Combining and Relating Control Effects and their Semantics

Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a programming language which includes these features, as well as higher-order references. They are obtained by contrasting methodologies: by annotating sequences of moves with "control pointers" indicating where exceptions are thrown and caught, and by composing the exceptions and continuations monads. The former approach allows an explicit representation of control flow in games for exceptions, and hence a straightforward proof of definability (full abstraction) by factorization, as well as offering the possibility of a semantic approach to control flow analysis of exception-handling. However, establishing soundness of such a concrete and complex model is a non-trivial problem. It may be resolved by establishing a correspondence with the monad semantics, based on erasing explicit exception moves and replacing them with control pointers.Comment: In Proceedings COS 2013, arXiv:1309.092

On the Expressive Power of User-Defined Effects: Effect Handlers, Monadic Reflection, Delimited Control

We compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers, Filinski's monadic reflection, and delimited control without answer-type-modification. This comparison allows a precise discussion about the relative expressiveness of each programming abstraction. It also demonstrates the sensitivity of the relative expressiveness of user-defined effects to seemingly orthogonal language features. We present three calculi, one per abstraction, extending Levy's call-by-push-value. For each calculus, we present syntax, operational semantics, a natural type-and-effect system, and, for effect handlers and monadic reflection, a set-theoretic denotational semantics. We establish their basic meta-theoretic properties: safety, termination, and, where applicable, soundness and adequacy. Using Felleisen's notion of a macro translation, we show that these abstractions can macro-express each other, and show which translations preserve typeability. We use the adequate finitary set-theoretic denotational semantics for the monadic calculus to show that effect handlers cannot be macro-expressed while preserving typeability either by monadic reflection or by delimited control. We supplement our development with a mechanised Abella formalisation

No value restriction is needed for algebraic effects and handlers

We present a straightforward, sound Hindley-Milner polymorphic type system for algebraic effects and handlers in a call-by-value calculus, which allows type variable generalisation of arbitrary computations, not just values. This result is surprising. On the one hand, the soundness of unrestricted call-by-value Hindley-Milner polymorphism is known to fail in the presence of computational effects such as reference cells and continuations. On the other hand, many programming examples can be recast to use effect handlers instead of these effects. Analysing the expressive power of effect handlers with respect to state effects, we claim handlers cannot express reference cells, and show they can simulate dynamically scoped state

A Type-Theoretic Foundation of Delimited Continuations

International audienceThere is a correspondence between classical logic and programming language calculi with first-class continuations. With the addition of control delimiters, the continuations become composable and the calculi become more expressive. We present a fine-grained analysis of control delimiters and formalise that their addition corresponds to the addition of a single dynamically-scoped variable modelling the special top-level continuation. From a type perspective, the dynamically-scoped variable requires effect annotations. In the presence of control, the dynamically-scoped variable can be interpreted in a purely functional way by applying a store-passing style. At the type level, the effect annotations are mapped within standard classical logic extended with the dual of implication, namely subtraction. A continuation-passing-style transformation of lambda-calculus with control and subtraction is defined. Combining the translations provides a decomposition of standard CPS transformations for delimited continuations. Incidentally, we also give a direct normalisation proof of the simply-typed lambda-calculus with control and subtraction

Sequentially Constructive Concurrency: A Conservative Extension of the Synchronous Model of Computation

Synchronous languages ensure deterministic concurrency, but at the price of heavy restrictions on what programs are considered valid, or constructive. Meanwhile, sequential languages such as C and Java offer an intuitive, familiar programming paradigm but provide no guarantees with regard to deterministic concurrency. The sequentially constructive model of computation (SC MoC) presented here harnesses the synchronous execution model to achieve deterministic concurrency while addressing concerns that synchronous languages are unnecessarily restrictive and difficult to adopt. In essence, the SC MoC extends the classical synchronous MoC by allowing variables to be read and written in any order as long as sequentiality expressed in the program provides sufficient scheduling information to rule out race conditions. This allows to use programming patterns familiar from sequential programming, such as testing and later setting the value of a variable, which are forbidden in the standard synchronous MoC. The SC MoC is a conservative extension in that programs considered constructive in the common synchronous MoC are also SC and retain the same semantics. In this paper, we identify classes of variable accesses, define sequential constructiveness based on the concept of SC-admissible scheduling, and present a priority-based scheduling algorithm for analyzing and compiling SC programs