• Journal of KIISE:Computer Systems and Theory
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• v.35 no.4
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• pp.178-185
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• 2008

This research presents an translation technique of encoding rewrite rules with patterns into the lambda calculus. We show, following the theory of Böhm separability, rewrite rules with distinctive patterns, called separable systems, can be translated into the lambda calculus. Moreover, according to the property of Böhm equivalence classes, we can also encode rewrite systems with default rules, which allows to interpret some of 'undefined' terms of TRSs as an identified lambda term.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.3
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• pp.141-149
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• 2008

Most functional programming languages allows programmers to write ambiguous rules, under the strategy that pattern-matching will be performed in a direction of 'from top to bottom' way. While providing programmers with convenience and intuitive understanding of defining default rules, such ambiguous rules may make the semantics of functional languages unclear. More specifically, it may fail to apply the equational reasoning, one of most significant advantage of functional programming, and may cause to obscure finding a formal way of translating functional languages into the ${\lambda}$-calculus; as a result, we only get an ad hoc translation. In this paper, we associate with separability of term rewriting systems, holding purely-declarative property, pattern-matching semantics of lazy functional languages. Separability can serve a formalism for translating lazy functional languages into the ${\lambda}$-calculus.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.658-666
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• 2004

Separable systems are defined in term rewriting systems, respecting the notion of separability in the λ-calculus. In this research, we generalize separable systems of term rewriting systems, which was studied in restrictive systems such as constructive systems. We also associate separability with index-transitivity and with forward branching Separability is identified with forward branching, and strong sequentiality with index-transitivity satisfies separability. These are such good properties that enable us to describe the procedure of pattern-matching as an index tree, which is a sort of automata, and to transform separable systems into a constructor system with a simple pattern. Separable systems, in particular, can be translated into the λ-calculus. This research can serve a theoretical basis which allows functional languages to be explained by the λ-calculus, since functional languages such as ML and Haskell belong to a subclass of separable systems.

• Journal of KIISE:Software and Applications
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• v.28 no.8
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• pp.582-592
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• 2001

직교항 개서 시스템은 함수형 언어와 그 구현 과정을 잘 반영하고 있다. 본 논문에서는 룰의 왼쪽 부분을 매우 간략한 형태로 된 flat 시스템으로 번역하는 기법에 대해서 논의한다. 직교항 개서 시스템의 한 부류인 transformable OTRSs를 정의하고, 이 시스템들은 flat 시스템으로 변환될 수 있음을 보인다. 이 변환은 람다 계산법에서 연구된 분리성 이론을 기반으로 하고 있는데, 본 논문에서는 직교항 개서 시스템에서의 분리성과 강력 순차성에 대한 연관성에 대해서도 논의하고 있다.