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A Framework for Program Development Based on Schematic Proof
, 1993
"... Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that suppor ..."
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Cited by 11 (5 self)
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Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach.
Timing Analysis of Combinational Circuits in Intuitionistic Propositional Logic
 Formal Methods in System Design
, 1999
"... Classical logic has so far been the logic of choice in formal hardware verification. This paper proposes the application of intuitionistic logic to the timing analysis of digital circuits. The intuitionistic setting serves two purposes. The modeltheoretic properties are exploited to handle the s ..."
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Cited by 5 (1 self)
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Classical logic has so far been the logic of choice in formal hardware verification. This paper proposes the application of intuitionistic logic to the timing analysis of digital circuits. The intuitionistic setting serves two purposes. The modeltheoretic properties are exploited to handle the secondorder nature of bounded delays in a purely propositional setting without need to introduce explicit time and temporal operators. The proof theoretic properties are exploited to extract quantitative timing information and to reintroduce explicit time in a convenient and systematic way. We present a natural Kripkestyle semantics for intuitionistic propositional logic, as a special case of a Kripke constraint model for Propositional Lax Logic [15], in which validity is validity up to stabilisation, and implication oe comes out as "boundedly gives rise to." We show that this semantics is equivalently characterised by a notion of realisability with stabilisation bounds as realisers...
Some Normalization Properties of MartinLof's Type Theory, and Applications
 in Proc. 1st Internat. Conf. on Theoretical Aspects of Computer Software, Lecture Notes in Computer Science
, 1991
"... For certain kinds of applications of type theories, the faithfulness of formalization in the theory depends on intensional, or structural, properties of objects constructed in the theory. For type theories such as LF, such properties can be established via an analysis of normal forms and types. In t ..."
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Cited by 3 (1 self)
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For certain kinds of applications of type theories, the faithfulness of formalization in the theory depends on intensional, or structural, properties of objects constructed in the theory. For type theories such as LF, such properties can be established via an analysis of normal forms and types. In type theories such as Nuprl or MartinLof's polymorphic type theory, which are much more expressive than LF, the underlying programming language is essentially untyped, and terms proved to be in types do not necessarily have normal forms. Nevertheless, it is possible to show that for MartinLof's type theory, and a large class of extensions of it, a sufficient kind of normalization property does in fact hold in certain wellbehaved subtheories. Applications of our results include the use of the type theory as a logical framework in the manner of LF, and an extension of the proofsasprograms paradigm to the synthesis of verified computer hardware. For the latter application we point out some ...
Nuprl and its Use in Circuit Design
, 1992
"... Nuprl is an interactive theorem proving system in the LCF tradition. It has a higher order logic and a very expressive type theory; the type theory includes dependent function types (\Pi types), dependent product types (\Sigma types) and set types. Nuprl also has a well developed XWindows user inte ..."
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Cited by 2 (0 self)
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Nuprl is an interactive theorem proving system in the LCF tradition. It has a higher order logic and a very expressive type theory; the type theory includes dependent function types (\Pi types), dependent product types (\Sigma types) and set types. Nuprl also has a well developed XWindows user interface and allows for the use of clear and concise notations, close to ones used in print. Proofs are objects which can be viewed, and serve as readable explanations of theorems. Tactics provide a highlevel extendible toolkit for proof development, while the soundness of the system relies only a fixed set of rules. We give an overview of the Nuprl system, focusing in particular on the advantages that the type theory brings to formal methods for circuit design. We also discuss ongoing projects in verifying floatingpoint circuits, verifying the correctness of hardware synthesis systems, and synthesizing circuits by exploiting the constructivity of Nuprl's logic. Keyword Codes: F.4.1; B.6.2; I...
Recursive Program Optimization Through Inductive Synthesis Proof Transformation
, 1999
"... The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the target, which yields a computationally more efficient algorithm. We describe a working proof tran ..."
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The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the target, which yields a computationally more efficient algorithm. We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming inductive proofs. We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability and generality.