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- Alexandre Miquel
- TLCA
- 2001

In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Curry-style variant of the Calculus of Constructions that we extend by adding an intersection typeâ€¦ (More)

- Alexandre Miquel
- 2001

In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Curry-style variant of the Calculus of Constructions that we extend by adding an intersection typeâ€¦ (More)

- Alexandre Miquel, Benjamin Werner
- TYPES
- 2002

It is well-known that the Calculus of Constructions (CC) bears a simple set-theoretical model in which proof-terms are mapped onto a single objectâ€”a property which is known as proof-irrelevance. Inâ€¦ (More)

- Alexandre Miquel
- LICS
- 2000

We introduce a new model based on coherence spaces for interpreting large impredicative type systems such as t he Extended Calculus of Constructions (ECC). Moreover, we show that this model isâ€¦ (More)

- Alexandre Miquel
- 2011 IEEE 26th Annual Symposium on Logic inâ€¦
- 2011

This paper is a study of the forcing translation through the proofs as programs correspondence in classical logic, following the methodology introduced by Krivine in [Kri08, Kri10]. For that, weâ€¦ (More)

- Alexandre Miquel
- TLCA
- 2009

Friedman showed how to turn a classical proof of a Î£ 1 formula into an intuitionistic proof of the same formula, thus giving an effective method to extract witnesses from classical proofs of suchâ€¦ (More)

- Walter Ferrer Santos, Jonas Frey, Mauricio Guillermo, Octavio Malherbe, Alexandre Miquel
- Mathematical Structures in Computer Science
- 2017

We propose the new concept of Krivine ordered combinatory algebra (KOCA) as foundation for the categorical study of Krivineâ€™s classical realizability, as initiated by Streicher (2013). We show thatâ€¦ (More)

We show how to express intuitionistic Zermelo set theory in deduction modulo (i.e. by replacing its axioms by rewrite rules) in such a way that the corresponding notion of proof enjoys theâ€¦ (More)

- Alexandre Miquel
- Logical Methods in Computer Science
- 2011

We show how to extract existential witnesses from classical proofs using Krivineâ€™s classical realizabilityâ€”where classical proofs are interpreted as Î»-terms with the call/cc control operator. Weâ€¦ (More)

- Alexandre Miquel
- CSL
- 2007

We show how to extract classical programs expressed in Krivine Î»c-calculus from proof-terms built in a proof-irrelevant and classical version of the calculus of constructions with universes. Forâ€¦ (More)