[PDF][PDF] First Steps in Synthetic Tait Computability: The Objective Metatheory of Cubical Type Theory
J Sterling - 2022 - csd.cmu.edu
The implementation and semantics of dependent type theories can be studied in a syntax-
independent way: the objective metatheory of dependent type theories exploits the universal …
independent way: the objective metatheory of dependent type theories exploits the universal …
[PDF][PDF] Synthetic topology: of data types and classical spaces
M Escardó - Electronic Notes in Theoretical Computer Science, 2004 - cyberleninka.org
Synthetic topology as conceived in this monograph has three fundamental aspects:(i) to
explain what has been done in classical topology in conceptual terms,(ii) to provide one …
explain what has been done in classical topology in conceptual terms,(ii) to provide one …
Comparing Cartesian closed categories of (core) compactly generated spaces
It is well known that, although the category of topological spaces is not Cartesian closed, it
possesses many Cartesian closed full subcategories, eg:(i) compactly generated Hausdorff …
possesses many Cartesian closed full subcategories, eg:(i) compactly generated Hausdorff …
Propositions as [types]
Image factorizations in regular categories are stable under pullbacks, so they model a
natural modal operator in dependent type theory. This unary type constructor [A] has turned …
natural modal operator in dependent type theory. This unary type constructor [A] has turned …
[PDF][PDF] History of lambda-calculus and combinatory logic
F Cardone, JR Hindley - Handbook of the History of Logic, 2006 - Citeseer
The formal systems that are nowadays called λ-calculus and combinatory logic were both
invented in the 1920s, and their aim was to describe the most basic properties of function …
invented in the 1920s, and their aim was to describe the most basic properties of function …
[KİTAP][B] The realizability approach to computable analysis and topology
A Bauer - 2000 - search.proquest.com
In this dissertation, I explore aspects of computable analysis and topology in the framework
of relative realizability. The computational models are partial combinatory algebras with …
of relative realizability. The computational models are partial combinatory algebras with …
Triposes, exact completions, and Hilbert's ε-operator
ME Maietti, F Pasquali, G Rosolini - 2017 - projecteuclid.org
Triposes were introduced as presentations of toposes by JME Hyland, PT Johnstone and
AM Pitts. They introduced a construction that, from a tripos P:C^op→Pos, produces an …
AM Pitts. They introduced a construction that, from a tripos P:C^op→Pos, produces an …
A lambda calculus for real analysis
P Taylor - Journal of Logic and Analysis, 2010 - infinitesimals.net
Abstract Stone Duality is a new paradigm for general topology in which computable
continuous functions are described directly, without using set theory, infinitary lattice theory …
continuous functions are described directly, without using set theory, infinitary lattice theory …
Admissibly represented spaces and Qcb-spaces
M Schröder - Handbook of computability and complexity in analysis, 2021 - Springer
A basic concept of Type Two Theory of Effectivity (TTE) is the notion of an admissibly
represented space. Admissibly represented spaces are closely related to qcb-spaces. The …
represented space. Admissibly represented spaces are closely related to qcb-spaces. The …
Lambda-calculus and combinators in the 20th century
F Cardone, J Roger Hindley - Handbook of the History of Logic. Volume …, 2009 - iris.unito.it
The formal systems that are nowadays called λ-calculus and combinatory logic were both
invented in the 1920s, and their aim was to describe the most basic properties of function …
invented in the 1920s, and their aim was to describe the most basic properties of function …