Related papers: Extensionality of lambda-*
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
We construct a left semi-model structure on the category of intensional type theories (precisely, on $\mathrm{CxlCat_{Id,1,\Sigma(,\Pi_{ext})}}$). This presents an $\infty$-category of such type theories; we show moreover that there is an…
The expressiveness of dependent type theory can be extended by identifying types modulo some additional computation rules. But, for preserving the decidability of type-checking or the logical consistency of the system, one must make sure…
In this paper, we show Langton's type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k
We answer Klop and de Vrijer's question whether adding surjective-pairing axioms to the extensional lambda calculus yields a conservative extension. The answer is positive. As a byproduct we obtain a "syntactic" proof that the extensional…
In the present article, we extend the fragment of inductive formulas for the hybrid language L(@) in [8] including a McKinsey-like formula, and show that every formula in the extended class has a first-order correspondent, by modifying the…
In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order four for the free summands.
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
This thesis is concerned with type-logical grammars and their practical applicability as tools of reasoning about sentence syntax and semantics. The focal point is narrowed to Dutch, a language exhibiting a large degree of word order…
We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central…
We provide a characterisation of strongly normalising terms of the lambda-mu-calculus by means of a type system that uses intersection and product types. The presence of the latter and a restricted use of the type omega enable us to…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
We prove that the unitary equivalence classes of extensions of C*_r(G) by any sigma-unital stable C"-algebra, taken modulo extensions which split via an asymptotic homomorphism, form a group which can be calculated from the universal…
Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for…