Read e-book online Typed Lambda Calculi and Applications: 5th International PDF

By Olivier Danvy (auth.), Samson Abramsky (eds.)

ISBN-10: 3540419608

ISBN-13: 9783540419600

ISBN-10: 3540454136

ISBN-13: 9783540454137

This ebook constitutes the refereed complaints of the fifth foreign convention on Typed Lambda Calculi and purposes, TLCA 2001, held in Krakow, Poland in may well 2001. The 28 revised complete papers offered have been rigorously reviewed and chosen from fifty five submissions. the quantity studies study effects on all present facets of typed lambda calculi. one of the subject matters addressed are sort structures, subtypes, coalgebraic equipment, pi-calculus, recursive video games, quite a few forms of lambda calculi, discount rates, substitutions, normalization, linear good judgment, cut-elimination, prelogical kin, and mu calculus.

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Yoshida Note on terminology. In this section, correspondence with typed transition and intensional structures of games is a central topic. Since there is some difference in terminology between process calculi and game semantics, we list the correspondence for reference. 1 Note that “O” is usually used to indicate “Opponent” in game semantics, which corresponds to input in our (process-algebraic) terminology. To avoid confusion, we shall consistently use “input” and “output” rather than “Opponent” and “Player”.

1 , we build sequential processes one by one, starting from inaction. 1 b. 1 b = ⊥b and O I =O where “⊥b” means name b is no longer composable. c since b is affine. ω b. a | b since O O is undefined. a and b, two messages to a will appear in parallel. 2 for Nat◦ ). ω I [[succ]]u . 36 M. Berger, K. Honda, and N. ω . ω u. a copies all behaviour starting at one channel to those starting at another. ω and Γ = x : τ ·y : τ . ω y. c, we can check that all actions of P are copied from x to y (this does not include c which is emitted by P ).

In (iii) we let → → = ≡ ∪(−→)∗ . Proposition 1. (i) (weakening) If ∆ ≤ Γ and ∆ φ P then Γ φ P . (ii) (minimal type) A typable process has a minimum base and action type. Further, if Γ φ P and ∆ ψ P then φ = ψ. → Q then Γ φ Q. (iii) (subject reduction) If Γ φ P and P → We say an occurrence (subterm) in a process is an active input (resp. active output) if it is an input-prefixed (resp. output-prefixed) term which neither occurs under an input prefix nor has its subject bound by an output prefix.

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Typed Lambda Calculi and Applications: 5th International Conference, TLCA 2001 Kraków, Poland, May 2–5, 2001 Proceedings by Olivier Danvy (auth.), Samson Abramsky (eds.)


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