Unique normal forms in term rewriting systems with repeated variables

1981 ◽  
Author(s):  
Paul Chew
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Unique Normal Forms

scholarly journals Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm

2014 ◽  
Vol 22 (1) ◽  
pp. 37-56
Author(s):  
Grzegorz Bancerek
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Educational Content ◽  
Term Rewriting Systems ◽  
Rewriting Systems

Summary Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, Church- Rosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].

scholarly journals Derivational Complexity and Context-Sensitive Rewriting

2021 ◽  
Author(s):  
Salvador Lucas
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Linear Term ◽  
The Other ◽  
Term Rewriting Systems ◽  
Context Sensitive ◽  
Rewriting Systems ◽  
Other Hand

AbstractContext-sensitive rewriting is a restriction of rewriting where reduction steps are allowed on specific arguments $$\mu (f)\subseteq \{1,\ldots ,k\}$$ μ ( f ) ⊆ { 1 , … , k } of k-ary function symbols f only. Terms which cannot be further rewritten in this way are called $$\mu $$ μ -normal forms. For left-linear term rewriting systems (TRSs), the so-called normalization via$$\mu $$ μ -normalization procedure provides a systematic way to obtain normal forms by the stepwise computation and combination of intermediate $$\mu $$ μ -normal forms. In this paper, we show how to obtain bounds on the derivational complexity of computations using this procedure by using bounds on the derivational complexity of context-sensitive rewriting. Two main applications are envisaged: Normalization via $$\mu $$ μ -normalization can be used with non-terminating TRSs where the procedure still terminates; on the other hand, it can be used to improve on bounds of derivational complexity of terminating TRSs as it discards many rewritings.

scholarly journals Free Term Algebras

2012 ◽  
Vol 20 (3) ◽  
pp. 239-256
Author(s):  
Grzegorz Bancerek
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Free Term ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Free Generators

Summary We interoduce a new characterization of algebras of normal forms of term rewriting systems [35] as algerbras of term free in itself (any function from free generators into the algebra generates endomorphism of the algebra). Introduced algebras are free in classes of algebras satisfying some sets of equalities. Their universes are subsets of all terms and the denotations of operation symbols are partially identical with the operations of construction of terms. These algebras are compiler algebras requiring some equalities of terms, e.g., associativity of addition.

scholarly journals Automatic Inference of Term Equivalence in Term Rewriting Systems

10.29007/qsmm ◽  
2018 ◽  
Author(s):  
Marco Comini ◽  
Luca Torella
Keyword(s):  
Normal Forms ◽  
Logical Consequence ◽  
Source Code ◽  
Algebraic Property ◽  
Term Rewriting ◽  
Proof Of Concept ◽  
Inference Method ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Term Equivalence

In this paper we propose a parametric technique to automatically infer algebraic property-oriented specifications from Term Rewriting Systems. Namely, given the source code of a TRS we infer a specification which consists of a set of most general equations relating terms that rewrite, for all possible instantiations, to the same set of normal forms.The semantic-based inference method that we propose can cope with non-constructor-based TRSs, and considers non-ground terms. Particular emphasis is posed to avoid the generation of “redundant” equations that can be a logical consequence of other ones.To experiment on the validity of our proposal we have considered an instance of the method employing a novel (condensed) semantics for left-linear TRSs and we have implemented a “proof of concept” prototype in Haskell which is available online.

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