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A standardisation proof for algebraic pattern calculi

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Delia Kesner (PPS, CNRS, Universite Paris Diderot - France), Carlos Lombardi (Universidad Nacional de Quilmes - Argentina), Alejandro Ríos (Universidad de Buenos Aires - Argentina)

Logic in Computer Science · Submitted 18 Feb 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove the Standardisation Theorem by using the technique developed by Takahashi and Crary for lambda-calculus.

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arXiv ID1102.3734 (version 1)
Pith IDQR3QIPRF, Pith's permanent record of this paper and its review
CitationAlejandro R\'ios (Universidad de Buenos Aires - Argentina), Carlos Lombardi (Universidad Nacional de Quilmes - Argentina), CNRS, Delia Kesner (PPS, Universite Paris Diderot - France). "A standardisation proof for algebraic pattern calculi." arXiv:1102.3734 (2011). https://pith.science/paper/QR3QIPRF
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,176 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on reduction steps that are needed to match an argument with respect to a given pattern. We prove the Standardisation Theorem by using the technique developed by Takahashi and Crary for lambda-calculus. The proof is based on the fact that any development can be specified as a sequence of head steps followed by internal reductions, i.e. reductions in which no head steps are involved.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This work gives some insights and results on standardisation for call-by-name pattern calculi. contribution 0.97 0.88 0.21 asserted 0.72
s1 More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. contribution 0.99 0.95 0.09 asserted 1.00
s2 This notion is based on reduction steps that are needed to match an argument with respect to a given pattern. method 0.65 0.47 0.04 asserted 1.00
s3 We prove the Standardisation Theorem by using the technique developed by Takahashi and Crary for lambda-calculus. method 0.89 0.84 0.59 asserted 1.00
s4 The proof is based on the fact that any development can be specified as a sequence of head steps followed by internal reductions, i.e. reductions in which no head steps are involved. method 0.99 0.70 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on reduction steps that are needed to match an argument with respect to a given pattern. We prove the Standardisation Theorem by using the technique developed by Takahashi and Crary for lambda-calculus. The proof is based on the fact that any development can be specified as a sequence of head steps followed by internal reductions, i.e. reductions in which no head steps are involved.

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