Foundational Proof Certificates in First-Order Logic

Chihani, Zakaria; Miller, Dale; Renaud, Fabien

doi:10.1007/978-3-642-38574-2_11

Cited by 25 publications

(33 citation statements)

References 26 publications

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“…An FPC defining binary resolution refutations has been given in [16] and we describe it briefly here since the experimental results described in Section 7 build on this example. A clause is a formula of the form ∀x 1 …”

Section: Resolution Refutationsmentioning

confidence: 99%

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Translating Between Implicit and Explicit Versions of Proof

Blanco

Chihani

Miller

2017

Automated Deduction – CADE 26

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Abstract. The Foundational Proof Certificate (FPC) framework can be used to define the semantics of a wide range of proof evidence. For example, such definitions exist for a number of textbook proof systems as well as for the proof evidence output from some existing theorem proving systems. An important decision in designing a proof certificate format is the choice of how many details are to be placed within certificates. Formats with fewer details are smaller and easier for theorem provers to output but they require more sophistication from checkers since checking will involve some proof reconstruction. Conversely, certificate formats containing many details are larger but are checkable by less sophisticated checkers. Since the FPC framework is based on well-established proof theory principles, proof certificates can be manipulated in meaningful ways. In this paper, we illustrate how it is possible to automate moving from implicit to explicit (elaboration) and from explicit to implicit (distillation) proof evidence via the proof checking of a pair of proof certificates. Performing elaboration makes it possible to transform a proof certificate with details missing into a certificate packed with enough details so that a simple kernel (without support for proof reconstruction) can check the elaborated certificate. We illustrate how trust in only a single, simple checker of explicitly described proofs can be used to provide trust in a range of theorem provers employing a range of proof structures.

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Section: Resolution Refutationsmentioning

confidence: 99%

“…Foundational Proof Certificates (FPC) is a recently proposed framework for defining the semantics of a wide range of proof languages for first-order classical and intuitionistic logic [13,16,17]. Instead of starting with dependently typed λ-calculus, the FPC framework is based on Gentzen's more low-level notion of sequent calculus proof.…”

Section: Introductionmentioning

confidence: 99%

Translating Between Implicit and Explicit Versions of Proof

Blanco

Chihani

Miller

2017

Automated Deduction – CADE 26

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“…In many scenarios, such as proof-carrying code [47] and foundational proof certificates [20,45], it is advocated that proofs should be made more pervasive and universal [22]. A proof checker (or a proof consumer, more generally), in these scenarios, will not be an isolated application processing a single proof on a dedicated machine with a large amount of resources.…”

Section: Introductionmentioning

confidence: 99%

“…This is the common way to process all kinds of proofs in proof checking systems such as CERes [25], GAPT [24,26,36,44,55], the Checkers tool [19] for foundational proof certificates [20] and Dedukti [2,17]. Moreover, when the conclusion clauses of resolution inferences (or chains of inferences) are omitted in propositional resolution proofs in the TraceCheck format, only top-down checking is possible, because the conclusion clauses need to be recomputed based on their premises.…”

Section: Definition 4 (Proof Processing)mentioning

confidence: 99%

Greedy pebbling for proof space compression

Fellner

Paleo

2017

Int J Softw Tools Technol Transfer

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Automated reasoning tools for the verification and synthesis of software often produce proofs to allow independent certification of the correctness of the produced solutions. As proofs can be large, this paper considers the problem of compressing proofs with respect to their space, which is approximately proportional to the memory necessary to check them. Proof checking with a small amount of available memory is analogous to playing a pebbling game with a small number of pebbles. This paper exploits this analogy and describes novel algorithms for playing a pebbling game. The sequence of moves executed in the pebbling game then corresponds to an improved topological ordering of the nodes of the proof, leading to smaller memory consumption when the proof is checked. Because the number of possible pebbling strategies and topological orderings is too large, brute-force approaches to find optimal solutions are impractical, and hence, the new pebbling algorithms proposed here are based on heuristics for finding good, though not necessarily optimal, solutions. The algorithms are evaluated on the task of compressing the space of thousands of propositional resolution proofs generated by SAT-and SMT-solvers.

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“…Nondeterminism in the specification of proof semantics has been considered in other systems as well. In particular, nondeterminism is allowed in the Foundational Proof Certificates (FPC) framework [7,19] where client-side inference rules (i.e., rules implemented in theorem provers) are translated into low-level rules of sequent calculus. The checkers proof certifier [5], based on the FPC framework, used the λProlog logic programming language [20] to provide for a backtracking search approach to exploring any nondeterminism in such translations.…”

Section: Denoting Semantics As Logic Programsmentioning

confidence: 99%

Defining the meaning of TPTP formatted proofs

Blanco

Libal

Miller

EPiC Series in Computing

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The TPTP library is one of the leading problem libraries in the automated theorem proving community. Over time, support was added for problems beyond those in first-order clausal form. TPTP has also been augmented with support for various proof formats output by theorem provers. Such proofs can also be maintained in the TSTP proof library. In this paper we propose an extension of this framework to support the semantic specification of the inference rules used in proofs.

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Foundational Proof Certificates in First-Order Logic

Cited by 25 publications

References 26 publications

Translating Between Implicit and Explicit Versions of Proof

Translating Between Implicit and Explicit Versions of Proof

Greedy pebbling for proof space compression

Defining the meaning of TPTP formatted proofs

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