Term rewriting and lambda calculus

2012 27th Annual IEEE Symposium on Logic in Computer Science Pub Date : 2012-06-25 DOI:10.1109/LICS.2012.12

J. Klop

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Abstract

This tutorial will cover the following topics: (i) The origins of term rewriting systems and λ -calculus. (ii) Rewriting lingo: the basic vocabulary about confluence and termination. (iii) Newman’s Lemma, tiling games, and decreasing diagrams. (iv) Word rewriting: the free idempotent monoid; braids. (v) Term rewriting: some universal algebra; braids revisited; how hidden functions may help. Modularity: divide et impera. RPO revisited: ILPO, iterative lexicographic path ordering. (vi) Rewrite, rewrite, rewrite, rewrite, rewrite, rewrite, rewrite, rewrite, rewrite, rewrite, infinitary TRSs; Cauchy convergence versus strong convergence; a coinductive definition; loops make the difference. (vii) Orthogonal iTRSs: collapsing rules cause non-confluence; equivalence of global infinitary weak and strong normalization WN∞ ⇐⇒ SN∞; continuity of infinitary rewriting ; breakdown of properties for weakly orthogonal iTRSs. (viii) Infinitary lambda calculus λ ∞-calculus; subsumption of Scott’s Induction Rule SIR; Lego blocks for new fixed point combinators; the threefold path; looping λ -terms; clocked semantics of λ -calculus. (ix) παντα ρει : Streams and productivity. 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science

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项重写和微积分

本教程将涵盖以下主题:(i)术语重写系统和λ微积分的起源。(ii)改写行话:关于汇流和终止的基本词汇。(iii)纽曼引理、平铺博弈和递减图。(iv)字重写:自由幂等单群;辫子。(v)项改写:一些通用代数;辫子重新审视;隐藏函数如何提供帮助。模块化:分而治之。重新审视RPO: ILPO，迭代字典路径排序。(vi)重写，重写，重写，重写，重写，重写，重写，重写，重写，重写，重写，无限TRSs;柯西收敛与强收敛;协归纳定义;循环产生了不同。(vii)正交itrs:坍缩规则导致不合流;全局无穷弱正则化与强正则化WN∞=⇒SN∞;无穷改写的连续性;弱正交itrs的性能分解。(viii)无穷λ微积分λ∞微积分;斯科特归纳法的归纳;用于新的定点组合器的乐高积木;三重路径;循环λ项;λ微积分的时钟语义。(ix) παντα ρει:流与生产力。2012年第27届ACM/IEEE计算机科学逻辑研讨会

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2012 27th Annual IEEE Symposium on Logic in Computer Science

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