Internal Program Extraction in the Calculus of Inductive Constructions

Extending the Calculus of Constructions with Tarski's fix-point theorem

We propose to use Tarski’s least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in typetheory based theorem proving tool to potentially non-terminating functions. This is only possible if we extend the logical framework by adding the axioms that correspond to classical logic. We claim t...

Extracting Purely Functional Contents from Logical Inductive Types

We propose a method to extract purely functional contents from logical inductive types in the context of the Calculus of Inductive Constructions. This method is based on a mode consistency analysis, which veri es if a computation is possible w.r.t. the selected inputs/outputs, and the code generation itself. We prove that this extraction is sound w.r.t. the Calculus of Inductive Constructions. ...

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

The Rooster and the Syntactic Bracket

We propose an extension of pure type systems with an algebraic presentation of inductive and co-inductive type families with proper indices. This type theory supports coercions toward from smaller sorts to bigger sorts via explicit type construction, as well as impredicative sorts. Type families in impredicative sorts are constructed with a bracketing operation. The necessary restrictions of pa...

Developing Certified Programs in the System Coq - The Program Tactic

The system Coq is an environment for proof development based on the Calculus of Constructions extended by inductive deenitions. The speciication of a program can be represented by a logical formula and the program itself can be extracted from the constructive proof of the speciication. In this paper, we look at the possibility of inverting the extraction process. More precisely, we present a me...