منابع مشابه
2-Dimensional Directed Type Theory
Recent work on higher-dimensional type theory has explored connections between Martin-Löf type theory, higher-dimensional category theory, and homotopy theory. These connections suggest a generalization of dependent type theory to account for computationally relevant proofs of propositional equality—for example, taking IdSet A B to be the isomorphisms between A and B. The crucial observation is...
متن کامل2-Dimensional Directed Dependent Type Theory
The groupoid interpretation of dependent type theory given by Hofmann and Streicher associates to each closed type a category whose objects represent the elements of that type and whose maps represent proofs of equality of elements. The categorial structure ensures that equality is reflexive (identity maps) and transitive (closure under composition); the groupoid structure, which demands that e...
متن کاملFoundations and Applications of Higher-Dimensional Directed Type Theory
Intuitionistic type theory [43] is an expressive formalism that unifies mathematics and computation. A central concept is the propositions-as-types principle, according to which propositions are interpreted as types, and proofs of a proposition are interpreted as programs of the associated type. Mathematical propositions are thereby to be understood as specifications, or problem descriptions, t...
متن کاملFoundations and Applications of Higher-Dimensional Directed Type Theory
Intuitionistic type theory [43] is an expressive formalism that unifies mathematics and computation. A central concept is the propositions-as-types principle, according to which propositions are interpreted as types, and proofs of a proposition are interpreted as programs of the associated type. Mathematical propositions are thereby to be understood as specifications, or problem descriptions, t...
متن کاملLévy-type diffusion on one-dimensional directed Cantor graphs.
Lévy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2011
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2011.09.026