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Inductive families

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-52335-9_47openalex-snapshot

Inductively defined types

inferredcites →https://doi.org/10.1007/bf00248324openalex-snapshot

The foundation of a generic theorem prover

inferredcites →https://doi.org/10.1007/bf01245632openalex-snapshot

Normalising the associative law: An experiment with Martin-Löf's type theory

inferredcites →https://doi.org/10.1007/bf01887198openalex-snapshot

Do-it-yourself type theory

inferredcites →https://doi.org/10.1007/bf01941137openalex-snapshot

Terminating general recursion

inferredcites →https://doi.org/10.1007/bf03037052openalex-snapshot

Foundation of logic programming based on inductive definition

inferredcites →https://doi.org/10.1007/bfb0018349openalex-snapshot

A set constructor for inductive sets in Martin-Löf's type theory

inferredcites →https://doi.org/10.1007/bfb0037116openalex-snapshot

Inductive definitions in the system Coq rules and properties

inferredcites →https://doi.org/10.1016/0167-6423(90)90058-lopenalex-snapshot

Comparing integrated and external logics of functional programs

inferredcites →https://doi.org/10.1016/0304-3975(91)90230-yopenalex-snapshot

An abstract framework for environment machines

inferredcites →https://doi.org/10.1016/0890-5401(88)90005-3openalex-snapshot

The calculus of constructions

inferredcites →https://doi.org/10.1016/0890-5401(91)90066-bopenalex-snapshot

Telescopic mappings in typed lambda calculus

inferredcites →https://doi.org/10.1016/s0049-237x(08)70847-4openalex-snapshot

Hauptsatz for the Intuitionistic Theory of Iterated Inductive Definitions

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/s0049-237x(09)70189-2openalex-snapshot

Constructive Mathematics and Computer Programming

inferredcites →https://doi.org/10.1017/cbo9780511569807.012openalex-snapshot

Inductive sets and families in Martin-Löf's type theory and their set-theoretic semantics

inferredcites →https://doi.org/10.1145/96709.96712openalex-snapshot

Explicit substitutions

inferredcites →https://doi.org/10.1305/ndjfl/1093635159openalex-snapshot

Propositional functions and families of types.

inferredcites →https://doi.org/10.2307/2274279openalex-snapshot

A natural extension of natural deduction

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Order-Sorted Inductive Types

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Combining Testing and Proving in Dependent Type Theory

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Changing Data Representation within the Coq System

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Partial Recursive Functions in Martin-Löf Type Theory

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A Dependently Typed Framework for Static Analysis of Program Execution Costs

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Formalising Formulas-as-Types-as-Objects

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Indexed Induction-Recursion

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An Introduction to Dependent Type Theory

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Monadic Presentations of Lambda Terms Using Generalized Inductive Types

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A Finite Axiomatization of Inductive-Recursive Definitions

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Infinite objects in type theory

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Inductive definitions and type theory an introduction (preliminary version)

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A Comparison of Type Theory with Set Theory

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Dialogues, Reasons and Endorsement

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Dialogues, Reasons and Endorsement

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Constructive Hybrid Games

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$$\pi $$ with Leftovers: A Mechanisation in Agda

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ProofViz: An Interactive Visual Proof Explorer

inferred← citeshttps://doi.org/10.1007/978-3-031-30044-8_5openalex-snapshot

Builtin Types Viewed as Inductive Families

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Structural Refactorings for Exploring Dependently Typed Programming

inferred← citeshttps://doi.org/10.1007/978-3-031-99536-1_2openalex-snapshot

Deep Induction for Inductive Families

inferred← citeshttps://doi.org/10.1007/978-3-319-12736-1_8openalex-snapshot

A Formalized Proof of Strong Normalization for Guarded Recursive Types

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The Lean Theorem Prover (System Description)

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Homotopy Type Theory in Lean

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Quotient Inductive-Inductive Types

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Concluding Remarks: A Plaidoyer for the Play Level

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Inductive Families Need Not Store Their Indices

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Random Generators for Dependent Types

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Algebra of Programming Using Dependent Types

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Testing and Proving Distributed Algorithms in Constructive Type Theory

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Ivor, a Proof Engine

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Initial Algebra Semantics for Cyclic Sharing Structures

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Dependent Types at Work

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A Brief Overview of Agda – A Functional Language with Dependent Types

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Inductive-Inductive Definitions

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Indexed Induction and Coinduction, Fibrationally

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A Categorical Semantics for Inductive-Inductive Definitions

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GMeta: A Generic Formal Metatheory Framework for First-Order Representations

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Dependently Typed Programming Based on Automated Theorem Proving

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Overlapping and Order-Independent Patterns

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Proof principles for datatypes with iterated recursion

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Higman's lemma in type theory

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A comparison of HOL and ALF formalizations of a categorical coherence theorem

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Topological Quantum Gates in Homotopy Type Theory

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A principled approach to programming with nested types in Haskell

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The Justification of Identity Elimination in Martin-Löf’s Type Theory

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A compact kernel for the calculus of inductive constructions

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Pretopologies and a uniform presentation of sup-lattices, quantales and frames

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Towards Formalizing Categorical Models of Type Theory in Type Theory

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Canonicity of Weak ω-groupoid Laws Using Parametricity Theory

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Finitary Higher Inductive Types in the Groupoid Model

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Game semantics for dependent types

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Verifying Haskell programs by combining testing, model checking and interactive theorem proving

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Indexed induction–recursion

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An integrated tool set for verifying CafeOBJ specifications

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Interfaces as functors, programs as coalgebras—A final coalgebra theorem in intensional type theory

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The Curry-Howard isomorphism

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Parametricity and dependent types

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Transporting functions across ornaments

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Transporting functions across ornaments

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Rely-guarantee references for refinement types over aliased mutable data

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Rely-guarantee references for refinement types over aliased mutable data

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Typed syntactic meta-programming

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Relational algebraic ornaments

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Dependent type providers

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Typed syntactic meta-programming

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Constructing Higher Inductive Types as Groupoid Quotients

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A novice-friendly induction tactic for lean

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(Deep) induction rules for GADTs

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Datatype-generic programming meets elaborator reflection

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Defunctionalization with Dependent Types

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A Calculus of Inductive Linear Constructions

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Scoped and Typed Staging by Evaluation

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Generic Bidirectional Typing for Dependent Type Theories

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Canonicity for Indexed Inductive-Recursive Types

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Tagless staged interpreters for typed languages

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Tagless staged interpreters for typed languages

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Natural communities in large linked networks

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Type-Theoretic Signatures for Algebraic Theories and Inductive Types

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Inductive Data Types Based on Fibrations Theory in Programming

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Initial Algebra Semantics for Cyclic Sharing Tree Structures

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Refining Inductive Types

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Modularising inductive families

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Programming Metamorphic Algorithms: An Experiment in Type-Driven Algorithm Design

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A general formulation of simultaneous inductive-recursive definitions in type theory

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Integration of the Process Algebra CSP in Dependent Type Theory - Formalisation and Verification

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A New Paradigm for Component-based Development

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Generic bidirectional typing in a logical framework for dependent type theories

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