Related papers: Guarded Dependent Type Theory with Coinductive Typ…
We present a conservative extension ICaTT of the dependent type theory CaTT for weak $\omega$-categories with a type witnessing coinductive invertibility of cells. This extension allows for a concise description of the "walking equivalence"…
Guided by Tarksi's fixpoint theorem in order theory, we show how to derive monotone recursive types with constant-time roll and unroll operations within Cedille, an impredicative, constructive, and logically consistent pure typed lambda…
The chase algorithm is a fundamental tool for query evaluation and query containment under constraints, where the constraints are (sub-classes of) tuple-generating dependencies (TGDs) and equality generating depencies (EGDs). So far, most…
Many variants of type theory extend a basic theory with additional primitives or properties like univalence, guarded recursion or parametricity, to enable constructions or proofs that would be harder or impossible to do in the original…
It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Congruence closure procedures are used extensively in automated reasoning and are a core component of most satisfiability modulo theories solvers. However, no known congruence closure algorithms can support any of the expressive logics…
The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary…
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…
Attention-based Transformer models have been increasingly employed for automatic music generation. To condition the generation process of such a model with a user-specified sequence, a popular approach is to take that conditioning sequence…
The type-theoretic modelling of DRT that [degroote06] proposed features continuations for the management of the context in which a clause has to be interpreted. This approach, while keeping the standard definitions of quantifier scope,…
In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be…
We present a new type system combining occurrence typing, previously used to type check programs in dynamically-typed languages such as Racket, JavaScript, and Ruby, with dependent refinement types. We demonstrate that the addition of…
Within dependent type theory, we provide a topological counterpart of well-founded trees (for short, W-types) by using a proof-relevant version of the notion of inductively generated suplattices introduced in the context of formal topology…
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…
Linear dependent types allow to precisely capture both the extensional behaviour and the time complexity of lambda terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
Type refinements combine the compositionality of typechecking with the expressivity of program logics, offering a synergistic approach to program verification. In this paper we apply dependent type refinements to SAX, a futures-based…