Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in ruby. In C. C. Morgan R. S. Bird and J. C. P. Woodcock, editors, Mathematics of Program Construction, Lecture Notes in Computer Science. Springer Verlag, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on these graphs. Their application to asynchronous systems also sets them apart from HHL, which treats synchronous systems. Sheeran s Ruby is a relational calculus for circuit design that uses pictorial icons to specify circuit relations, though the icons are not used to reason about circuits [50, 51]. Several verification tools have supported diagrams through translation into sentential logic. The LAMBDA theorem prover provides a circuit schematic interface for specifying systems [31] Tool support for timing diagrams has increased in recent years. Schlor has used timing diagrams to state ....

Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in ruby. In R. S. Bird, C. C. Morgan, and J. C. P. Woodcock, editors, Mathematics of Program Construction. Springer-Verlag, 1993. Lecture Notes in Computer Science 669.

....underlies much of the recent categorical work on relations [10, 7, 9] A natural generalisation of the paradigm of representation changers adopted in this paper is to allow the functions f, h in a specification h C c o f to be in fact difunctional relations. This generalisation is addressed in [15, 11]. 4 Satisfying the specification Typically for representation changers it is easy to define programs f: C1 A and 9: C2 A directly, while defining a program h: C1 C2 that satisfies h C 9c o f requires some creative effort. Rather than defining an and proving after the fact that is ....

....Bird and Wadler [5] are synthesized in a similar fashion, but the application to representation changers in this paper is new. Let us consider an example: a function add that takes a binary number (represented as a list of bits) and a bit (0 or 1) and adds them together to give a binary number [15, 11]. For any bit b the function add b is a representation changer, specified by the requirement that add b C (eval2) c o ( b) o eval2. 5) The specification expresses that we can add a bit b to a binary number by first converting the binary number to a natural number, adding b, and then ....

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Geraint Jones and Mary Sheeran. Designing arithmetic circuits by re- finement in Ruby. In Proc. Second International Conference on Mathematics of Program Construction, Lecture Notes in Computer Science. Springer-Verlag, 1992. To appear.

....which encapsulate typical templates of parallelism. Skeletons were introduced by Cole [7] and have been studied by the group of Darlington at Imperial College [9] the group around Pepper [24, 25] Partsch and Geerling [23, 11] etc. 1 Closely related work is the Ruby system by Jones and Sheeran [18], the research carried out at Belfast [6] the P 3 L project at Pisa [1] the KIDS system by Smith [30] and the functional approach by O Donnell [22] This paper reports results of a case study on the systematic use of BMF in the process of parallel program development. We are trying to go all ....

G. Jones and M. Sheeran. Designing arithmetic circuits by refinement in Ruby. In C. Morgan R. Bird and J. Woodcock, editors, Mathematics of Program Construction, Lecture Notes in Computer Science 669, pages 208--232, 1992.

....relational calculi developed by Jones and Sheeran [14, 15] Their language, called Ruby , is designed specifically for the derivation of hardware like programs that denote finite networks of simple primitives. Ruby has been used to derive a number of different kinds of hardware like programs [13, 22, 23, 16]. Programs in Ruby are built piecewise from smaller programs using a simple set of combining forms. Ruby is not meant as a programming language in its own right, but as a tool for developing and explaining algorithms. Fundamental to Ruby is the use of terse notation; most formulae fit onto a ....

Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. Glasgow University, February 1992.

....of primitive relations connected by wires, which is important when layout is considered in circuit design. Ruby has been continually developed since 1986, and has been used to design many different kinds of circuits, including systolic arrays [7] butterfly networks [8] and arithmetic circuits [5]. The Ruby approach to circuit design is to derive implementations from specifications in the following way. We first formulate a Ruby program that clearly expresses the desired relationship between inputs and outputs, but typically has no direct translation as a circuit. We then transform this ....

Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. In Proc. Second International Conference on Mathematics of Program Construction, Lecture Notes in Computer Science. Springer-Verlag, 1992.

....and combining terms, and a natural treatment of non determinism. Furthermore, in practice many methods for combining functions in networks are unified if the distinction between input and output is relaxed [14] and many specifications can be expressed very naturally as representation changers [10], that is, as the relational composition of a function with the converse of a function. Jones and Sheeran s relational calculus Ruby has been used to derive various kinds of hardware circuit from abstract behavioural specifications: examples include systolic arrays [15] butterfly networks [16] ....

....composition of a function with the converse of a function. Jones and Sheeran s relational calculus Ruby has been used to derive various kinds of hardware circuit from abstract behavioural specifications: examples include systolic arrays [15] butterfly networks [16] and arithmetic circuits [8, 10]. Other relational languages under development include that of Backhouse et al. [1] and Bird and de Moor [2, 12] Since these languages have the same underlying algebraic structure as Ruby, our techniques also apply to them. Much informal reasoning in Ruby depends on a pictorial interpretation of ....

Geraint Jones and Mary Sheeran, Designing arithmetic circuits by refinement in Ruby, in Proc. Second International Conference on Mathematics of Program Construction, 1992, to appear in LNCS, SpringerVerlag.

.... Isabelle, interactive and tactic guided proof by higher order resolution has been used to construct programs in type theory [23] develop functional programs using classical logics [1, 8] and synthesize logic programs [2] There is also a growing body of work on proof based hardware synthesis [21, 24, 25, 26] including synthesis based on higher order resolution using the Lambda system [10, 12, 13] We present work here on combining two different development methodologies: synthesis based on higher order resolution and a particular methodology for the top down deductive refinement of specifications ....

Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. In Morgan Bird and Woodcock, editors, Mathematics of Program Construction, volume 669 of LNCS. Springer-Verlag, 1992.

.... Introduction 1 A Graphical Interface for Ruby 3 Introduction Ruby is a hardware description language in which, by defining a relation between a domain and a range, a circuit that realises the relation can be designed [JonShe90, JonShe91, JonShe93]. Other hardware description languages capture behaviour of circuits, but normally not the layout. The circuit designed in Ruby describes both the behaviour and the layout of the circuit, and therefore suggests the actual layout on the implementation technology. Ruby is a relational language, ....

Geraint Jones and Mary Sheeran, Designing arithmetic circuits by refinement in Ruby, in Mathematics of Program Construction, R. S. Bird, C. C. Morgan and J. C. P. Woodcock (eds), Springer Verlag, LNCS 669, 1993.

.... many methods for combining circuits (viewed as networks of functions) are unified if the distinction between input and output is removed [57] Ruby has been used to design many different kinds of circuits, including systolic arrays [58] butterfly networks [59] and arithmetic circuits [42]. We identify two shortcomings with derivations made using Ruby. The first is that the notion of a program being an implementation of a specification has never been made precise. The second is to do with types. Fundamental to the use of type information in deriving programs is the idea of having ....

....of a program being an implementation of a specification has never been made precise. The second is to do with types. Fundamental to the use of type information in deriving programs is the idea of having types as special kinds of programs. In Ruby, types are partial equivalence relations (pers) [42, 37]. Unfortunately, manipulating some formulae involving types has proved difficult within Ruby. In particular, the preconditions of the induction laws that are much used within program derivation often work out to be assertions about types; such assertions have typically been verified either by ....

[Article contains additional citation context not shown here]

Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. In Proc. Second International Conference on Mathematics of Program Construction, Lecture Notes in Computer Science. Springer-Verlag, 1992. To appear.

....methodology that is very similar in spirit to ours. The main difference is that we choose different ways to represent circuit function. Bryant s hierarchical verification method has its roots in work by Lai and Sastry [9] while ours is based on the notion of refinement in FP and Ruby [10]. Bryant is developing a verification system, whose aims seem to be very similar to those of the Lava project, of which this work is a part. A possible problem with BMDs in general is that they may become very large for incorrect circuits. This is not a problem in the logical representation of ....

M. Sheeran, G. Jones, Designing arithmetic circuits by refinement in Ruby Science of Computer Programming 22(1-2), 1994.

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Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in ruby. In C. C. Morgan R. S. Bird and J. C. P. Woodcock, editors, Mathematics of Program Construction, Lecture Notes in Computer Science. Springer Verlag, 1993.

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Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. In R. S. Bird, C. C. Morgan, and J. C. P. Woodcock, editors, Mathematics of Program Construction, pages 388--395. Springer Verlag, 1993. LNCS 669. 21

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Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. In R. S. Bird, C. C. Morgan, and J. C. P. Woodcock, editors, Mathematics of Program Construction, pages 388--395. Springer Verlag, 1993. LNCS 669. 23

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Geraint Jones and Mary Sheeran. Designing arithmetic circuits by refinement in Ruby. In R. S. Bird, C. C. Morgan, and J. C. P. Woodcock, editors, Mathematics of Program Construction, pages 388--395. Springer Verlag, 1993. LNCS 669.

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