Writing programs that construct proofs

Constable, Robert L.; Knoblock, Todd B.; Bates, Joseph L.

doi:10.1007/bf00244273

Cited by 25 publications

(9 citation statements)

References 14 publications

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“…Automating reasoning The Nuprl system is a tactic style theorem prover in the spirit of Edinburgh LCF [50]; moreover it introduced the notion of a tactic-tree so that users could interact directly with the proof object [37,52]. We take the approach that the basic elements of automated proof development can be seen as providing algorithms for formal metamathematical results, so it is computation in the metalanguage [33,71].…”

Section: Propositions and Logical Truthmentioning

confidence: 99%

Innovations in computational type theory using Nuprl

Allen

Bickford

Constable

et al. 2006

Journal of Applied Logic

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For twenty years the Nuprl ("new pearl") system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT)-a formal theory of computation closely related to Martin-Löf's intuitionistic type theory (ITT) and to the calculus of inductive constructions (CIC) implemented in the Coq prover.This article focuses on the theory and practice underpinning our use of Nuprl for much of the last decade. We discuss innovative elements of type theory, including new type constructors such as unions and dependent intersections, our theory of classes, and our theory of event structures.We also discuss the innovative architecture of Nuprl as a distributed system and as a transactional database of formal mathematics using the notion of abstract object identifiers. The database has led to an independent project called the Formal Digital Library, FDL, now used as a repository for Nuprl results as well as selected results from HOL, MetaPRL, and PVS. We discuss Howe's set theoretic semantics that is used to relate such disparate theories and systems as those represented by these provers.

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Section: Propositions and Logical Truthmentioning

confidence: 99%

Innovations in computational type theory using Nuprl

Allen

Bickford

Constable

et al. 2006

Journal of Applied Logic

Self Cite

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“…If the recovery tuple has a non-empty event trigger field, the pre-compiler declares a new global variable -recovery action index rai rt (lines [7][8]. If the recovery tuple predicate is a safety predicate, the pre-compiler replaces the triggering event execution according to the code in lines 11-21, i.e., by taking a snapshot of some variable before the event execution, by creating a variable temp and by assigning it with the current value of the variable from the triggering event and by checking if the predicate still holds with regards to the temp variable after the execution of the triggering event method on temp (lines [12][13].…”

Section: Recovery Oriented Programmingmentioning

confidence: 99%

Recovery oriented programming

Brukman

Sihman

2005

Proceedings of the Twentieth ACM Symposium on Operating Systems Principles

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Abstract. Writing a perfectly correct code is a challenging and a nearly impossible task. In this work we suggest the recovery oriented programming paradigm in order to cope with eventual Byzantine programs. The program specification composer enforces the program specifications (both the safety and the liveness properties) in run time using predicates over input and output variables. The component programmer will use these variables in the program implementation. We suggest using the "sand-box" approach in which every instruction of the program that changes a specification variable, is executed first with temporary variables and that is in order to avoid execution of an instruction that violates the specifications. In addition, external monitoring is used for coping with transient faults and for ensuring convergence to a legal state. The implementation of these ideas includes the definition of new instructions in the programming language with the purpose of allowing addition of predicates and recovery actions. We suggest a design for a tool that extends the Java programming language. In addition to that, we provide a correctness proof scheme for proving that the code combined with the predicates and the recovery actions is self-stabilizing and, under the restartability assumption, eventually fulfills its specifications.

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“…Except for the representational details, this destructive version is Warshall's algorithm as described in [2]. 3 Warshall's Algorithm Using Integer Representation…”

Section: Transforming the Initial Proofmentioning

confidence: 99%

“…NuPrl [4] provides sophisticated machine support for program development using this proofs as programs paradigm. It allows extraction of veried programs from completed proofs, unveried programs from partial proofs, and the writing of tactics to automate part of the program synthesis and verication process [3,8]. Goad in [6] showed that proof transformations can improve the eciency of extracted programs in the context of specialization, that is, in situations where a very general program is applied to inputs satisfying some given constraints.…”

Section: Introductionmentioning

confidence: 99%

Program development through proof transformation

Pfenning¹

1990

Logic and Computation

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Abstract. We present a methodology for deriving veried programs that combines theorem proving and proof transformation steps. It extends the paradigm employed in systems like NuPrl where a program is developed and veried through the proof of the specication in a constructive type theory. We illustrate our methodology through an extended example | a derivation of Warshall's algorithm for graph reachability. We also outline how our framework supports the denition, implementation, and use of abstract data types.

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Writing programs that construct proofs

Cited by 25 publications

References 14 publications

Innovations in computational type theory using Nuprl

Innovations in computational type theory using Nuprl

Recovery oriented programming

Program development through proof transformation

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