scholarly journals Partial intersection type assignment in applicative term rewriting systems

1993 ◽  
pp. 29-44 ◽  
Author(s):  
Steffen van Bakel
Keyword(s):  
Term Rewriting ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Type Assignment

COMBINING TERM REWRITING AND TYPE ASSIGNMENT SYSTEMS

1990 ◽  
Vol 01 (03) ◽  
pp. 165-184 ◽  
Author(s):  
FRANCO BARBANERA
Keyword(s):  
Term Rewriting ◽  
Second Order ◽  
Term Rewriting Systems ◽  
Strong Normalization ◽  
First Order ◽  
Rewriting Systems ◽  
Type Assignment ◽  
Natural Way

Recently some attention has been paid to the properties enjoyed by combinations of term rewriting and λ-calculus based systems. In this paper strong normalization and confluence are proved for λ-terms obtained by merging pure λ-terms and first order canonical term rewriting systems, in the framework of a system which extends the Coppo-Dezani intersection type assignment system. On terms of the resulting calculus we can perform ordinary β and η reductions, as well as the reductions induced in a natural way by the term rewriting systems. In some parts of our analysis we follow rather closely the development contained in a recent paper by Val Breazu-Tannen and Jean Gallier. There, the same properties of strong normalization and confluence are proved for systems obtained by combining the second order polymorphic λ-calculus with first order canonical term rewriting systems. The strong normalization result of Breazu-Tannen and Gallier is proved to be implied by the corresponding property of our system.

Type assignment and termination of interaction nets

1998 ◽  
Vol 8 (6) ◽  
pp. 593-636 ◽  
Author(s):  
MARIBEL FERNÁNDEZ
Keyword(s):  
Type System ◽  
Term Rewriting ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Programming Paradigm ◽  
Type Assignment ◽  
Computational Aspects ◽  
Rank 2 ◽  
Intersection Types ◽  
Simple Interaction

Interaction nets have proved to be a useful tool for the study of computational aspects of various formalisms (e.g. λ-calculus, term rewriting systems), but they are also a programming paradigm in themselves, and this is actually how they were introduced by Lafont. In this paper we consider semi-simple interaction nets as a programming language, and present a type assignment system using intersection types. First we show that interactions preserve types (i.e., the system enjoys subject reduction), and we compare this type assignment system with the intersection systems for λ-calculus and term rewriting systems. Then we define a recursion scheme that ensures termination of all interaction sequences. By relaxing the scheme and using the type assignment system, we derive another sufficient condition for termination of interaction nets. Finally, we show that although the type system based on general intersection types is not decidable, its restriction to rank 2 types is, and we give an algorithm that computes principal types for nets.

scholarly journals Semantics and strong sequentiality of priority term rewriting systems

1998 ◽  
Vol 208 (1-2) ◽  
pp. 87-110 ◽  
Author(s):  
Masahiko Sakai ◽  
Yoshihito Toyama
Keyword(s):  
Term Rewriting ◽  
Term Rewriting Systems ◽  
Rewriting Systems

PATTERN MATCHING CODE MINIMIZATION IN REWRITING-BASED PROGRAMMING LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 873-887
Author(s):  
NADIA NEDJAH ◽  
LUIZA DE MACEDO MOURELLE
Keyword(s):  
Programming Languages ◽  
Pattern Matching ◽  
Term Rewriting ◽  
Directed Acyclic Graphs ◽  
Tree Automaton ◽  
Minimal Tree ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Acyclic Graphs ◽  
Space Requirements

We compile pattern matching for overlapping patterns in term rewriting systems into a minimal, tree matching automata. The use of directed acyclic graphs that shares all the isomorphic subautomata allows us to reduce space requirements. These are duplicated in the tree automaton. We design an efficient method to identify such subautomata and avoid duplicating their construction while generating the dag automaton. We compute some bounds on the size of the automata, thereby improving on previously known equivalent bounds for the tree automaton.

scholarly journals Infinite normal forms for non-linear term rewriting systems

1995 ◽  
Vol 152 (2) ◽  
pp. 285-303
Author(s):  
Paola Inverardi ◽  
Monica Nesi
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Linear Term ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Non Linear
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