Powerlists in Coq: Programming and Reasoning

Loulergue, Frédéric; Niculescu, Virginia; Robillard, Simon

doi:10.1109/candar.2013.17

Cited by 2 publications

(6 citation statements)

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“…As BSML is also formalised in Coq [13], it is possible to verify the correctness of pure functional parallel versions of the powerlist functions presented in this paper. We intend to join the results presented in [27] with the work presented here, in order to be used in a complete, more general framework; this will allow the development of correct and verifiable parallel programs with predictable performances using theories and tools that facilitate the development of efficient applications by implementing simple programs satisfying conditions easily, or ideally automatically, proved. The framework will use the axiomatisation of lower level parallel programming primitives and their use to implement the high-level primitives in order to extract [28] actual parallel code from the developments made within proof assistants.…”

Section: Related and Future Workmentioning

confidence: 95%

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Implementing Powerlists with Bulk Synchronous Parallel ML

Loulergue¹,

Niculescu²,

Tesson³

2014

2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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Tools and methods able to simplify the development process of parallel software, but also to assure a high level of performance and robustness, are necessary. Powerlists and their variants are data structures that can be successfully used in a simple, provably correct, functional description of parallel programs, which are divide-and-conquer in nature. The paper presents how programs defined based on powerlists could be implemented in the functional language OCaml plus calls to the parallel functional programming library Bulk Synchronous Parallel ML. BSML functions follow the BSP model requirements, and so its advantages are introduced in OCaml parallel code. In order to write powerlist programs in BSML we provide a datatype for powerlists and a set of skeletons (higher-order functions implemented in parallel) to manipulate them. Examples are given and concrete experiments for their executions are conducted. Keywords-Parallel recursive structures; Functional parallel programming; Bulk synchronous parallelism I. CONTEXT AND MOTIVATIONThe latest developments of the computation systems lead to an increase of the requirements in using parallel computation. Still, for many years, parallel computation has been considered difficult and error-prone. This imposes using tools and methodologies able to simplify the development process of parallel software, but also to assure a high level of performance and robustness.This calls for a strongly structured form of parallelism [1], [2], [3], which should not only be based on an abstraction or model that conceals much of the complexity of parallel computation, but also provide a systematic way of developing such parallelism from specifications for practically nontrivial examples. Since correctness is very important in this context, high-level algebraic theories are appropriate to be used as fundamentals. Among them at least two seem suitable for parallel programming: the theory of lists [4] and parallel recursive structures such as powerlists [5].Powerlists and their variants are data structures that can be successfully used in a simple, provably correct, functional description of parallel programs, which are divide and conquer in nature [5], [6]. For each data structure, theories based on algebras and structural induction principles have been specified, which make them well suited to formally define recursive, data-parallel algorithms. These theories can be considered together a base for a model of parallel computation with a very high level of abstraction [7].In order to be useful, a model of parallel computation must also address very carefully issues such as efficient implementation and costs evaluation. BSP model [2] is famous especially because it provides a very accurate cost analysis, and a rigorous development that could provide robustness. From these, the idea of using BSP development methodology in the process of implementing powerlists programs came natural.Powerlist programs are defined in a very high-level way. While their divide-and-conquer nature makes them suita...

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Section: Related and Future Workmentioning

confidence: 95%

“…We have presented in [27] a formalisation of powerlists in the Coq [9] proof assistant. Our methodology was to obtain a small axiomatisation of this data structure, as close as possible to the pen-and-paper version, and then to build on it.…”

Section: Related and Future Workmentioning

confidence: 99%

Implementing Powerlists with Bulk Synchronous Parallel ML

Loulergue¹,

Niculescu²,

Tesson³

2014

2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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“…A number of theorem provers are available besides Poiti′n, e.g., Nuprl, Coq and automatic recursive program synthesis system [4,5,6], which can be used to verify programs, and can be used to construct programs from the proofs of the specifications. Most of the theorem provers and program synthesis systems use axioms or intermediate lemmas and generalizations in order to complete the proof successfully.…”

Section: A Validation and Correctnessmentioning

confidence: 99%

“…So far we know from on-line literature search, no research work is found on automatic construction of Java programs from input specifications, and www.ijacsa.thesai.org the available theorem provers can only be used to construct functional programs [1,2,3,4,5]. This paper presents a new approach for the construction of Java programs from the input functional program specifications expressed in the functional language of the theorem prover Poiti′n.…”

Section: Introductionmentioning

confidence: 99%

“…A number of theorem provers are available, for example, Poiti′n, Nuprl1, and Coq, which can be used to construct functional programs from the proofs of their specifications [1,2,3,4,5,6]. Several code generation tools e.g., Rational Rose, Microgold and Umbrello have been developed for automatic generation of Java or C++ program code from UML design specification expressed in terms of class diagrams for a particular computing problem solution [1].…”

Section: Introductionmentioning

confidence: 99%

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Automatic Construction of Java Programs from Functional Program Specifications

Humayun

2015

ijacsa

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Abstract-This paper presents a novel approach to construct Java programs automatically from the input functional program specifications on natural numbers from the constructive proofs of the input specifications using an inductive theorem prover called Poiti′n. The construction of a Java program from the input functional program specification involves two phases. The theorem prover is used to construct a higher order functional (HOF) program from the input specification expressed as an existential theorem. A set of mapping rules for a Programming Language Translation System (PLTS) is defined for translating functional expressions to their semantic equivalent Java code. The generated functional program is translated into intermediate Java code in the form of a Java function using the PLTS module. The generated Java function requires a small refinement to obtain a syntactically correct Java function. This Java function is encapsulated within a user defined Java class as a member operation, which is invoked within a Java application class consisting of a main function by creating objects resulting in an executable Java program. The constructed functional program and the generated Java program both are correct with respect to the input specification as they produce the same output.

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Powerlists in Coq: Programming and Reasoning

Cited by 2 publications

References 20 publications

Implementing Powerlists with Bulk Synchronous Parallel ML

Implementing Powerlists with Bulk Synchronous Parallel ML

Automatic Construction of Java Programs from Functional Program Specifications

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