Related papers: A Graded Modal Dependent Type Theory with Erasure,…
We define a naturality construction for the operations of weak omega-categories, as a meta-operation in a dependent type theory. Our construction has a geometrical motivation as a local tensor product with a directed interval, and behaves…
In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must…
The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra B to each formula. We show some basic results regarding the effect of the properties of B on the behavior of…
The $\lambda$$\Pi$-calculus modulo theory is an extension of simply typed $\lambda$-calculus with dependent types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules of a theory of the…
A theorem of Lurie and Pridham establishes a correspondence between formal moduli problems and differential graded Lie algebras in characteristic zero, thereby formalising a well-known principle in deformation theory. We introduce a variant…
In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
We study a dependently typed extension of a multi-stage programming language \`a la MetaOCaml, which supports quasi-quotation and cross-stage persistence for manipulation of code fragments as first-class values and an evaluation construct…
We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…
This paper presents a construction which transforms categorical models of additive-free propositional linear logic, closely based on de Paiva's dialectica categories and Oliva's functional interpretations of classical linear logic. The…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and…
We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely. Going beyond plain, strong…
We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
Affine type systems are substructural type systems where copying of information is restricted, but discarding of information is permissible at all types. Such type systems are well-suited for describing quantum programming languages,…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
Traditionally, semantic models of imperative languages use an auxiliary structure which mimics memory. In this way, ownership and other encapsulation properties need to be reconstructed from the graph structure of such global memory. We…
Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, a strictly linear setting is somewhat…