An exercise in transformational programming: Backtracking and Branch-and-Bound

We present a formal derivation of program schemes that are usually called Backtracking programs and Branch-and-Bound programs. The derivation consists of a series of transformation steps, specifically algebraic manipulations, on the initial specification until the desired programs are obtained. The well-known notions of linear recursion and tail recursion are extended, for structures, to elementwise linear recursion and elementwise tail recursion; and a transformation between them is derived too

Automated Termination Proofs for Logic Programs by Term Rewriting

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a logic program into a term rewrite system (TRS) and then analyze termination of the resulting TRS instead. Thus, transformational approaches make all methods previously developed for TRSs available for logic programs as well. However, the applicability of most existing transformations is quite restricted, as they can only be used for certain subclasses of logic programs. (Most of them are restricted to well-moded programs.) In this paper we improve these transformations such that they become applicable for any definite logic program. To simulate the behavior of logic programs by TRSs, we slightly modify the notion of rewriting by permitting infinite terms. We show that our transformation results in TRSs which are indeed suitable for automated termination analysis. In contrast to most other methods for termination of logic programs, our technique is also sound for logic programming without occur check, which is typically used in practice. We implemented our approach in the termination prover AProVE and successfully evaluated it on a large collection of examples.Comment: 49 page

An engineering approach to automatic programming

An exploratory study of the automatic generation and optimization of symbolic programs using DECOM - a prototypical requirement specification model implemented in pure LISP was undertaken. It was concluded, on the basis of this study, that symbolic processing languages such as LISP can support a style of programming based upon formal transformation and dependent upon the expression of constraints in an object-oriented environment. Such languages can represent all aspects of the software generation process (including heuristic algorithms for effecting parallel search) as dynamic processes since data and program are represented in a uniform format

Building an IDE for the Calculational Derivation of Imperative Programs

In this paper, we describe an IDE called CAPS (Calculational Assistant for Programming from Specifications) for the interactive, calculational derivation of imperative programs. In building CAPS, our aim has been to make the IDE accessible to non-experts while retaining the overall flavor of the pen-and-paper calculational style. We discuss the overall architecture of the CAPS system, the main features of the IDE, the GUI design, and the trade-offs involved.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338

Deciding Full Branching Time Logic by Program Transformation

We present a method based on logic program transformation, for verifying Computation Tree Logic (CTL*) properties of finite state reactive systems. The finite state systems and the CTL* properties we want to verify, are encoded as logic programs on infinite lists. Our verification method consists of two steps. In the first step we transform the logic program that encodes the given system and the given property, into a monadic ω -program, that is, a stratified program defining nullary or unary predicates on infinite lists. This transformation is performed by applying unfold/fold rules that preserve the perfect model of the initial program. In the second step we verify the property of interest by using a proof method for monadic ω-program

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

Program transformation for development, verification, and synthesis of programs

This paper briefly describes the use of the program transformation methodology for the development of correct and efficient programs. In particular, we will refer to the case of constraint logic programs and, through some examples, we will show how by program transformation, one can improve, synthesize, and verify programs