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Showing 1 to 6 of 6 for “"homotopy type theory"”.
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Cubical Models of Homotopy Type Theory - An Internal Approach
… presents an account of the cubical sets model of homotopy type theory using an internal type theory for elementary topoi. Homotopy type theory is a variant of Martin-Lof type theory where we think of types as spaces, with terms as points in the space and elements of the identity type as paths. We …
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HOMOTOPY SETOIDS AND GENERALIZED QUOTIENT COMPLETION
… arising from the Martin-Löf Intuitionistic Type Theory. In the first part, we introduce the homotopy setoids, considering ideas from the homotopy type theory, and we study their categorical properties. In order to do that, we use the categorical framework of the elementary doctrines …
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Formalisation and execution of Linear Algebra: theorems and algorithms
… matrix representation has been refined to datatypes that admit a representation in functional programming languages. This enables the generation of programs from such verified algorithms. In particular, several well-known Linear Algebra algorithms have been formalised involving both the …
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Linear/non-Linear Types For Embedded Domain-Specific Languages
… when the domain-specific language uses linear types, existing techniques for embedded languages fall short. Linear type systems, which have applications in a wide variety of programming domains including mutable state, I/O, concurrency, and quantum computing, can manipulate embedded non-linear …
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Type theoretic weak factorization systems
… factorization systems that can interpret the theory of intensional dependent type theory with Σ, Π, and identity types. We use display map categories to serve as models of intensional dependent type theory. If a display map category (C, D) models Σ and identity types, then this structure …
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Internal Yoneda Ext Groups, Central H-spaces, and Banded Types
We develop topics in synthetic homotopy theory using the language of homotopy type theory, and study their semantic counterparts in an ∞-topos. Specifically, we study Grothendieck categories and Yoneda Ext groups in this setting, as well as a novel class of central H-spaces along with their …