Another approach is to reduce cycle termination to string termination by a sound and complete transformation and then applying a termination prover for termination of string rewrite systems. Several of those transformations and combinations of these techniques and torpacyc are included in the tool cycsrs which can also be used online.

Cycle rewriting was introduced in [1] where its complexity was analyzed and termination techniques using arctic and tropical matrix interpretations based on type graphs were developed. In [2] further termination techniques for cycle termination were introduced: trace-decreasing matrix interpretations as well as sound and complete transformations from cycle to string termination.

- Channel 4: The Early Years and the Jeremy Isaacs Legacy.
- Your Answer.
- String Rewriting Systems in: Formalized Mathematics Volume 15 Issue 3 ().
- Semi-Thue system - Wikiwand.

Cycle Rewriting From Termination-Portal. Matching Logic Rosu, Grigore. This paper presents matching logic, a first-order logic FOL variant for specifying and reasoning about structure by means of patterns and pattern matching.

Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain the set of values that match it , in contrast to FOL where functions and predicates map into a regular domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, modal logic, and separation logic.

We study an extension of Plotkin's call-by-value lambda-calculus via two commutation rules sigma-reductions. These commutation rules are sufficient to remove harmful call-by-value normal forms from the calculus, so that it enjoys elegant characterizations of many semantic properties.

## String rewriting systems

We prove that this extended calculus is a conservative refinement of Plotkin's one. In particular, the notions of solvability and potential valuability for this calculus coincide with those for Plotkin's call-by-value lambda-calculus. The proof rests on a standardization theorem proved by generalizing Takahashi's approach of parallel reductions to our set of reduction rules.

The standardization is weak i.

## Semi-Thue system - Wikipedia

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence. This makes the framework especially suitable for formalizations in theorem provers. A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments.

To avoid semantic ambiguity, such a semantics is expected to be coherent, i. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping.

## Semi-Thue system

The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing. We present a method for synthesizing compositions of mixins using type inhabitation in intersection types.

First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators.

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We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis.

- Control Words of String Rewriting P Systems - Hope's Institutional Research Archive (HIRA).
- String rewriting systems - BOOK RONALD V., Springer - , Libro Inglese | Libreria Universitaria;
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Geser, D. Hofbauer, J. Waldmann, H.

### Examples of use

Finding finite automata that certify termination of string rewriting systems. N2 - We present a technique based on the construction of finite automata to prove termination of string rewriting systems. Using this technique the tools Matchbox and TORPA are able to prove termination of particular string rewriting systems completely automatically for which termination was considered to be very hard until recently. AB - We present a technique based on the construction of finite automata to prove termination of string rewriting systems.