An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On full abstraction for PCF: I, II, and III
Information and Computation
Information and Computation
Parallel beta reduction is not elementary recursive
Information and Computation
Hereditarily Sequential Functionals
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
From Hilbert Spaces to Dilbert Spaces: Context Semantics Made Simple
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Conservation of information: applications in functional, reversible, and quantum computing
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Relating complexity and precision in control flow analysis
ICFP '07 Proceedings of the 12th ACM SIGPLAN international conference on Functional programming
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We give a tutorial and first-principles description of the context semantics of Gonthier, Abadi, and Lévy [5, 4], a computer-science analogue of Girard's geometry of interaction [3]. In the spirit of the invited presentation of Tom Knight (see this Proceedings [7]), the semantics is reversible, and supports pseudo-quantum computation via a superposed sharing of terms and evaluation contexts [2].Context semantics provides a mechanism for modelling ?-calculus, and more generally multiplicative-exponential linear logic (MELL); we explain the the call-by-name (CBN) coding of the ?-calculus, and sketch a proof of the correctness of readback, where the normal form of a ?-term is recovered from its semantics. This analysis yields the algorithmic correctness of Lamping's optimal reduction algorithm [8]. We relate the context semantics to linear logic types and to ideas from game semantics, used to prove full abstraction theorems for PCF and other ?-calculus variants [1, 6, 10]. Readback is essentially a game played by an environment (the Opponent) who wants to discover the Böhm tree (normal form) of a term known by a Player. A type plays the role---using the games jargon---of an arena of possible moves, and a term of that type provides a winning strategy for the Player, permitting the Player to respond correctly to moves made by the Opponent. The interaction between Opponent and Player describes a perfect flow analysis which answers questions like, "can call site a ever call procedure p?" The context semantics provides a low-level coding mechanism for describing such flows, the positions of subexpressions and head variables in Böhm trees, as well as moves in the above described two-player games.