The Calculus of Constructions

Towards an Implicit Calculus of Inductive Constructions. Extending the Implicit Calculus of Constructions with Union and Subset Types

We present extensions of Miquel’s Implicit Calculus of Constructions (ICC) and Barras and Bernardo’s decidable Implicit Calculus of Constructions (ICC*) with union and subset types. The purpose of these systems is to solve the problem of interaction betweeen logical and computational data. This is a work in progress and our long term goal is to add the whole inductive types to ICC and ICC* in o...

Extensionality in the Calculus of Constructions

This paper presents a method to translate a proof in an extensional version of the Calculus of Constructions into a proof in the Calculus of Inductive Constructions extended with a few axioms. We use a specific equality in order to translate the extensional conversion relation into an intensional system.

Boomborg-PC: A Proof-Checker of Calculus of Constructions

Boomborg-PC is a proof-checker of Calculus of Constructions that runs on a bu er of GNU Emacs. Calculus of Constructions, proposed by Thierry Coquand and G erard Huet [2], is one of the so-called higher-order typed -calculi [1]. A typed -calculus is a formal system for writing typed -terms, and Boomborg-PC is a program that typechecks -terms written by the rules of Calculus of Constructions. A ...

CoqInE: Translating the Calculus of Inductive Constructions into the λΠ-calculus Modulo

We show how to translate the Calculus of Inductive Constructions (CIC) as implemented by Coq into the λΠ-calculus modulo, a proposed common backend proof format for heterogeneous proof assistants.

Extraction de programmes dans le Calcul des Constructions. (Program Extraction in the Calculus of Constructions)

Interpreting HOL in the calculus of constructions

The purpose of this paper is to consider a representation of the HOL theorem-prover in the calculus of constructions with the property that consistency results from the calculus of constructions imply such results in HOL. This kind of representation is impossible using the propositions-as-types representation of logic and equality, but it is possible if a different representation is used.