Keiichirou Kusakari

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We enhance the dependency pair method in order to prove termination using recursive structure analysis in simply-typed term rewriting systems, which is one of the computational models of functional programs. The primary advantage of our method is that one can exclude higher-order variables which are difficult to analyze theoretically, from recursive(More)
The static dependency pair method is a method for proving the termination of higher-order rewrite systems à la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability introduced for typed λ-calculi. Argument filterings and usable rules are two important methods of the dependency pair(More)
This paper explores how to extend the dependency pair technique for proving termination of higher-order rewrite systems. In the first order case, the termination of term rewriting systems are proved by showing the non-existence of an infinite R-chain of the dependency pairs. However, the termination and the non-existence of an infinite R-chain do not(More)
Higher-order rewrite systems (HRSs) and simply-typed term rewriting systems (STRSs) are computational models of functional programs. We recently proposed an extremely powerful method, the static dependency pair method, which is based on the notion of strong computability, in order to prove termination in STRSs. In this paper, we extend the method to HRSs.(More)
Simply-typed term rewriting systems (STRSs) are an extension of term rewriting systems. STRSs can be naturally handle higher order functions, which are widely used in existing functional programming languages. In this paper we design recursive and lexicographic path orders, which can efficiently prove the termination of STRSs. Moreover we discuss an(More)
To simplify the task of proving termination and AC-termination of term rewriting systems, elimination transformations have been vigorously studied since the 1990s. Dummy elimination, distribution elimination, general dummy elimination, and improved general dummy elimination are examples of elimination transformations. In this paper we clarify the essence of(More)
Recently, rewriting induction, which is one of the induction principles for proving inductive theorems in equational theory, has been extended to deal with constrained term rewriting systems. Rewriting induction has been applied to developing a method for proving the equivalence of imperative programs. To prove inductive theorems, there are many cases where(More)
A static dependency pair method, proposed by us, can effectively prove termination of simply-typed term rewriting systems (STRSs). The theoretical basis is given by the notion of strong computability. This method analyzes a static recursive structure based on definition dependency. By solving suitable constraints generated by the analysis result, we can(More)