Interview de Vladimir Voevodsky : http://blogs.scientificamerican.com/guest-blog/2013/10/01/voevodskys-mathematical-revolution/

Nov 22 2013

## Séminaire Marelle : A Coq formalization of finitely presented modules.

On Friday 22/11/2013, at 10h30, in room Byron Beige,

**Speaker:** Cyril Cohen.

**Joint work with:** Anders Mortberg.

**Title:** A Coq formalization of finitely presented modules.

Abstract:

The use of vector spaces in homology theory does not give as precise

information as with modules. A generalization to finitely presented modules

covers computable Z-homology, which gives finer-grained topological invariants.

We formalize a construction of finitely presented modules over coherent and

strongly discrete rings and discuss its properties. This formalization gives

basic building blocks that lead to a clean definition of homology groups.

Nov 20 2013

## Séminaire Marelle : Types and Data types in Continuation Calculus and lambda calculus

On Wednesday 20/11/2013, at 10h30, in room Byron blanc.

**Speaker: ** Herman Geuvers.

**Joint work with: **Bram Geron, Universty of Birmingham.

**Title: ** Types and Data types in Continuation Calculus and lambda calculus.

Abstract:Continuation Calculus (CC), as defined in [1], is a model for functional

computations that aims at (1) being simple (simpler than lambda calculus

and term rewriting), (2) remaining close to actual implementations and

(3) being generic (incorporating various evaluation strategies).

The original system is untyped, but there is a standard procedure for

defining data in CC and writing functions over this data.

In the talk we present a typing system for CC and compare it with the

typing of data in lambda calculus. In lambda calculus, one has the

iterative representation of data (e.g. the Church numerals), but also

the less well-known recursive representation (e.g. the so called “Scott

numerals”). In CC, the recursive data are the “standard” ones and we

show how to type them, compute with them and reason over them.[1] Bram Geron and Herman Geuvers — Continuation calculus,

Proceedings First Workshop on Control Operators and their Semantics,

2013, edited by: Ugo de’Liguoro and Alexis Saurin, EPTCS 127, pp 66-85.

Aug 26 2013

## Séminaire Marelle : Certified, Efficient and Sharp Univariate Taylor Models in COQ.

On Monday 26/08/2013, at 14h30, in room Byron Blanc.

**Speaker:** Érik Martin-Dorel.

**Title:** Certified, Efficient and Sharp Univariate Taylor Models in COQ.

Abstract:

We present a formalisation, within the COQ proof assistant, of

univariate Taylor models. This formalisation being executable, we get a

generic library whose correctness has been formally proved and with

which one can effectively compute rigorous and sharp approximations of

univariate functions composed of usual functions such as 1/x, sqrt(x),

exp(x), sin(x) among others. In this talk, we present the key parts of

the formalisation and we evaluate the quality of our certified library

on a set of examples.

- Joint work with members of the CoqApprox working group

http://tamadi.gforge.inria.fr/CoqApprox - URL of the paper: HAL page