Related papers: The Yoneda Reduction of Polymorphic Types (Extende…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
Postulating an impredicative universe in dependent type theory allows System F style encodings of finitary inductive types, but these fail to satisfy the relevant {\eta}-equalities and consequently do not admit dependent eliminators. To…
We establish a formal correspondence between resource calculi an appropriate linear multicategories. We consider the cases of (symmetric) representable, symmetric closed and autonomous multicategories. For all these structures, we prove…
Type isomorphism is useful for retrieving library components, since a function in a library can have a type different from, but isomorphic to, the one expected by the user. Moreover type isomorphism gives for free the coercion required to…
Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…
The lambda-Pi-calculus Modulo is a variant of the lambda-calculus with dependent types where beta-conversion is extended with user-defined rewrite rules. It is an expressive logical framework and has been used to encode logics and type…
Programming benefits from a clear separation between pure, mathematical computation and impure, effectful interaction with the world. Existing approaches to enforce this separation include monads, type-and-effect systems, and capability…
These notes provide an explanation of the type classification of von Neumann algebras, which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature…
We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with $\eta$-conversion. Because these systems verify the proofs-as-objects paradigm, the proof synthesis method is a one level process…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
A forcing extension may create new isomorphisms between two models of a first order theory. Certain model theoretic constraints on the theory and other constraints on the forcing can prevent this pathology. A countable first order theory is…
We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…
We fix any bicategory $\mathscr{A}$ together with a class of morphisms $\mathbf{W}_{\mathscr{A}}$, such that there is a bicategory of fractions $\mathscr{A}[\mathbf{W}_{\mathscr{A}}^{-1}]$. Given another such pair…
The importance of subtyping to enable a wider range of well-typed programs is undeniable. However, the interaction between subtyping, recursion, and polymorphism is not completely understood yet. In this work, we explore subtyping in a…
The term UniMath refers both to a formal system for mathematics, as well as a computer-checked library of mathematics formalized in that system. The UniMath system is a core dependent type theory, augmented by the univalence axiom. The…
This paper defines a notion of binding trees that provide a suitable model for second-order type systems with F-bounded quantifiers and equirecursive types. It defines a notion of regular binding trees that correspond in the right way to…
Most type systems that support polymorphic functions are based on a version of System-F. We argue that this limits useful programming paradigms for languages with lazy evaluation. We motivate an extension of System-F alleviating this…
In this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of $\beta$-reduction in the polymorphic $\lambda$-calculus, to prove the termination of various kinds of rewrite relations on…
A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. In \cite{DR2} we gave characterizations of monomorphisms (resp. epimorphisms) in arbitrary pro-categories, pro-(C), where (C) has…