Strong reduction for typed lambda calculus with first-class environments

Authors:
Shin-ya Nishizaki;Mizuki Fujii
Affiliations:
Department of Computer Science, Tokyo Institute of Technology, Tokyo, Japan;Department of Computer Science, Tokyo Institute of Technology, Tokyo, Japan
Venue:
ICICA'12 Proceedings of the Third international conference on Information Computing and Applications
Year:
2012

Citing 6
Cited 0

An abstract frame work for environment machines

Theoretical Computer Science
Confluence properties of weak and strong calculi of explicit substitutions

Journal of the ACM (JACM)
An operational semantics of sharing in lazy evaluation

Science of Computer Programming
A Polymorphic Environment Calculus and its Type-Inference Algorithm

Higher-Order and Symbolic Computation
Higher-order Unification via Explicit Substitutions

LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Revised [6] Report on the Algorithmic Language Scheme

Revised [6] Report on the Algorithmic Language Scheme

Quantified Score

Hi-index	0.00

Visualization

Abstract

Programs contain variables, and the bindings of these variables to the corresponding values are kept in a so-called 'environment'. A first-class environment is a mechanism that the environments in programs can be treated as first-class entities, which are objects that can to be passed and returned between functions and procedures. Nishizaki proposed the lambda calculus with first-class environments, called the environment lambda calculus, and has investigated its theoretical properties [6---8, 10]. The various systems of the environment lambda calculus are based on weak reduction, that is, application of a substitution to a lambda abstraction is postponed until an argument is applied to it. In this paper, we propose a simply-typed lambda calculus with strong reduction. We investigate several theoretical properties such as the subject reduction theorem.