an:06690918
Zbl 1368.03020
Nakazawa, Koji; Fujita, Ken-etsu
Compositional Z: confluence proofs for permutative conversion
EN
Stud. Log. 104, No. 6, 1205-1224 (2016).
00360575
2016
j
03B40
lambda calculus; lambda-mu calculus; confluence; permutative conversion
The Z-theorem of \textit{P. Dehorney} and \textit{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.
Martin W. Bunder (Wollongong)