CoLL author: Kiraku Shintani (JAIST) version: 1.3 code: OCaml - - PowerPoint PPT Presentation

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Jul 31, 2023 469 likes •519 views

CoLL: Commutation prover for Left-Linear TRSs ( R , S ) YES/NO CoLL author: Kiraku Shintani (JAIST) version: 1.3 code: OCaml (4000 LoC) MAYBE CoLL: Commutation prover for Left-Linear TRSs - Knuth-Bendix ( R , S ) - AC theory YES/NO -

SLIDE 1

CoLL: Commutation prover for Left-Linear TRSs

(R, S) YES/NO MAYBE

CoLL

author: Kiraku Shintani (JAIST) version: 1.3 code: OCaml (4000 LoC)

SLIDE 2

CoLL: Commutation prover for Left-Linear TRSs

(R, S)

Knuth-Bendix
AC theory
development closed
rule-labeling

YES/NO MAYBE

MAYBE?

SLIDE 3

CoLL: Commutation prover for Left-Linear TRSs

(R, S)

Knuth-Bendix
AC theory
development closed
rule-labeling

are there commuting subsystems?

YES/NO MAYBE

MAYBE {R1, . . . , Rm} × {S1, . . . , Sn} ∅

based on Hindley’s commutation lemma:
i Ri and

j Sj commute if Ri and Sj commute for all i, j

CoLL 1/1

SLIDE 4

CoLL: Commutation prover for Left-Linear TRSs

(R, S)

Knuth-Bendix
AC theory
development closed
rule-labeling

are there commuting subsystems?

YES/NO MAYBE

MAYBE {R1, . . . , Rm} × {S1, . . . , Sn} ∅

based on Hindley’s commutation lemma:
i Ri and

j Sj commute if Ri and Sj commute for all i, j

left-linearity is essential for commutative decomposition

CoLL 1/1