This paper presents a mechanizable framework for software development by re nement. The framework is based on a category of higher-order speci cations. The key idea is representing knowledge about programming concepts, such as algorithm design, datatype re nement, and expression simpli cation, by means of taxonomies of speci cations and morphisms. The framework is partially implemented in the r...

The goal of this paper is to explain the usage and semantics of hierarchical defaults in logical speciications. We discuss the usefulness of defaults for diierent speciication scenarios like specialization, aggregation, explanation, revision, etc. To understand defaults formally, we introduce a general framework parameterized on the underlying logical institution extended by an instantiation me...

In this thesis, we introduce a rigorous formally founded method to address the interoperability of a family of domain specific languages (DSLs). Our approach targets DSLs from the same business domain and consists in constructing a unifying language. The unification is obtained by using a categorical approach. For this, we use the category of algebraic specifications of each language in the fam...

One fundamental aspect of Lawvere’s categorical semantics is that every algebraic theory (eg. of monoid, of Lie algebra) induces a free construction (eg. of free monoid, of free Lie algebra) computed as a Kan extension. Unfortunately, the principle fails when one shifts to linear variants of algebraic theories, like Adams and Mac Lane’s PROPs, and similar PROs and PROBs. Here, we introduce the ...

Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CW-complex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such th...

This paper uses concepts from sheaf theory to explicate phenomena in concurrent systems, including object, inheritance, deadlock, and non-interference, as used in computer security. The approach is very general, and applies not only to concurrent object oriented systems, but also to systems of diierential equations, electrical circuits, hardware description languges, and much more. Time can be ...

where D is some small category, F is a functor from D to the category of spaces, and, for each object d ∈ D, F (d) has the homotopy type of BH for some subgroup H of G. The operator “hocolim” is the homotopy colimit in the sense of Bousfield and Kan [4], which amounts to a homotopy invariant method of gluing together the values of the functor F according to the pattern of the maps in D. There i...

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. resolve a serious deficit in existing theory by constructing good notion of presheaves, with suitable sheafification functor. Using sheafification, we develop general modules ring, give explicit constructions infinite products and introduce an analogue skyscraper sheaves. These results underlie re...

Let G be a discrete group and let BG denote its classifying space. Recall that a group is said to be perfect if it is equal to it’s own commutator subgroup. If G is an arbitrary group, then write BG for the Quillen “plus” construction applied to BG with respect to the unique maximal normal perfect subgroup ΠG of G [32]. The space BG can be obtained by attaching 2 and 3 cells to BG and has the d...

A non empty class C of connected spaces is said to be a closed class if it is closed under weak equivalences and pointed homotopy colimits. A closed class can be characterized as a non empty class of connected spaces which is closed under weak equivalences and is closed under certain simple operations: arbitrary wedges, homotopy push-outs and homotopy sequential colimits. The notion of a closed...