preserving and type-unifying strategies. S γ offers traversal combi...

Term Rewriting in Logics of Partial Functions

We devise a theoretical foundation of directed rewriting, a term rewriting strategy for logics of partial functions, inspired by term rewriting in the Rodin platform. We prove that directed rewriting is sound and show how to supply new rewrite rules in a soundness preserving fashion. In the context of Rodin, we show that directed rewriting makes a significant number of conditional rewrite rules...

Term rewriting theory for the recursive functions

The termination of rewrite systems for parameter recursion, simple nested recursion and unnested multiple recursion is shown by using monotone interpretations both on the ordinals below the first primitive recursively closed ordinal and on the natural numbers. We show that the resulting derivation lengths are primitive recursive. As a corollary we obtain transparent and illuminating proofs of t...