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The Marriage of Univalence and Parametricity
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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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Eliminating Dependent Pattern Matching
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Changing Data Structures in Type Theory: A Study of Natural Numbers
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Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL
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Wellfounded Trees and Dependent Polynomial Functors
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Dependently Typed Programming in Agda
inferredcites →https://doi.org/10.1007/978-3-642-39634-2_10openalex-snapshot
Data Refinement in Isabelle/HOL
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Automatic Data Refinement
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Types for Proofs and Programs: International Workshop, TYPES 2003, Torino, Italy, April 30 - May 4, 2003, Revised Selected Papers
inferredcites →https://doi.org/10.1016/0304-3975(94)00126-4openalex-snapshot
Parametricity as isomorphism
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The calculus of constructions
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A Presheaf Model of Parametric Type Theory
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Homotopical inverse diagrams in categories with attributes
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An Intuitionistic Theory of Types: Predicative Part
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Transporting functions across ornaments
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A coherence theorem for Martin-Löf's type theory
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Univalence for inverse diagrams and homotopy canonicity
inferredcites →https://doi.org/10.1145/1159803.1159811openalex-snapshot
Simple unification-based type inference for GADTs
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Dependently typed programming in Agda
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A relationally parametric model of dependent type theory
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The HoTT library: a formalization of homotopy type theory in Coq
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The next 700 syntactical models of type theory
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Parametric quantifiers for dependent type theory
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Equivalences for free: univalent parametricity for effective transport
inferredcites →https://doi.org/10.1145/3341691openalex-snapshot
Cubical agda: a dependently typed programming language with univalence and higher inductive types
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Coq Coq correct! verification of type checking and erasure for Coq, in Coq
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Internalizing Relational Parametricity in the Extensional Calculus of Constructions
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Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities
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A Homological Theory of Functions: Nonuniform Boolean Complexity Separation and VC Dimension Bound Via Algebraic Topology, and a Homological Farkas Lemma
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Ornaments for Proof Reuse in Coq
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Formalising Inductive and Coinductive Containers
inferredcites →https://doi.org/10.4230/lipics.types.2015.3openalex-snapshot
Towards a Cubical Type Theory without an Interval
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/10.46298/lmcs-17(4:5)2021openalex-snapshot
Internal Parametricity for Cubical Type Theory
inferredcites →https://doi.org/10.48550/arxiv.1505.05028openalex-snapshot
Automatic and Transparent Transfer of Theorems along Isomorphisms in the Coq Proof Assistant
inferredcites →https://doi.org/10.48550/arxiv.1705.01163openalex-snapshot
Revisiting Parametricity: Inductives and Uniformity of Propositions
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/978-3-031-34518-0_8openalex-snapshot
Some Remarks About Dependent Type Theory
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/s0956796821000034openalex-snapshot
Cubical Agda: A dependently typed programming language with univalence and higher inductive types
inferred← citeshttps://doi.org/10.1145/3434293openalex-snapshot
Internalizing representation independence with univalence
inferred← citeshttps://doi.org/10.1145/3498667openalex-snapshot
Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages
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How to safely use extensionality in Liquid Haskell
inferred← citeshttps://doi.org/10.1145/3573105.3575676openalex-snapshot
Compositional Pre-processing for Automated Reasoning in Dependent Type Theory
inferred← citeshttps://doi.org/10.1145/3632850openalex-snapshot
Internal and Observational Parametricity for Cubical Agda
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/10.1145/3776685openalex-snapshot
Canonicity for Indexed Inductive-Recursive Types
inferred← citeshttps://doi.org/10.48550/arxiv.2101.09655openalex-snapshot
Relational Type Theory (All Proofs)
inferred← citeshttps://doi.org/10.48550/arxiv.2310.14022openalex-snapshot
Trocq: Proof Transfer for Free, With or Without Univalence
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