Program synthesis from polymorphic refinement types

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two reasons. First, they offer a unique combination of expressive power and decidability, which enables automatic verification—and hence synthesis—of nontrivial programs. Second, a type-based specification for a program can often be effectively decomposed into independent specifications for its components, causing the synthesizer to consider fewer component combinations and leading to a combinatorial reduction in the size of the search space. At the core of our synthesis procedure is a newalgorithm for refinement type checking, which supports specification decomposition. We have evaluated our prototype implementation on a large set of synthesis problems and found that it exceeds the state of the art in terms of both scalability and usability. The tool was able to synthesize more complex programs than those reported in prior work (several sorting algorithms and operations on balanced search trees), as well as most of the benchmarks tackled by existing synthesizers, often starting from a more concise and intuitive user input.National Science Foundation (U.S.) (Grant CCF-1438969)National Science Foundation (U.S.) (Grant CCF-1139056)United States. Defense Advanced Research Projects Agency (Grant FA8750-14-2-0242

Synthesis of Recursive ADT Transformations from Reusable Templates

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often requires nontrivial effort from the user, which impedes the usability of the synthesizer. We present a solution to this problem in the context of recursive transformations on algebraic data-types. Our approach relies on polymorphic synthesis constructs: a small but powerful extension to the language of syntactic templates, which makes it possible to define a program space in a concise and highly reusable manner, while at the same time retains the scalability benefits of conventional templates. This approach enables end-users to reuse predefined templates from a library for a wide variety of problems with little effort. The paper also describes a novel optimization that further improves the performance and scalability of the system. We evaluated the approach on a set of benchmarks that most notably includes desugaring functions for lambda calculus, which force the synthesizer to discover Church encodings for pairs and boolean operations

A mathematical approach towards hardware design

Today the hardware for embedded systems is often specified in VHDL. However, VHDL describes the system at a rather low level, which is cumbersome and may lead to design faults in large real life applications. There is a need of higher level abstraction mechanisms. In the embedded systems group of the University of Twente we are working on systematic and transformational methods to design hardware architectures, both multi core and single core. The main line in this approach is to start with a straightforward (often mathematical) specification of the problem. The next step is to find some adequate transformations on this specification, in particular to find specific optimizations, to be able to distribute the application over different cores. The result of these transformations is then translated into the functional programming language Haskell since Haskell is close to mathematics and such a translation often is straightforward. Besides, the Haskell code is executable, so one immediately has a simulation of the intended system. Next, the resulting Haskell specification is given to a compiler, called CëaSH (for CAES LAnguage for Synchronous Hardware) which translates the specification into VHDL. The resulting VHDL is synthesizable, so from there on standard VHDL-tooling can be used for synthesis. In this work we primarily focus on streaming applications: i.e. applications that can be modeled as data-flow graphs. At the moment the CëaSH system is ready in prototype form and in the presentation we will give several examples of how it can be used. In these examples it will be shown that the specification code is clear and concise. Furthermore, it is possible to use powerful abstraction mechanisms, such as polymorphism, higher order functions, pattern matching, lambda abstraction, partial application. These features allow a designer to describe circuits in a more natural and concise way than possible with the language elements found in the traditional hardware description languages. In addition we will give some examples of transformations that are possible in a mathematical specification, and which do not suffer from the problems encountered in, e.g., automatic parallelization of nested for-loops in C-programs

Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis

We describe ongoing work on a framework for automatic composition synthesis from a repository of software components. This work is based on combinatory logic with intersection types. The idea is that components are modeled as typed combinators, and an algorithm for inhabitation {\textemdash} is there a combinatory term e with type tau relative to an environment Gamma? {\textemdash} can be used to synthesize compositions. Here, Gamma represents the repository in the form of typed combinators, tau specifies the synthesis goal, and e is the synthesized program. We illustrate our approach by examples, including an application to synthesis from GUI-components.Comment: In Proceedings ITRS 2012, arXiv:1307.784

Type-driven Synthesis of Evolving Data Mode

Modern commercial software is often framed under the umbrella of data-centric applications. Data-centric applications define data as the main and permanent asset. These applications use a single data model for application functionality, data management, and analytical activities, which is built before the applications. Moreover, since applications are temporary, in contrast to data, there is the need to continuously evolve and change the data schema to accommodate new functionality. In this sense, the continuously evolving (rich) feature set that is expected of state-of-the-art applications is intrinsically bound by not only the amount of available data but also by its structure, its internal dependencies, and by the ability to transparently and uniformly grow and evolve data representations and their properties on the fly. The GOLEM project aims to produce new methods of program automation integrated in the development of data-centric applications in low-code frameworks. In this context, one of the key targets for automation is the data layer itself, encompassing the data layout and its integrity constraints, as well as validation and access control rules. The aim of this dissertation, which is integrated in GOLEM, is to develop a synthesis framework that, based on high-level specifications, correctly defines and evolves a rich data layer component by means of high-level operations. The construction of the framework was approached by defining a specification language to express richly-typed specifications, a target language which is the goal of synthesis and a type-directed synthesis procedure based on proof-search concepts. The range of real database operations the framework is able to synthesize is demonstrated through a case study. In a component-based synthesis style, with an extensible library of base operations on database tables (specified using the target language) in context, the case study shows that the synthesis framework is capable of expressing and solving a wide variety of data schema creation and evolution problems.Os sistemas modernos de software comercial são frequentemente caracterizados como aplicações centradas em dados. Estas aplicações definem os dados como o seu principal e persistente ativo, e utilizam um único modelo de dados para as suas funcionalidades, gestão de dados, e atividades analíticas. Além disso, uma vez que as aplicações são efémeras, contrariamente aos dados, existe a necessidade de continuamente evoluir o esquema de dados para introduzir novas funcionalidades. Neste sentido, o conjunto rico de características e em constante evolução que é esperado das aplicações modernas encontra-se restricto, não só pela quantidade de dados disponíveis, mas também pela sua estrutura, dependências internas, e a capacidade de crescer e evoluir a representação dos dados de uma forma uniforme e rápida. O projeto GOLEM tem como objetivo a produção de novos métodos de automação de programas integrado no desenvolvimento de aplicações centradas nos dados em sistemas low-code. Neste contexto, um dos objetivos principais de automação é a camada de dados, compreendendo a estrutura dos dados e as respectivas condições de integridade, como também as regras de validação e controlo de acessos. O objetivo desta dissertação, integrada no projeto GOLEM, é o desenvolvimento de um sistema de síntese que, baseado em especificações de alto nível, define e evolui corretamente uma camada de dados rica com recurso a operações de alto nível. A construção deste sistema baseia-se na definição de uma linguagem de especificação que permite definir especificações com tipos ricos, uma linguagem de expressões que é considerada o objetivo da síntese e um procedimento de síntese orientada pelos tipos. O espectro de operações reais de bases de dados que o sistema consegue sintetizar é demonstrado através de um caso de estudo. Com uma biblioteca extensível de operações sobre tabelas no contexto, o caso de estudo demonstra que o sistema de síntese é capaz de expressar e resolver uma grande variedade de problemas de criação e evolução de esquemas de dados