Related papers: On the Identity Type as the Type of Computational …
It is common to model inductive datatypes as least fixed points of functors. We show that within the Cedille type theory we can relax functoriality constraints and generically derive an induction principle for Mendler-style lambda-encoded…
We prove a conjecture about the constructibility of coinductive types - in the principled form of indexed M-types - in Homotopy Type Theory. The conjecture says that in the presence of inductive types, coinductive types are derivable.…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…
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…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of…
In this paper, the results of part I regarding a special case of Feynman identity are extended. The sign rule for a path in terms of data encoded by its word and formulas for the numbers of distinct equivalence classes of nonperiodic paths…
The group identification problem asks to identify a socially qualified subgroup among a group of individuals based on their pairwise valuations. There are several different rules that can be used to determine the social qualification…
Identifying the nature of interactions in a quantum system is essential in understanding any physical phenomena. Acquiring information on the Hamiltonian can be a tough challenge in many-body systems because it generally requires access to…
New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point…
We study identification in models of aggregate choice generated by unobserved behavioral types. An analyst observes only aggregate choice behavior, while the population distribution of types and their type-level choice patterns are latent.…
In the first part of this paper we show that path categories are enriched over groupoids, in a way that is compatible with a suitable 2-category of path categories. In the second part we introduce a new notion of homotopy exponential and…
Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and…
Information-flow security type systems ensure confidentiality by enforcing noninterference: a program cannot leak private data to public channels. However, in practice, programs need to selectively declassify information about private data.…
Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
Type and effect systems are a tool to analyse statically the behaviour of programs with effects. We present a proof based on the so called reducibility candidates that a suitable stratification of the type and effect system entails the…