Observational Semantics for a Concurrent Lambda Calculus with Reference Cells and Futures

International audienceWe present an observational semantics for lambda(fut), a concurrent lambda calculus with reference cells and futures. The calculus lambda(fut) models the operational semantics of the concurrent higher-order programming language Alice ML. Our result is a powerful notion of equivalence that is the coarsest nontrivial congruence distinguishing observably different processes. It justifies a maximal set of correct program transformations, and it includes all of lambda(fut)'s deterministic reduction rules, in particular, call-by-value beta reduction

Adequacy of compositional translations for observational semantics

We investigate methods and tools for analysing translations between programming languages with respect to observational semantics. The behaviour of programs is observed in terms of may- and must-convergence in arbitrary contexts, and adequacy of translations, i.e., the reflection of program equivalence, is taken to be the fundamental correctness condition. For compositional translations we propose a notion of convergence equivalence as a means for proving adequacy. This technique avoids explicit reasoning about contexts, and is able to deal with the subtle role of typing in implementations of language extension

Algorithms for Extended Alpha-Equivalence and Complexity

Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-binding “let ” may make alpha-equivalence as hard as finding graph-isomorphisms, and that the replication operator in the pi-calculus may lead to an EXPSPACE-hard alpha-equivalence problem

On conservativity of concurrent Haskell

The calculus CHF models Concurrent Haskell extended by concurrent, implicit futures. It is a process calculus with concurrent threads, monadic concurrent evaluation, and includes a pure functional lambda-calculus which comprises data constructors, case-expressions, letrec-expressions, and Haskell’s seq. Futures can be implemented in Concurrent Haskell using the primitive unsafeInterleaveIO, which is available in most implementations of Haskell. Our main result is conservativity of CHF, that is, all equivalences of pure functional expressions are also valid in CHF. This implies that compiler optimizations and transformations from pure Haskell remain valid in Concurrent Haskell even if it is extended by futures. We also show that this is no longer valid if Concurrent Haskell is extended by the arbitrary use of unsafeInterleaveIO

On proving the equivalence of concurrency primitives

Various concurrency primitives have been added to sequential programming languages, in order to turn them concurrent. Prominent examples are concurrent buffers for Haskell, channels in Concurrent ML, joins in JoCaml, and handled futures in Alice ML. Even though one might conjecture that all these primitives provide the same expressiveness, proving this equivalence is an open challenge in the area of program semantics. In this paper, we establish a first instance of this conjecture. We show that concurrent buffers can be encoded in the lambda calculus with futures underlying Alice ML. Our correctness proof results from a systematic method, based on observational semantics with respect to may and must convergence

On correctness of buffer implementations in a concurrent lambda calculus with futures

Motivated by the question of correctness of a specific implementation of concurrent buffers in the lambda calculus with futures underlying Alice ML, we prove that concurrent buffers and handled futures can correctly encode each other. Correctness means that our encodings preserve and reflect the observations of may- and must-convergence. This also shows correctness wrt. program semantics, since the encodings are adequate translations wrt. contextual semantics. While these translations encode blocking into queuing and waiting, we also provide an adequate encoding of buffers in a calculus without handles, which is more low-level and uses busy-waiting instead of blocking. Furthermore we demonstrate that our correctness concept applies to the whole compilation process from high-level to low-level concurrent languages, by translating the calculus with buffers, handled futures and data constructors into a small core language without those constructs

Attractor Equivalence: An Observational Semantics for Reaction Networks

International audienceWe study observational semantics for networks of chemical reactions as used in systems biology. Reaction networks without kinetic information, as we consider, can be identified with Petri nets. We present a new observational semantics for reaction networks that we call the attractor equivalence. The main idea of the attractor equivalence is to observe reachable attractors and reachability of an attractor divergence in all possible contexts. The attractor equivalence can support powerful simplifications for reaction networks as we illustrate at the example of the Tet-On system. Alternative semantics based on bisimulations or traces, in contrast, do not support all needed simplifications