Semantics for Combinatory Logic With Intersection Types

Author:

Ghilezan Silvia,Kašterović Simona

Abstract

There is a plethora of semantics of computational models, nevertheless, the semantics of combinatory logic are among the less investigated ones. In this paper, we propose semantics for the computational system of combinatory logic with intersection types. We define extensional applicative structures endowed with special elements corresponding to primitive combinators. We prove two soundness and completeness results. First, the equational theory of untyped combinatory logic is proven to be sound and complete with respect to the proposed semantics. Second, the system of the combinatory logic with intersection types is proven to be sound and complete with respect to the proposed semantics. The usual approach to the semantics for calculi with types that can be found in the literature is based on models for the untyped calculus endowed with a valuation of type variables which enables the interpretation of types to be defined inductively. We propose, however, a different approach. In the semantics we propose, the interpretation of types is represented as a family of subsets that satisfies certain properties, whereas for a given valuation of term variables, the interpretation of terms is defined inductively. Due to the wide applicability of semantics of computational models, the presented approach could be further developed to other computational models and beyond—to current and foreseen application of semantics to large distributed systems and new challenging technologies.

Publisher

Frontiers Media SA

Subject

Computer Science Applications,Computer Vision and Pattern Recognition,Human-Computer Interaction,Computer Science (miscellaneous)

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3