Combinatorial realizability models of type theory
نویسندگان
چکیده
منابع مشابه
Combinatorial realizability models of type theory
We introduce a new model construction for Martin-Löf intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines, by gluing along the functor from the category of contexts to the category of groupoids, the syntactic model with a notion of realizability. As our main application, we use the model to analyse the syntactic groupoid ass...
متن کاملRealizability of interaction models
In scenarios where a set of independent business partners engage in complex conversations, interaction models are a means to specify the allowed interaction behavior from a global perspective. Atomic interactions serve as basic building blocks and behavioral dependencies are defined between them. The notion of realizability centers around the question whether there exist a set of roles that col...
متن کاملGeneralizing realizability and Heyting models for constructive set theory
This article presents a generalisation of the two main methods for obtaining class models of constructive set theory. Heyting models are a generalisation of the Boolean models for classical set theory which are a kind of forcing, while realizability is a decidedly constructive method that has first been develloped for number theory by Kleene and was later very fruitfully adapted to constructive...
متن کاملA type theory which is complete for Kreisel's modified realizability
We define a type theory with a strong elimination rule for existential quantification. As in Martin-Löf’s type theory, the “axiom of choice” is thus derivable. Proofs are also annotated by realizers which are simply typed λ-terms. A new rule called “type extraction” which extract the type of a realizer allows us to derive the so-called “independance of premisses” schema. Consequently, any formu...
متن کاملComputational Higher Type Theory II: Dependent Cubical Realizability
This is the second in a series of papers extending Martin-Löf’smeaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I, and extend it to a meaning explanation of dependent higher-dimensional type theory. This extension requires generalizing the computational Kan condition given in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2013
ISSN: 0168-0072
DOI: 10.1016/j.apal.2013.05.002