Term rewriting is a general model of computation that investigates a wide range of (potentially non-deterministic) methods of replacing subterms of syntactic expression, more precisely an element of a term-algebra (over some set of variables) with other terms.

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Term Rewriting vs Unification

How is term rewriting different from unification, and what's the difference between term rewriting languages and logic programming, like Prolog?
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Term rewrite system is non-confluent, but cannot find different normal forms of term

I wrote a simple TRS that I believe is non-confluent, but I'm not able to find a term with two normal forms for it. The TRS is defined on the signature $\mathcal F=\{f,\ l,\ s,\ o\}$ and the rewrite ...
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Misunderstanding the Church-Rosser property

I am contemplating the Church-Rosser property and I clearly misunderstand it, but I do not exactly know why. If $x$ and $y$ are such that $x \overset{*}{\leftrightarrow} y$, then $x ...
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What is a rewrite-based system?

I am reading about this in the context of the K semantic framework. I keep encountering terms such as rewrite-term and rewrite logic. My main aim is to understand what is K doing and how it works, so ...
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Why Term Rewriting?

I've done a bit of googleing and have come up a bit short. I am wondering what are the main reasons for computing scientists, programmers, to study term rewriting, and/or term graph rewriting. As ...
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Is “duplicate” in RPN enough for replacing variable binding in term expressions?

I try to work out some consequences of storing (or "communicating"/"transmitting") a rational number by a term expression using the following operators: $0$, $\mathsf{inc}$, $\mathsf{add}$, ...
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Where can I find rules for source to source transformation optimization rules?

Upon reading Do source code optimizers exist? I knew that such programs existed but the ones I have worked with use a set of rules to drive a transformation algorithm. Ira Baxter provided a link to ...
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Is this $\beta$-reduction well defined?

Would it be possible to apply $(\lambda x.\lambda y. x)$ to the argument $y$? It seems to me that this must not be possible as it would give a different answer if applied to a constant, call it ...
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Implementation of datatypes in Haskell?

In Haskell, are datatypes converted to the "Church encoding" i.e. folding the data type. For example, given data N = Z | S N in Haskell, it can be converted to ...
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TAPL: Explanation and example(s) for satisfied

This question arises from my reading of "Types and Programming Languages" (WorldCat) by Benjamin C. Pierce. On page 36 is the definition for satisfied A rule is satisfied by a relation if, for ...
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Proving non-confluency and adding an equation to make it confluent and terminating

I currently have a system that has {f(a) = b, f(f(x)) = x} (part of an exam question - look at page 5 - exercise 1). To start off with proving non-confluency, I am ...
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Example of a parsing/rewriting system?

I am studying formal languages and playing with writing my own parsers for them. I have a context free grammar parser already that works well. I am wondering if anyone can point me towards actually ...
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The meaning of modulo in “formula modulo a background theory”

I have been reading some papers where I keep reading stuff like “first-order formula modulo a background theory”. Does anyone know what modulo means in this case ? Is it something like “with respect ...
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Reduction rule for IF?

I'm working through Simon Peyton Jones' "The Implementation of Functional Programming Languages" and on page 20 I see: IF TRUE ((λp.p) 3) ↔ IF TRUE 3 (per β red) (1) ...
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Confluence proof for a simple rewriting system

Assume we have a simple language that consists of the terms: $\mathtt{true}$ $\mathtt{false}$ if $t_1,t_2,t_3$ are terms then so is $\mathtt{if}\: t_1 \:\mathtt{then}\: t_2 \:\mathtt{else}\: t_3$ ...
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Is it possible to derive a string in this rewriting system?

Rewriting system is a set of rules in the form of $A \leftrightarrow B$. If we apply that rule to a string $w$ we replace any substring $A$ in $w$ with a substring $B$ and vice versa. Given a ...