Canonicity for 2-dimensional type theory
نویسندگان
چکیده
منابع مشابه
Canonicity for Cubical Type Theory
Cubical type theory is an extension of Martin-Löf type theory recently proposed by Cohen, Coquand, Mörtberg and the author which allows for direct manipulation of n-dimensional cubes and where Voevodsky’s Univalence Axiom is provable. In this paper we prove canonicity for cubical type theory: any natural number in a context build from only name variables is judgmentally equal to a numeral. To a...
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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...
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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...
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We describe an abstract proof-theoretic framework based on normal-form proofs, defined using well-founded orderings on proof objects. This leads to robust notions of canonical presentation and redundancy. Fairness of deductive mechanisms – in this general framework – leads to completeness or saturation. The method has so far been applied to the equational, Horn-clause, and deduction-modulo cases.
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ژورنال
عنوان ژورنال: ACM SIGPLAN Notices
سال: 2012
ISSN: 0362-1340,1558-1160
DOI: 10.1145/2103621.2103697