Computational type theory
نویسندگان
چکیده
منابع مشابه
Guarded Computational Type Theory
We develop a computational interpretation of guarded dependent type theory with clocks called CTT which enjoys a straightforward operational semantics and immediate canonicity result for base types. Our realizability-style presentation of guarded type theory is a computational and syntactic alternative to category-theoretic accounts of guarded recursion, emphasizing type theory’s role as the ul...
متن کاملComputational type theory
Computational type theory provides answers to questions such as: What is a type? What is a natural number? How do we compute with types? How are types related to sets? Can types be elements of types? How are data types for numbers, lists, trees, graphs, etc. related to the corresponding notions in mathematics? What is a real number? Are the integers a subtype of the reals? Can we form the type ...
متن کاملComputational semantics in type theory
This paper aims to show how Montague-style grammars can be completely formalized and thereby declaratively implemented by using the Grammatical Framework GF. The implementation covers the fundamental operations of Montague’s PTQ model: the construction of analysis trees, the linearization of trees into strings, and the interpretation of trees as logical formulas. Moreover, a parsing algorithm i...
متن کاملCartesian Cubical Computational Type Theory
We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both fibrant and non-fibrant types. The fibrant fragment includes Voevodsky’s univalence axiom and a circle type, while the non-fibrant fragment includes exact (strict) equality types satisfying equality reflection. Our type theory is defined by a semantics in cu...
متن کاملComputational Higher Type Theory IV: Inductive Types
This is the fourth in a series of papers extending Martin-Löf’s meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of cubical inductive types, inductive types whose constructors may take dimension parameters and may have specified boundaries. Using this schema, we are able to speci...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2009
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.7618