34 research outputs found
Foundations for programming and implementing effect handlers
First-class control operators provide programmers with an expressive and efficient
means for manipulating control through reification of the current control state as a first-class object, enabling programmers to implement their own computational effects and
control idioms as shareable libraries. Effect handlers provide a particularly structured
approach to programming with first-class control by naming control reifying operations
and separating from their handling.
This thesis is composed of three strands of work in which I develop operational
foundations for programming and implementing effect handlers as well as exploring
the expressive power of effect handlers.
The first strand develops a fine-grain call-by-value core calculus of a statically
typed programming language with a structural notion of effect types, as opposed to the
nominal notion of effect types that dominates the literature. With the structural approach,
effects need not be declared before use. The usual safety properties of statically typed
programming are retained by making crucial use of row polymorphism to build and
track effect signatures. The calculus features three forms of handlers: deep, shallow,
and parameterised. They each offer a different approach to manipulate the control state
of programs. Traditional deep handlers are defined by folds over computation trees,
and are the original con-struct proposed by Plotkin and Pretnar. Shallow handlers are
defined by case splits (rather than folds) over computation trees. Parameterised handlers
are deep handlers extended with a state value that is threaded through the folds over
computation trees. To demonstrate the usefulness of effects and handlers as a practical
programming abstraction I implement the essence of a small UNIX-style operating
system complete with multi-user environment, time-sharing, and file I/O.
The second strand studies continuation passing style (CPS) and abstract machine
semantics, which are foundational techniques that admit a unified basis for implementing deep, shallow, and parameterised effect handlers in the same environment. The
CPS translation is obtained through a series of refinements of a basic first-order CPS
translation for a fine-grain call-by-value language into an untyped language. Each refinement moves toward a more intensional representation of continuations eventually
arriving at the notion of generalised continuation, which admit simultaneous support for
deep, shallow, and parameterised handlers. The initial refinement adds support for deep
handlers by representing stacks of continuations and handlers as a curried sequence of
arguments. The image of the resulting translation is not properly tail-recursive, meaning some function application terms do not appear in tail position. To rectify this the
CPS translation is refined once more to obtain an uncurried representation of stacks
of continuations and handlers. Finally, the translation is made higher-order in order to
contract administrative redexes at translation time. The generalised continuation representation is used to construct an abstract machine that provide simultaneous support for
deep, shallow, and parameterised effect handlers. kinds of effect handlers.
The third strand explores the expressiveness of effect handlers. First, I show that
deep, shallow, and parameterised notions of handlers are interdefinable by way of typed
macro-expressiveness, which provides a syntactic notion of expressiveness that affirms
the existence of encodings between handlers, but it provides no information about the
computational content of the encodings. Second, using the semantic notion of expressiveness I show that for a class of programs a programming language with first-class
control (e.g. effect handlers) admits asymptotically faster implementations than possible in a language without first-class control
Programming Languages and Systems
This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems
On the Versatility of Open Logical Relations: Continuity, Automatic Differentiation, and a Containment Theorem
International audienceLogical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differen-tiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue , we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed λ-calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first-order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with con-ditionals, and prove the soundness of the type system using open logical relations
Spy Game: Verifying a Local Generic Solver in Iris
International audienceWe verify the partial correctness of a "local generic solver", that is, an on-demand, incremental, memoizing least fixed point computation algorithm. The verification is carried out in Iris, a modern breed of concurrent separation logic. The specification is simple: the solver computes the optimal least fixed point of a system of monotone equations. Although the solver relies on mutable internal state for memoization and for "spying", a form of dynamic dependency discovery, it is apparently pure: no side effects are mentioned in its specification. As auxiliary contributions, we provide several illustrations of the use of prophecy variables, a novel feature of Iris; we establish a restricted form of the infinitary conjunction rule; and we provide a specification and proof of Longley's modulus function, an archetypical example of spying