Work it, wrap it, fix it, fold it

The worker/wrapper transformation is a general-purpose technique for refactoring recursive programs to improve their performance. The two previous approaches to formalising the technique were based upon different recursion operators and different correctness conditions. In this paper we show how these two approaches can be generalised in a uniform manner by combining their correctness conditions, extend the theory with new conditions that are both necessary and sufficient to ensure the correctness of the worker/wrapper technique, and explore the benefits that result. All the proofs have been mechanically verified using the Agda system

Towards safe and efficient functional reactive programming

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on time-varying values (signals). FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discrete-time signals (hybrid systems). What sets FRP apart from most other reactive languages is its support for systems with highly dynamic structure (dynamism) and higher-order reactive constructs (higher-order data-flow). However, the price paid for these features has been the loss of the safety and performance guarantees provided by other, less expressive, reactive languages. Statically guaranteeing safety properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checks that guarantee domain-specific constraints, such as feedback being well-formed (causality analysis). However, compared with FRP, they are limited in their capacity to support dynamism and higher-order data-flow. On the other hand, as established static techniques do not suffice for highly structurally dynamic systems, FRP generally enforces few domain-specific constraints, leaving the FRP programmer to manually check that the constraints are respected. Thus, there is currently a trade-off between static guarantees and dynamism among reactive languages. This thesis contributes towards advancing the safety and efficiency of FRP by studying highly structurally dynamic networks of functions operating on mixed (yet distinct) continuous-time and discrete-time signals. First, an ideal denotational semantics is defined for this kind of FRP, along with a type system that captures domain-specific constraints. The correctness and practicality of the language and type system are then demonstrated by proof-of-concept implementations in Agda and Haskell. Finally, temporal properties of signals and of functions on signals are expressed using techniques from temporal logic, as motivation and justification for a range of optimisations

Towards safe and efficient functional reactive programming

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on time-varying values (signals). FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discrete-time signals (hybrid systems). What sets FRP apart from most other reactive languages is its support for systems with highly dynamic structure (dynamism) and higher-order reactive constructs (higher-order data-flow). However, the price paid for these features has been the loss of the safety and performance guarantees provided by other, less expressive, reactive languages. Statically guaranteeing safety properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checks that guarantee domain-specific constraints, such as feedback being well-formed (causality analysis). However, compared with FRP, they are limited in their capacity to support dynamism and higher-order data-flow. On the other hand, as established static techniques do not suffice for highly structurally dynamic systems, FRP generally enforces few domain-specific constraints, leaving the FRP programmer to manually check that the constraints are respected. Thus, there is currently a trade-off between static guarantees and dynamism among reactive languages. This thesis contributes towards advancing the safety and efficiency of FRP by studying highly structurally dynamic networks of functions operating on mixed (yet distinct) continuous-time and discrete-time signals. First, an ideal denotational semantics is defined for this kind of FRP, along with a type system that captures domain-specific constraints. The correctness and practicality of the language and type system are then demonstrated by proof-of-concept implementations in Agda and Haskell. Finally, temporal properties of signals and of functions on signals are expressed using techniques from temporal logic, as motivation and justification for a range of optimisations

Safe functional reactive programming through dependent types

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals. FRP is based on the synchronous dataflow paradigm and supports both continuous-time and discrete-time signals (hybrid systems).What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order reactive constructs. Statically guaranteeing correctness properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checks that guarantee domain-specific properties, such as feedback loops always being well-formed. However, they are limited in their capabilities to support dynamism and higher-order data-flow compared with FRP. Thus, the onus of ensuring such properties of FRP programs has so far been on the programmer as established static techniques do not suffice. In this paper, we show how dependent types allow this concern to be addressed. We present an implementation of FRP embedded in the dependently-typed language Agda, leveraging the type system of the host language to craft a domain-specific (dependent) type system for FRP. The implementation constitutes a discrete, operational semantics of FRP, and as it passes the Agda type, coverage, and termination checks, we know the operational semantics is total, which means our type system is safe

2015 Workshop on Continuations: pre-proceedings

This volume contains the papers presented at WoC 2015, the 2015 Workshopon Continuations held on April 12, 2015 in London, UK

Funcons for HGMP:the fundamental constructs of homogeneous generative meta-programming

The PLanCompS project proposes a component-based approach to programming-language development in which fundamental constructs (funcons) are reused across language definitions. Homogeneous Generative Meta-Programming (HGMP) enables writing programs that generate code as data, at run-time or compile-time, for manipulation and staged evaluation. Building on existing formalisations of HGMP, this paper introduces funcons for HGMP and demonstrates their usage in component-based semantics

The constrained-monad problem

In Haskell, there are many data types that would form monads were it not for the presence of type-class constraints on the operations onthat data type. This is a frustrating problem in practice, because there is a considerable amount of support and infrastructure for monads that these data types cannot use. Using several examples,we show that a monadic computation can be restructured into a normal form such that the standard monad class can be used. The technique is not specific to monads, and we show how it can also be applied to other structures, such as applicative functors. One significant use case for this technique is domain-specific languages,where it is often desirable to compile a deep embedding of a computation to some other language, which requires restricting the types that can appear in that computation

Keeping calm in the face of change: towards optimisation of FRP by reasoning about change

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals (time-varying values). FRP is based on the synchronous data-flow paradigm and supports both (an approximation to) continuous-time and discrete-time signals (hybrid systems).What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order reactive constructs. This paper contributes towards advancing the state of the art of FRP implementation by studying the notion of signal change and change propagation in a setting of structurally dynamic networks of n-ary signal functions operating on mixed continuous-time and discrete-time signals. We first define an ideal denotational semantics (time is truly continuous) for this kind of FRP, along with temporal properties, expressed in temporal logic, of signals and signal functions pertaining to change and change propagation. Using this framework, we then show how to reason about change; specifically, we identify and justify a number of possible optimisations, such as avoiding recomputation of unchanging values. Note that due to structural dynamism, and the fact that the output of a signal function may change because time is passing even if the input is unchanging, the problem is significantly more complex than standard change propagation in networks with static structure

The HERMIT in the machine: a plugin for the interactive transformation of GHC core language programs

The importance of reasoning about and refactoring programs is a central tenet of functional programming. Yet our compilers and development toolchains only provide rudimentary support for these tasks. This paper introduces a programmatic and compiler-centric interface that facilitates refactoring and equational reasoning. To develop our ideas, we have implemented HERMIT, a toolkit enabling informal but systematic transformation of Haskell programs from inside the Glasgow Haskell Compiler’s optimization pipeline. With HERMIT, users can experiment with optimizations and equational reasoning, while the tedious heavy lifting of performing the actual transformations is done for them. HERMIT provides a transformation API that can be used to build higher-level rewrite tools. One use-case is prototyping new optimizations as clients of this API before being committed to the GHC toolchain. We describe a HERMIT application - a read-eval-print shell for performing transformations using HERMIT. We also demonstrate using this shell to prototype an optimization on a specific example, and report our initial experiences and remaining challenges

A modular structural operational semantics for delimited continuations

It has been an open question as to whether the Modular Structural Operational Semantics framework can express the dynamic semantics of call/cc. This paper shows that it can, and furthermore, demonstrates that it can express the more general delimited control operators control and shift