Neil Sculthorpe

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 data-flow 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.

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 Compilers 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.

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 on that 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

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.

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 article 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.

The remote monad design pattern

Remote Procedure Calls are expensive. This paper demonstrates how to reduce the cost of calling remote procedures from Haskell by using the remote monad design pattern, which amortizes the cost of remote calls. This gives the Haskell community access to remote capabilities that are not directly supported, at a surprisingly inexpensive cost. We explore the remote monad design pattern through six models of remote execution patterns, using a simulated Internet of Things toaster as a running example. We consider the expressiveness and optimizations enabled by each remote execution model, and assess the feasibility of our approach. We then present a full-scale case study: a Haskell library that provides a Foreign Function Interface to the JavaScript Canvas API. Finally, we discuss existing instances of the remote monad design pattern found in Haskell libraries.

Reasoning with the HERMIT: tool support for equational reasoning on GHC core programs

A benefit of pure functional programming is that it encourages equational reasoning. However, the Haskell language has lacked direct tool support for such reasoning. Consequently, reasoning about Haskell programs is either performed manually, or in another language that does provide tool support (e.g. Agda or Coq). HERMIT is a Haskell-specific toolkit designed to support equational reasoning and user-guided program transformation, and to do so as part of the GHC compilation pipeline. This paper describes HERMITs recently developed support for equational reasoning, and presents two case studies of HERMIT usage: checking that type-class laws hold for specific instance declarations, and mechanising textbook equational reasoning.

The HERMIT in the Tree

This paper describes our experience using the HERMIT toolkit to apply well-known transformations to the internal core language of the Glasgow Haskell Compiler. HERMIT provides several mechanisms to support writing general-purpose transformations: a domain-specific language for strategic programming specialized to GHC’s core language, a library of primitive rewrites, and a shell-style–based scripting language for interactive and batch usage.

The Kansas University rewrite engine - A Haskell-Embedded Strategic Programming Language with Custom Closed Universes.

When writing transformation systems, a significant amount of engineering effort goes into setting up the infrastructure needed to direct individual transformations to specific targets in the data being transformed. Strategic programming languages provide general-purpose infrastructure for this task, which the author of a transformation system can use for any algebraic data structure. The Kansas University Rewrite Engine (KURE) is a typed strategic programming language, implemented as a Haskell-embedded domain-specific language. KURE is designed to support typed transformations over typed data, and the main challenge is how to make such transformations compatible with generic traversal strategies that should operate over any type. Strategic programming in a typed setting has much in common with datatype-generic programming. Compared to other approaches to datatype-generic programming, the distinguishing feature of KURE’s solution is that the user can configure the behaviour of traversals based on the location of each datum in the tree, beyond their behaviour being determined by the type of each datum. This article describes KURE’s approach to assigning types to generic traversals, and the implementation of that approach. We also compare KURE, its design choices, and their consequences, with other approaches to strategic and datatype-generic programming.