This thesis considers the problem of program correctness within a rich theory of dependent types, the Extended Calculus of Constructions (ECC). This system contains a powerful programming language of higher-order primitive recursion and higher-order intuitionistic logic. It is supported by Pollack's versatile LEGO implementation, which I use extensively to develop the mathematical constructions studied here. I systematically investigate Burstall's notion of deliverable, that is, a program paired with a proof of correctness. This approach separates the concerns of programming and logic, since I want a simple program extraction mechanism. The Sigma-types of the calculus enable us to achieve this. There are many similarities with the subset interpretation of Martin-Löf type theory. I show that deliverables have a rich categorical structure, so that correctness proofs may be decomposed in a principled way. The categorical combinators which I define in the system package up much logical book-keeping, allowing one to concentrate on the essential structure of algorithms. I demonstrate our methodology with a number of small examples, culminating in a machine-checked proof of the Chinese remainder theorem, showing the utility of the deliverables idea. Some drawbacks are also encountered. I consider also semantic aspects of deliverables, examining the definitions in an abstract setting, again firmly based on category theory. The aim is to overcome the clumsiness of the language of categorical combinators, using dependent type theories and their interpretation in fibrations. I elaborate a concrete instance based on the category of sets, which generalises to an arbitrary topos. In the process, I uncover a subsystem of ECC within which one may speak of deliverables defined over the topos. In the presence of enough extra structure, the interpretation extends to the whole of ECC. The wheel turns full circle.

The aim of this study is to fill the gap in mathematics education research concerning the relationship between identity and positioning in mathematical collaboration in groups. This study elaborates on the relationship between how pupils see themselves as math students in sixth grade, how they show their identities as math students, in contrast to how they position themselves reflexively in group collaboration while engaging in mathematical problem solving. The theoretical concepts linked to this study are discourse, identity and positioning. Discourse is used to describe and form the setting and context of the study. Identity is seen as a transient and elusive concept formed by the students own perceptions of self through narratives. The reflexive form of positioning, where the students choose to position themselves in discourse, is derived from acts and speech in group collaboration. This form of positioning is then used as comparison to the narratives of identity to explore the relationship between these two concepts. Data has been collected through participative observation and dialogue, and discourse analysis is partially used to identify the relationship. The results may have implications for future structuring and planning of mathematics education in our classrooms, and the findings provide a narrowing of the gap in mathematics education research within this area. The findings also open up new questions concerning the social constructions of identity among children. Finally, the findings related to the need of reflexive positioning among children in their early teens, and how educators can benefit from this need, are other aspects worth further research.

Texte remanié de: Th. doct.--Hist.--Caen, 2001. Titre de soutenance : Archéologie de l'habitat rural dans le nord de la Gaule du IVe au XIIe siècle. / Bibliogr. vol. 1, p. 363-427. Notes bibliogr. Index à la fin du vol. 1. AFAM = Association française d'archéologie mérovingienne.

Thèse de doctorat--Mécanique énergétique--Grenoble 1, 2007. / Notice réd. d'après la couv. Bibliogr. p. 198-204. Résumé en anglais et en français.

Texte remanié de: Doctoral thesis--University of London, 1998. / Résumé en arabe. Bibliogr. p. 205-214.

Reproduction de : Thèse de doctorat : Mécanique appliquée : Reims : 2004. / Texte en chinois. Titre provenant de l'écran titre. Bibliogr. p. 118-120.

Thèse de doctorat : Géographie : Lyon 2 : 2000. / Titre provenant de l'écran-titre. Bibliogr.

Thèse doctorat : Génie Civil : Villeurbanne, INSA : 2004. / Titre provenant de l'écran-titre. Bibliogr. p. 199-202.

Thèse doctorat : Génie Civil : Villeurbanne, INSA : 2001. / Titre provenant de l'écran-titre. Bibliogr. p. 205-223.

Thèse de doctorat : Génie civil - Hydrosystèmes - Géotechnique : INPL : 2007. / Titre provenant de l'écran-titre.