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It is the exception that provers share and trust each others proofs. One reason for this is that different provers structure their proof evidence in remarkably different ways, including, for example, proof scripts, resolution refutations, tableaux, Herbrand expansions, natural deductions, etc. In this paper, we propose an approach to foundational proof… (More)

We define a framework called the prismoid of resources where each vertex is a λ-calculus with the possibility of having different explicit resources and/or explicit cut elimination based on a different choice to make explicit or implicit (meta-level) the definition of the contraction, weakening, substitution operations. For all the calculi in the prismoid… (More)

We present the design philosophy of a proof checker based on a notion of foundational proof certificates. At the heart of this design is a semantics of proof evidence that arises from recent advances in the theory of proofs for classical and intuitionistic logic. That semantics is then performed by a (higher-order) logic program: successful performance… (More)

Inspired by the Multiplicative Exponential fragment of Linear Logic, we define a framework called the prismoid of resources where each vertex is a language which refines the λ-calculus by using a different choice to make explicit or implicit (meta-level) the definition of the contraction, weakening, and substitution operations. For all the calculi in the… (More)

- Fabien Renaud
- 2011

Theorem provers produce evidence of proof in many different formats, such as proof scripts, natural deductions, resolution refutations, Herbrand expansions, and equational rewritings. In implemented provers, numerous variants of such formats are actually used: consider, for example, such variants of or restrictions to resolution refutations as binary… (More)

We present the design philosophy of a proof checker based on a notion of foundational proof certificates. At the heart of this design is a semantics of proof evidence that arises from recent advances in the theory of proofs for classical and intuitionistic logic. That semantics is then performed by a (higher-order) logic program: successful performance… (More)

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