Compositional Z: confluence proofs for permutative conversion. (English) Zbl 1368.03020

The Z-theorem of P. Dehorney and Z. van Oostrom [“Proving confluence by monotonic single-step upperbound functions”, in: Logical models of reasoning and computation (LMRC-08) (2008)] allows the proof of confluence for a number of variants of the \(\lambda\)-calculus. In the current paper, the authors generalise this to a compositional Z-theorem, which is easily proved from the Z-theorem. The new theorem allows, in addition, proofs of confluence for \(\lambda\)-calculi corresponding to intuitionistic and classical natural deduction with disjunction and permutative conversions as well as a \(\lambda\)-calculus with explicit substitution.


03B40 Combinatory logic and lambda calculus
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