Typed Equivalence of Effect Handlers and Delimited Control

It is folklore that effect handlers and delimited control operators are closely related: recently, this relationship has been proved in an untyped setting for deep handlers and the shift_0 delimited control operator. We positively resolve the conjecture that in an appropriately polymorphic type system this relationship can be extended to the level of types, by identifying the necessary forms of polymorphism, thus extending the definability result to the typed context. In the process, we identify a novel and potentially interesting type system feature for delimited control operators. Moreover, we extend these results to substantiate the folklore connection between shallow handlers and control_0 flavour of delimited control, both in an untyped and typed settings

A Concurrent Logical Relation

Abstract—We present a logical relation for showing the correctness of program transformations based on a new type-and-effect system for a concurrent extension of an ML-like language with higher-order functions, higher-order store and dynamic memory allocation. We show how to use our model to verify a number of interesting program transformations that rely on effect annotations. In particular, we prove a Parallelization Theorem, which expresses when it is sound to run two expressions in parallel instead of sequentially. The conditions are expressed solely in terms of the types and effects of the expressions. To the best of our knowledge, this is the first such result for a concurrent higher-order language with higher-order store and dynamic memory allocation. I

Transfinite Step-Indexing: Decoupling Concrete and Logical Steps

International audienceStep-indexing has proven to be a powerful technique for defining logical relations for languages with advanced type systems and models of expressive program logics. In both cases, the model is stratified using natural numbers to solve a recursive equation that has no naive solutions. As a result of this stratification, current models require that each unfolding of the recursive equation – each logical step – must coincide with a concrete reduction step. This tight coupling is problematic for applications where the number of logical steps cannot be statically bounded. In this paper we demonstrate that this tight coupling between logical and concrete steps is artificial and show how to loosen it using transfinite step-indexing. We present a logical relation that supports an arbitrary but finite number of logical steps for each concrete step

Dag-calculus: a calculus for parallel computation

International audienceIncreasing availability of multicore systems has led to greater focus on the design and implementation of languages for writing parallel programs. Such languages support various abstractions for parallelism, such as fork-join, async-finish, futures. While they may seem similar, these abstractions lead to different semantics, language design and implementation decisions, and can significantly impact the performance of end-user applications. In this paper, we consider the question of whether it would be possible to unify various paradigms of parallel computing. To this end, we propose a calculus, called dag calculus, that can encode fork-join, async-finish, and futures, and possibly others. We describe dag calculus and its semantics, establish translations from the afore-mentioned paradigms into dag calculus. These translations establish that dag calculus is sufficiently powerful for encoding programs written in prevailing paradigms of parallelism. We present concurrent algorithms and data structures for realizing dag calculus on multi-core hardware and prove that the proposed techniques are consistent with the semantics. Finally, we present an implementation of the calculus and evaluate it empirically by comparing its performance to highly optimized code from prior work. The results show that the calculus is expressive and that it competes well with, and sometimes outperforms, the state of the art

Automating Derivations of Abstract Machines from Reduction Semantics: A Generic Formalization of Refocusing in Coq

Abstract. We present a generic formalization of the refocusing transformation for functional languages in the Coq proof assistant. The refocusing technique, due to Danvy and Nielsen, allows for mechanical transformation of an evaluator implementing a reduction semantics into an equivalent abstract machine via a succession of simple program transformations. So far, refocusing has been used only as an informal procedure: the conditions required of a reduction semantics have not been formally captured, and the transformation has not been formally proved correct. The aim of this work is to formalize and prove correct the refocusing technique. To this end, we first propose an axiomatization of reduction semantics that is sufficient to automatically apply the refocusing method. Next, we prove that any reduction semantics conforming to this axiomatization can be automatically transformed into an abstract machine equivalent to it. The article is accompanied by a Coq development that contains the formalization of the refocusing method and a number of case studies that serve both as an illustration of the method and as a sanity check on the axiomatization

The Essence of Generalized Algebraic Data Types

This paper considers direct encodings of generalized algebraic data types (GADTs) in a minimal suitable lambda-calculus. To this end, we develop an extension of System Fω with recursive types and internalized type equalities with injective constant type constructors. We show how GADTs and associated pattern-matching constructs can be directly expressed in the calculus, thus showing that it may be treated as a highly idealized modern functional programming language. We prove that the internalized type equalities in conjunction with injectivity rules increase the expressive power of the calculus by establishing a non-macro-expressibility result in Fω, and prove the system type-sound via a syntactic argument. Finally, we build two relational models of our calculus: a simple, unary model that illustrates a novel, two-stage interpretation technique, necessary to account for the equational constraints; and a more sophisticated, binary model that relaxes the construction to allow, for the first time, formal reasoning about data-abstraction in a calculus equipped with GADTs.</p

The Essence of Generalized Algebraic Data Types

This paper considers direct encodings of generalized algebraic data types (GADTs) in a minimal suitable lambda-calculus. To this end, we develop an extension of System F ω with recursive types and internalized type equalities with injective constant type constructors. We show how GADTs and associated pattern-matching constructs can be directly expressed in the calculus, thus showing that it may be treated as a highly idealized modern functional programming language. We prove that the internalized type equalities in conjunction with injectivity rules increase the expressive power of the calculus by establishing a non-macro-expressibility result in F ω , and prove the system type-sound via a syntactic argument. Finally, we build two relational models of our calculus: a simple, unary model that illustrates a novel, two-stage interpretation technique, necessary to account for the equational constraints; and a more sophisticated, binary model that relaxes the construction to allow, for the first time, formal reasoning about data-abstraction in a calculus equipped with GADTs. </jats:p

Analisi di missione di un MINI UAV non convenzionale per monitoraggio ambientale

Lo scopo del seguente elaborato consiste nell’analisi di missione di una configurazione non convenzionale di un MINI UAV. Verrà in seguito studiato il modello dell’apparato moto-propulsivo, al fine di ottimizzare l’autonomia oraria e chilometrica del velivolo