A Cellular, Language Directed Computer Architecture

If a VLSI computer architecture is to influence the field of computing in some major way, it must have attractive properties in all important aspects affecting the design, production, and the use of the resulting computers. A computer architecture that is believed to have such properties is briefly discussed

Synthesizing Functional Reactive Programs

Functional Reactive Programming (FRP) is a paradigm that has simplified the construction of reactive programs. There are many libraries that implement incarnations of FRP, using abstractions such as Applicative, Monads, and Arrows. However, finding a good control flow, that correctly manages state and switches behaviors at the right times, still poses a major challenge to developers. An attractive alternative is specifying the behavior instead of programming it, as made possible by the recently developed logic: Temporal Stream Logic (TSL). However, it has not been explored so far how Control Flow Models (CFMs), as synthesized from TSL specifications, can be turned into executable code that is compatible with libraries building on FRP. We bridge this gap, by showing that CFMs are indeed a suitable formalism to be turned into Applicative, Monadic, and Arrowized FRP. We demonstrate the effectiveness of our translations on a real-world kitchen timer application, which we translate to a desktop application using the Arrowized FRP library Yampa, a web application using the Monadic threepenny-gui library, and to hardware using the Applicative hardware description language ClaSH.Comment: arXiv admin note: text overlap with arXiv:1712.0024

Free Applicative Functors

Applicative functors are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell. Applicative functors are to be preferred to monads when the structure of a computation is fixed a priori. That makes it possible to perform certain kinds of static analysis on applicative values. We define a notion of free applicative functor, prove that it satisfies the appropriate laws, and that the construction is left adjoint to a suitable forgetful functor. We show how free applicative functors can be used to implement embedded DSLs which can be statically analysed.Comment: In Proceedings MSFP 2014, arXiv:1406.153

Parallel VLSI architecture emulation and the organization of APSA/MPP

The Applicative Programming System Architecture (APSA) combines an applicative language interpreter with a novel parallel computer architecture that is well suited for Very Large Scale Integration (VLSI) implementation. The Massively Parallel Processor (MPP) can simulate VLSI circuits by allocating one processing element in its square array to an area on a square VLSI chip. As long as there are not too many long data paths, the MPP can simulate a VLSI clock cycle very rapidly. The APSA circuit contains a binary tree with a few long paths and many short ones. A skewed H-tree layout allows every processing element to simulate a leaf cell and up to four tree nodes, with no loss in parallelism. Emulation of a key APSA algorithm on the MPP resulted in performance 16,000 times faster than a Vax. This speed will make it possible for the APSA language interpreter to run fast enough to support research in parallel list processing algorithms

(Leftmost-Outermost) Beta Reduction is Invariant, Indeed

Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is lambda-calculus a reasonable machine? Is there a way to measure the computational complexity of a lambda-term? This paper presents the first complete positive answer to this long-standing problem. Moreover, our answer is completely machine-independent and based over a standard notion in the theory of lambda-calculus: the length of a leftmost-outermost derivation to normal form is an invariant cost model. Such a theorem cannot be proved by directly relating lambda-calculus with Turing machines or random access machines, because of the size explosion problem: there are terms that in a linear number of steps produce an exponentially long output. The first step towards the solution is to shift to a notion of evaluation for which the length and the size of the output are linearly related. This is done by adopting the linear substitution calculus (LSC), a calculus of explicit substitutions modeled after linear logic proof nets and admitting a decomposition of leftmost-outermost derivations with the desired property. Thus, the LSC is invariant with respect to, say, random access machines. The second step is to show that LSC is invariant with respect to the lambda-calculus. The size explosion problem seems to imply that this is not possible: having the same notions of normal form, evaluation in the LSC is exponentially longer than in the lambda-calculus. We solve such an impasse by introducing a new form of shared normal form and shared reduction, deemed useful. Useful evaluation avoids those steps that only unshare the output without contributing to beta-redexes, i.e. the steps that cause the blow-up in size. The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties.Comment: arXiv admin note: substantial text overlap with arXiv:1405.331