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Internalizing representation independence with univalence
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Changing Data Representation within the Coq System
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Miranda: A non-strict functional language with polymorphic types
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Changing Data Structures in Type Theory: A Study of Natural Numbers
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On the Role of Scientific Thought
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Realms: A Structure for Consolidating Knowledge about Mathematical Theories
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A Computer-Algebra-Based Formal Proof of the Irrationality of ζ(3)
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The Lean Theorem Prover (System Description)
inferredcites →https://doi.org/10.1007/978-3-319-66107-0_30openalex-snapshot
Homotopy Type Theory in Lean
inferredcites →https://doi.org/10.1007/978-3-642-32347-8_11openalex-snapshot
Bag Equivalence via a Proof-Relevant Membership Relation
inferredcites →https://doi.org/10.1007/978-3-642-39634-2_10openalex-snapshot
Data Refinement in Isabelle/HOL
inferredcites →https://doi.org/10.1007/978-3-642-39634-2_9openalex-snapshot
Automatic Data Refinement
inferredcites →https://doi.org/10.1016/0022-0000(87)90023-7openalex-snapshot
On observational equivalence and algebraic specification
inferredcites →https://doi.org/10.1016/0304-3975(94)00126-4openalex-snapshot
Parametricity as isomorphism
inferredcites →https://doi.org/10.1016/j.entcs.2015.12.006openalex-snapshot
A Presheaf Model of Parametric Type Theory
inferredcites →https://doi.org/10.1016/s0049-237x(08)71945-1openalex-snapshot
An Intuitionistic Theory of Types: Predicative Part
inferredcites →https://doi.org/10.1016/s0304-3975(96)00163-6openalex-snapshot
The definition of Extended ML: A gentle introduction
inferredcites →https://doi.org/10.1017/cbo9780511530104openalex-snapshot
Purely Functional Data Structures
inferredcites →https://doi.org/10.1017/cbo9781139171519.015openalex-snapshot
What numbers could not be
inferredcites →https://doi.org/10.1017/s030500411900015xopenalex-snapshot
Semantics of higher inductive types
inferredcites →https://doi.org/10.1017/s095679681300018xopenalex-snapshot
Idris, a general-purpose dependently typed programming language: Design and implementation
inferredcites →https://doi.org/10.1017/s0956796820000155openalex-snapshot
Leibniz equality is isomorphic to Martin-Löf identity, parametrically
inferredcites →https://doi.org/10.1017/s0956796898003153openalex-snapshot
A coherence theorem for Martin-Löf's type theory
inferredcites →https://doi.org/10.1017/s0960129514000577openalex-snapshot
An experimental library of formalized Mathematics based on the univalent foundations
inferredcites →https://doi.org/10.1093/philmat/nkt030openalex-snapshot
Structuralism, Invariance, and Univalence
inferredcites →https://doi.org/10.1145/199448.199476openalex-snapshot
Applicative functors and fully transparent higher-order modules
inferredcites →https://doi.org/10.1145/3009837.3009892openalex-snapshot
Modules, abstraction, and parametric polymorphism
inferredcites →https://doi.org/10.1145/3018610.3018615openalex-snapshot
The HoTT library: a formalization of homotopy type theory in Coq
inferredcites →https://doi.org/10.1145/3018610.3018620openalex-snapshot
The next 700 syntactical models of type theory
inferredcites →https://doi.org/10.1145/3062341.3062348openalex-snapshot
HoTTSQL: proving query rewrites with univalent SQL semantics
inferredcites →https://doi.org/10.1145/3110276openalex-snapshot
Parametric quantifiers for dependent type theory
inferredcites →https://doi.org/10.1145/3209108.3209197openalex-snapshot
On Higher Inductive Types in Cubical Type Theory
inferredcites →https://doi.org/10.1145/3236787openalex-snapshot
Equivalences for free: univalent parametricity for effective transport
inferredcites →https://doi.org/10.1145/3290314openalex-snapshot
Higher inductive types in cubical computational type theory
inferredcites →https://doi.org/10.1145/3341691openalex-snapshot
Cubical agda: a dependently typed programming language with univalence and higher inductive types
inferredcites →https://doi.org/10.1145/3429979openalex-snapshot
The Marriage of Univalence and Parametricity
inferredcites →https://doi.org/10.1145/512644.512669openalex-snapshot
Representation independence and data abstraction
inferredcites →https://doi.org/10.23638/lmcs-13(1:15)2017openalex-snapshot
Notions of Anonymous Existence in Martin-L\"of Type Theory
inferredcites →https://doi.org/10.3217/jucs-023-01-0063openalex-snapshot
Higher Inductive Types in Programming
inferredcites →https://doi.org/10.4230/lipics.csl.2012.381openalex-snapshot
Parametricity in an Impredicative Sort
inferredcites →https://doi.org/10.4230/lipics.csl.2013.432openalex-snapshot
Internalizing Relational Parametricity in the Extensional Calculus of Constructions
inferredcites →https://doi.org/10.4230/lipics.csl.2018.6openalex-snapshot
Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities
inferredcites →https://doi.org/10.4230/lipics.csl.2020.13openalex-snapshot
Internal Parametricity for Cubical Type Theory
inferredcites →https://doi.org/10.4230/lipics.itcs.2018.56openalex-snapshot
A Homological Theory of Functions: Nonuniform Boolean Complexity Separation and VC Dimension Bound Via Algebraic Topology, and a Homological Farkas Lemma
inferredcites →https://doi.org/10.4230/lipics.itp.2019.26openalex-snapshot
Ornaments for Proof Reuse in Coq
inferredcites →https://doi.org/10.4230/lipics.types.2015.5openalex-snapshot
Cubical Type Theory: A Constructive Interpretation of the Univalence Axiom
inferredcites →https://doi.org/10.48550/arxiv.1705.01163openalex-snapshot
Revisiting Parametricity: Inductives and Uniformity of Propositions
inferredcites →https://doi.org/10.48550/arxiv.1911.00580openalex-snapshot
Introduction to Univalent Foundations of Mathematics with Agda
inferredcites →https://doi.org/10.48550/arxiv.2006.13694openalex-snapshot
The law of excluded middle in the simplicial model of type theory
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/978-3-031-29082-4_3openalex-snapshot
Curiously Empty Intersection of Proof Engineering and Computational Sciences
inferred← citeshttps://doi.org/10.1007/978-3-031-57262-3openalex-snapshot
Programming Languages and Systems
inferred← citeshttps://doi.org/10.1007/978-3-031-57262-3_10openalex-snapshot
Trocq: Proof Transfer for Free, With or Without Univalence
inferred← citeshttps://doi.org/10.1007/978-3-031-57262-3_11openalex-snapshot
Artifact Report: Trocq: Proof Transfer for Free, With or Without Univalence
inferred← citeshttps://doi.org/10.1007/978-981-99-8311-7_11openalex-snapshot
Transport via Partial Galois Connections and Equivalences
inferred← citeshttps://doi.org/10.1017/jsl.2024.78openalex-snapshot
HIGHER SCHREIER THEORY IN CUBICAL AGDA
inferred← citeshttps://doi.org/10.1017/s0956796821000034openalex-snapshot
Cubical Agda: A dependently typed programming language with univalence and higher inductive types
inferred← citeshttps://doi.org/10.1017/s0960129521000311openalex-snapshot
Cubical methods in homotopy type theory and univalent foundations
inferred← citeshttps://doi.org/10.1017/s0960129524000288openalex-snapshot
The category of iterative sets in homotopy type theory and univalent foundations
inferred← citeshttps://doi.org/10.1145/3474834openalex-snapshot
Logical Relations as Types: Proof-Relevant Parametricity for Program Modules
inferred← citeshttps://doi.org/10.1145/3498667openalex-snapshot
Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages
inferred← citeshttps://doi.org/10.1145/3573105.3575677openalex-snapshot
Computing Cohomology Rings in Cubical Agda
inferred← citeshttps://doi.org/10.1145/3632850openalex-snapshot
Internal and Observational Parametricity for Cubical Agda
inferred← citeshttps://doi.org/10.1145/3652561.3652563openalex-snapshot
What's in a Bag?: An “Application Proving Interface” for Finite Bags and its Implementation
inferred← citeshttps://doi.org/10.1145/3737283openalex-snapshot
Trocq: Proof Transfer for Free, Beyond Equivalence and Univalence
inferred← citeshttps://doi.org/10.1145/3763164openalex-snapshot
Proof Repair across Quotient Type Equivalences
inferred← citeshttps://doi.org/10.46298/entics.10492openalex-snapshot
Free Commutative Monoids in Homotopy Type Theory
inferred← citeshttps://doi.org/10.48550/arxiv.2310.14022openalex-snapshot
Trocq: Proof Transfer for Free, With or Without Univalence
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