Term Rewriting and All That

Baader, F., & Nipkow, T. (1998). Term Rewriting and All That. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

1998

DOI

10.1017/cbo9781139172752

ISBN

9780521455206

Link

https://doi.org/10.1017/CBO9781139172752

Cited from

computer_science

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Equivalence-Preserving Rewriting
  • Theorem proving: normal-form rewriting in term-rewriting systems, rewriting a proof for shorter or more standard form, tactic-based proof restructuring under preserved logical content.

    This sourceStandard reference on term-rewriting systems, normal forms, confluence, and termination — the formal apparatus for rewriting under a preserved equivalence.

Domain-specific

• Overlap (term rewriting)
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Reflexive closure
  • Taking its reflexive closure permits a state to reach itself in zero steps while still excluding all two-step consequences; those require transitive closure.

Mechanisms

• Rewrite or Transition Rule Engine
  • A rule set that is not terminating sends the engine into an infinite loop — the "nice" new rewrite rule that quietly creates a cycle is the classic culprit — and a rule set that is not confluent yields order-dependent answers

    This sourceExplains that termination prevents endless rewriting and confluence ensures a unique normal form independent of rule-application order.

Verification

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