Resourceful program synthesis from graded linear types

Linear types provide a way to constrain programs by specifying that some values must be used exactly once. Recent work on graded modal types augments and refines this notion, enabling fine-grained, quantitative specification of data use in programs. The information provided by graded modal types appears to be useful for type-directed program synthesis, where these additional constraints can be used to prune the search space of candidate programs. We explore one of the major implementation challenges of a synthesis algorithm in this setting: how does the synthesis algorithm efficiently ensure that resource constraints are satisfied throughout program generation? We provide two solutions to this resource management problem, adapting Hodas and Miller’s input-output model of linear context management to a graded modal linear type theory. We evaluate the performance of both approaches via their implementation as a program synthesis tool for the programming language Granule, which provides linear and graded modal typing

Integrating Lucid's Declarative Dataflow Paradigm into Object-Orientation

The dataflow language Lucid applies concepts from intensional logic to declarative ISWIM expressions which are intensionalised relative to the dimension of time, thus introducing the notion of an expression’s history. Lucian, a language derived from Lucid, embeds dataflow into object-orientation allowing the intensionalisation of objects. Lucian introduces the notion of a declarative intensional object as the history of an object’s transformations. This paper discusses the embedding relationships and semantics of conjoining the dataflow and object-oriented paradigms to provide the language Lucian for defining intensional objects Mathematics Subject Classification (2000). 68N15 68N19 68Q5

A Notation for Comonads

The category-theoretic concept of a monad occurs widely as a design pattern for functional programming with effects. The utility and ubiquity of monads is such that some languages provide syntactic sugar for this pattern, further encouraging its use. We argue that comonads, the dual of monads, similarly provide a useful design pattern, capturing notions of context dependence. However, comonads remain relatively under-used compared to monads—due to a lack of knowledge of the design pattern along with the lack of accompanying simplifying syntax. We propose a lightweight syntax for comonads in Haskell, analogous to the do-notation for monads, and provide examples of its use. Via our notation, we also provide a tutorial on programming with comonads

The semantic marriage of monads and effects

Wadler and Thiemann unified type-and-effect systems with monadic semantics via a syntactic correspondence and soundness results with respect to an operational semantics. They conjecture that a general, “coherent” denotational semantics can be given to unify effect systems with a monadic-style semantics. We provide such a semantics based on the novel structure of an indexed monad, which we introduce. We redefine the semantics of Moggi’s computational ?-calculus in terms of (strong) indexed monads which gives a oneto-one correspondence between indices of the denotations and the effect annotations of traditional effect systems. Dually, this approach yields indexed comonads which gives a unified semantics and effect system to contextual notions of effect (called coeffects), which we have previously describe

A theory of composing protocols

In programming, protocols are everywhere. Protocols describe the pattern of interaction (or communication) between software systems, for example, between a user-space program and the kernel or between a local application and an online service. Ensuring conformance to protocols avoids a significant class of software errors. Subsequently, there has been a lot of work on verifying code against formal protocol specifications. The pervading approaches focus on distributed settings involving parallel composition of processes within a single monolithic protocol description. However we observe that, at the level of a single thread/process, modern software must often implement a number of clearly delineated protocols at the same time which become dependent on each other, e.g., a banking API and one or more authentication protocols. Rather than plugging together modular protocol-following components, the code must re-integrate multiple protocols into a single component. We address this concern of combining protocols via a novel notion of ‘interleaving’ composition for protocols described via a process algebra. User-specified, domain-specific constraints can be inserted into the individual protocols to serve as ‘contact points’ to guide this composition procedure, which outputs a single combined protocol that can be programmed against. Our approach allows an engineer to then program against a number of protocols that have been composed (re-integrated), reflecting the true nature of applications that must handle multiple protocols at once. We prove various desirable properties of the composition, including behaviour preservation: that the composed protocol implements the behaviour of both component protocols. We demonstrate our approach in the practical setting of Erlang, with a tool implementing protocol composition that both generates Erlang code from a protocol and generates a protocol from Erlang code. This tool shows that, for a range of sample protocols (including real-world examples), a modest set of constraints can be inserted to produce a small number of candidate compositions to choose from. As we increasingly build software interacting with many programs and subsystems, this new perspective gives a foundation for improving software quality via protocol conformance in a multi-protocol setting

A Theory of Composing Protocols

In programming, protocols are everywhere. Protocols describe the pattern of interaction (or communication) between software systems, for example, between a user-space program and the kernel or between a local application and an online service. Ensuring conformance to protocols avoids a significant class of software errors. Subsequently, there has been a lot of work on verifying code against formal protocol specifications. The pervading approaches focus on distributed settings involving parallel composition of processes within a single monolithic protocol description. However we observe that, at the level of a single thread/process, modern software must often implement a number of clearly delineated protocols at the same time which become dependent on each other, e.g., a banking API and one or more authentication protocols. Rather than plugging together modular protocol-following components, the code must re-integrate multiple protocols into a single component. We address this concern of combining protocols via a novel notion of ‘interleaving’ composition for protocols described via a process algebra. User-specified, domain-specific constraints can be inserted into the individual protocols to serve as ‘contact points’ to guide this composition procedure, which outputs a single combined protocol that can be programmed against. Our approach allows an engineer to then program against a number of protocols that have been composed (re-integrated), reflecting the true nature of applications that must handle multiple protocols at once. We prove various desirable properties of the composition, including behaviour preservation: that the composed protocol implements the behaviour of both component protocols. We demonstrate our approach in the practical setting of Erlang, with a tool implementing protocol composition that both generates Erlang code from a protocol and generates a protocol from Erlang code. This tool shows that, for a range of sample protocols (including real-world examples), a modest set of constraints can be inserted to produce a small number of candidate compositions to choose from. As we increasingly build software interacting with many programs and subsystems, this new perspective gives a foundation for improving software quality via protocol conformance in a multi-protocol setting

Ypnos: declarative, parallel structured grid programming

A fully automatic, compiler-driven approach to parallelisation can result in unpredictable time and space costs for compiled code. On the other hand, a fully manual approach to parallelisation can be long, tedious, prone to errors, hard to debug, and often architecture-specific. We present a declarative domain-specific language, Ypnos, for expressing structured grid computations which encourages manual specification of causally sequential operations but then allows a simple, predictable, static analysis to generate optimised, parallel implementations. We introduce the language and provide some discussion on the theoretical aspects of the language semantics, particularly the structuring of computations around the category theoretic notion of a comonad

Effect Systems Revisited - Control-Flow Algebra and Semantics

Effect systems were originally conceived as an inference-based program analysis to capture program behaviour—as a set of (representations of) effects. Two orthogonal developments have since happened. First, motivated by static analysis, effects were generalised to values in an algebra, to better model control flow (e.g. for may/must analyses and concurrency). Second, motivated by semantic questions, the syntactic notion of set- (or semilattice-) based effect system was linked to the semantic notion of monads and more recently to graded monads which give a more precise semantic account of effects. We give a lightweight tutorial explanation of the concepts involved in these two threads and then unify them via the notion of an effect-directed semantics for a control-flow algebra of effects. For the case of effectful programming with sequencing, alternation and parallelism—illustrated with music—we identify a form of graded joinads as the appropriate structure for unifying effect analysis and semantics

A theory of protocol composition

Real-world communication protocols are often built out of a number of simpler protocols that cater for some specific functionality (e.g., banking, authentication). However much of the formal definitions of protocols used for program verification treat protocols as monolithic units. Composition is considered for implementations of a protocol, but not for the protocols themselves as engineering components. We propose primitives and techniques for the modular composition of protocols. Our notion of composition defines an interleaving of two or more protocols in a way that satisfies user-specified context-dependent constraints which serve to explain “contact points” between the protocols. The resulting approach gives a theoretical basis for protocol (re-)engineering based on a process calculus with constraint annotations. We have implemented our approach as a tool for Erlang that supports generation of protocol compositions with formal guarantees, and code generation/extraction