Related papers: Large and Infinitary Quotient Inductive-Inductive …
We study the character theory of inductive limits of $q$-deformed classical compact groups. In particular, we clarify the relationship between the representation theory of Drinfeld-Jimbo quantized universal enveloping algebras and our…
We define a simple dependent type theory and prove that its well-formed types correspond exactly to finite inverse categories.
This paper introduces an ML / Haskell like programming language with nested inductive and coinductive algebraic datatypes called \chariot. Functions are defined by arbitrary recursive definitions and can thus lead to non-termination and…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain…
We introduce the notion of a directed stratification for a finite-dimensional algebra. For algebras that admit such a stratification we characterise the projective resolutions of finitely generated modules and obtain a result for the…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
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…
Capretta's delay monad can be used to model partial computations, but it has the "wrong" notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the "right" notion of equality, weak bisimilarity.…
Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
In Martin-L\"of's Intensional Type Theory, identity type is a heavily used and studied concept. The reason for that is the fact that it's responsible for the recently discovered connection between Type Theory and Homotopy Theory. The main…
We prove that the representations numbers of a ternary definite integral quadratic form defined over F_q[t], where F_q is a finite field of odd characteristic, determine its integral equivalence class when q is large enough with respect to…
We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…
Formalizations of quantum information theory in category theory and type theory, for the design of verifiable quantum programming languages, need to express its two fundamental characteristics: (1) parameterized linearity and (2) metricity.…
We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…
We present AlgCo (Algebraic Coinductives), a practical framework for inductive reasoning over commonly used coinductive types such as conats, streams, and infinitary trees with finite branching factor. The key idea is to exploit the notion…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…