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The Implicit Calculus of Constructions

- Alexandre Miquel
- Computer Science
- TLCA
- 2 May 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 type… Expand

The Implicit Calculus of Constructions Extending Pure Type Systems with an Intersection Type Binder and Subtyping

- 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 type… Expand

Forcing as a Program Transformation

- Alexandre Miquel
- Mathematics, Computer Science
- IEEE 26th Annual Symposium on Logic in Computer…
- 21 June 2011

TLDR

The Not So Simple Proof-Irrelevant Model of CC

- Alexandre Miquel, Benjamin Werner
- Computer Science
- TYPES
- 24 April 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 object--a property which is known as proof-irrelevance. In… Expand

A model for impredicative type systems, universes, intersection types and subtyping

- Alexandre Miquel
- Mathematics, Computer Science
- Proceedings Fifteenth Annual IEEE Symposium on…
- 26 June 2000

TLDR

The λ-calculus with constructors: Syntax, confluence and separation

- Ariel Arbiser, Alexandre Miquel, Alejandro Ríos
- Computer Science
- Journal of Functional Programming
- 1 September 2009

Abstract We present an extension of the λ(η)-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the… Expand

Ordered combinatory algebras and realizability †

- W. Santos, Jonas Frey, M. Guillermo, Octavio Malherbe, Alexandre Miquel
- Mathematics, Computer Science
- Mathematical Structures in Computer Science
- 19 October 2014

TLDR

Implicative algebras: a new foundation for realizability and forcing

- Alexandre Miquel
- Mathematics, Computer Science
- Mathematical Structures in Computer Science
- 2 February 2018

TLDR

Realizability in the Unitary Sphere

- Alejandro Díaz-Caro, M. Guillermo, Alexandre Miquel, B. Valiron
- Computer Science, Mathematics
- 34th Annual ACM/IEEE Symposium on Logic in…
- 18 April 2019

TLDR

Existential witness extraction in classical realizability and via a negative translation

- Alexandre Miquel
- Computer Science, Mathematics
- Log. Methods Comput. Sci.
- 23 January 2011

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