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### Page 2837 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews
L C A®* is a Church-Rosser language if there are a CR system over the alphabet AU B, strings t;,t2 € B* and an accepting symbol Y € B such that, for all w € A*, w EL if and only if t;wt, — Y.  ...  A language L is a Church- Rosser congruential language if L is the union of finitely many congruence classes of some CR system.  ...

### Page 1747 of Mathematical Reviews Vol. 48, Issue 5 [page]

1974 Mathematical Reviews
systems and Church-Rosser theorems.  ...  Author’s summary: ‘“‘Subtree replacement systems form a broad class of tree-manipulating systems.  ...

### When is a monoid a group? the Church-Rosser case is tractable

Ronald V. Book
1982 Theoretical Computer Science
The following question is shown to be tractable: given a finite monadic Church-Rosser Thue system T and a finite set A, is the submonoid generated by A (of the monoid presented by T) a group?  ...  The Church-Rosser property is a powerful tool in the study of term-rewriting systems and tree-manipulating systems [lo, IS] .  ...  Theorem 4 . 1 . 41 Let T be a ?%ue system on the alphabet C. Suppose that T is Church-Rosser and that 97 is a group.  ...

### Decidable sentences of Church-Rosser congruences

Ronald V. Book
1983 Theoretical Computer Science
A decision procedure for a class of true sentences of congruences generated by finite monadic Church-Rosser systems is developed.  ...  Using this decision procedure it is shown that if *.tir is the monoid presented by such a system 7', then (i) it is decidable given T whether ,Wr is a group, (ii) it is decidable given T and a finite set  ...  Introduction The Church-Rosser property has been shown to be extremely powerful when possessed by term-rewriting systems, tree-manipulating systems, and other types of replacement systems [8, 14, 161.  ...

### Thue systems as rewriting systems

Ronald V. Book
1987 Journal of symbolic computation
The emphasis is on Thue systems with the Chureh-Rosser property, where the notion of reduction is based on length-decreasing rewriting rules.  ...  Since Thue systems may also be considered as presentations of monoids, the language of monoids (and groups) is used to describe some of these properties.  ...  For example, one might investigate the types of groups or monoids that are finitely generated but are presented by infinite regular or infinite context-free Church-Rosser Thue systems.  ...

### Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem

N.G de Bruijn
1972 Indagationes Mathematicae (Proceedings)
As an example the most essential part of a proof of the Church-Rosser theorem is presented in this namefree calculus.  ...  The system is claimed to be efficient for automatic formula manipulation as well aa for metdingual discussion.  ...  For a survey of proofs of the Church-Rosser theorem see [l] p. 1617. An elaborate treatment of the theorem can also be found in [4] .  ...

### Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem [chapter]

N.G. de Bruijn
1994 Studies in Logic and the Foundations of Mathematics
As an example the most essential part of a proof of the Church-Rosser theorem is presented in this namefree calculus.  ...  The system is claimed to be efficient for automatic formula manipulation as well aa for metdingual discussion.  ...  For a survey of proofs of the Church-Rosser theorem see [l] p. 1617. An elaborate treatment of the theorem can also be found in [4] .  ...

### Testing for the Church-Rosser property

Ronald V. Book, Colm P. O'Dunlaing
1981 Theoretical Computer Science
, tree manipulating sys;ems, graph grammars, etc.  ...  IRtroduction Replacement systems arise in the study of formula manipulation syMems such as theorem provers, program optimizers, and algebraic simplifiers, where: they take the form of term rewriting systems  ...  We state our result as follows: There is a polynomial time algorithm to determine whether a finite Thue system is Church-A!osser.  ...

### Complete sets of transformations for general E-unification

Jean H. Gallier, Wayne Snyder
1989 Theoretical Computer Science
We extend the method of transformations on systems of terms, developed by Martelli-Montanari for standard unification, to E-unification by giving two sets of transformations, %Y and Y, which are proved  ...  Given a tree t and some tree address LY E Dom( t), the subtree oft rooted at a is the tree, denoted t/a, whose domain is the set {/? ) C@ E Dom( t)} and such that t/a(P) = t(c@) for all p E Dom(t/a).  ...  It is now easy to adapt the proofs of Theorems 4.19 and 4.20 to the new definition of proof trees, in the case where (E, R) is ground Church-Rosser.  ...

### The theory and practice of first-class prompts

M. Felleisen
1988 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '88
a ranges over constants, xover Vars, and L, M, and Nover &-terms.  ...  2 The modified X,-C-calculus The term set A7 of the original X,-C-calculus is defined inductively over a set of algebraic constants, Con& and a set of variables, Vars: L ::= a 12 1 Xt.M 1 MN 1 FM, where  ...  End Unlike its predecessor, this calculus has the ordinary Church-Rosser Property: Theorem (Church-Rosser for X,-C).  ...

### A PVS Theory for Term Rewriting Systems

André L. Galdino, Mauricio Ayala-Rincón
2009 Electronical Notes in Theoretical Computer Science
A theory, called trs, for Term Rewriting Systems in the theorem Prover PVS is described.  ...  of elaborated criteria from the theory of Term Rewriting Systems such as the Knuth-Bendix Critical Pair Theorem.  ...  Also, specifications of λ-calculus, abstract reduction and term rewriting systems with formalizations of the Church-Rosser Theorem and Newman's Lemma have been presented in several proof assistants; eg  ...

### A types-as-sets semantics for milner-style polymorphism

Mitchell Wand
1984 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '84
An adaptation of llindley's Principal Typing Theorem then asserts that the (ype information can be reconstructed.  ...  The resulting semantics is simpler than that for fully polymorphic models [Leivant 83], and generalizes (,he standard constructions, such as retracts and ideals.  ...  We thank Ravi Sethi, David MacQueen, and Daniel Leivant for the opportunity to present the paper on very short notice. They, Dana Scott, and Albert Meyer provided useful discussion.  ...

### Learning of human-like algebraic reasoning using deep feedforward neural networks

Cheng-Hao Cai, Yanyan Xu, Dengfeng Ke, Kaile Su
2018 Biologically Inspired Cognitive Architectures
Also, to represent both top-down and bottom-up information of the expressions, a centralisation technique is used to improve the reduced partial trees.  ...  Briefly, in a reasoning system, a deep feedforward neural network is used to guide rewriting processes after learning from algebraic reasoning examples produced by humans.  ...  Usually, rewriting is based on a tree-manipulating system, as many algebraic expressions can be represented by using tree structures, and the manipulation of symbols in the expressions is equivalent to  ...

### Correctness of parallel programs: The Church-Rosser approach

Barry K Rosen
1976 Theoretical Computer Science
We conclude with a survey of prospects for computer assisted proofs structured by the Church Rosser approach. * A condensation of an earlier version of this paper was resented at the hmmatimd W'wosium  ...  on Proving and Improving Programs, Arc et Senans, France, July l-3, 1975.  ...  and the Church-Rosser approach in particular.  ...

### Chapter IX: Applications of SRS theory to LISP and lucid [chapter]

1977 Lecture Notes in Computer Science
Henderson and Morris describe the interpreter by replacement rules at the pointer manipulation level and conjecture (p. i00) that (i) the system is Church-Rosser, (2) the replacement rules are complete  ...  So, by Theorems 17, 6 and 3 (PP. 70, 38, 28), ~R has the confluence property and the Church-Rosser property.  ...
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