Download e-book for kindle: Adapting Proofs-as-Programs : The Curry-Howard Protocol by Iman Poernomo, Visit Amazon's John N. Crossley Page, search

By Iman Poernomo, Visit Amazon's John N. Crossley Page, search results, Learn about Author Central, John N. Crossley, , Martin Wirsing

ISBN-10: 0387237593

ISBN-13: 9780387237596

ISBN-10: 0387281835

ISBN-13: 9780387281834

This monograph information a number of very important advances within the zone often called the proofs-as-programs paradigm, a suite of methods to constructing courses from proofs in optimistic common sense. It serves the twin function of offering a cutting-edge assessment of the sector and detailing instruments and strategies to stimulate extra learn. one of many book’s imperative subject matters is a basic, summary framework for constructing new platforms of software synthesis by way of adapting proofs-as-programs to new contexts, which the authors name the Curry--Howard Protocol. This protocol is used to supply novel functions for industrial-scale, complicated software program engineering: contractual valuable software synthesis and dependent software program synthesis. those purposes represent an exemplary justification for the applicability of the protocol to diversified contexts. The booklet is meant for graduate scholars in laptop technological know-how or arithmetic who desire to expand their historical past in good judgment and kind concept in addition to achieve adventure operating with logical frameworks and sensible facts structures. additionally, the proofs-as-programs examine neighborhood, and the broader computational good judgment, formal equipment and software program engineering groups will profit. The purposes given within the booklet may be of curiosity for researchers operating within the aim challenge domain names.

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1 The Curry–Howard protocol Some work has been done in providing analogous results to the Curry–Howard isomorphism and proofs-as-programs for other logical systems and programming languages, often in the domain of classical logic. We contribute a novel result to the field by identifying a general framework that generalizes the form such analogies should take over arbitrary logical calculi and programming languages. The Curry–Howard protocol provides the framework. It is useful because it can then be used as a guide for adapting proofs-as-programs to new contexts, such as imperative program synthesis.

This is possible when we consider each schema application of the form Γ1 Int F1 . . Γn Γ Int F Int Fn to generate an axiom ((Γ1 ⇒ F1 ) ∧ . . ∧ (Γn ⇒ Fn )) ⇒ F in AX. The generated axiom and the schema application are equivalent, because repeated application of (⇒-E) on the former simulates satisfaction of premises in the latter. Induction schemata may be provided for the data types of Σ that can be generated by constructor functions. These schemata are defined in the usual fashion for a data type: to prove a statement over all elements of a type we show that the statement holds over the generation of the sort.

Chapter 9 describes how the Curry–Howard protocol is applied to achieve the synthesis of correct functions from proofs of our logic and how specifications can be consistently extended by these functions. — Chapter 10 extends our results to generic, parametrized specifications as they are treated in the algebraic specification language CASL [CoF01]. — Chapter 11 provides a methodology for using our results for the refinement of structured specifications into structured executable code. • Part V, Chapter 12, offers concluding remarks and suggests directions for future research.

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Adapting Proofs-as-Programs : The Curry-Howard Protocol by Iman Poernomo, Visit Amazon's John N. Crossley Page, search results, Learn about Author Central, John N. Crossley, , Martin Wirsing

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