Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
An algorithm for testing conversion in type theory
Logical frameworks
TAPSOFT '89 2nd international joint conference on Theory and practice of software development
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
The ALF proof editor and its proof engine
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
A Unifying Theory of Dependent Types: The Schematic Approach
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
Some Algorithmic and Proof-Theoretical Aspects of Coercive Subtyping
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
Journal of Functional Programming
Coherence and Transitivity in Coercive Subtyping
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Implementation Techniques for Inductive Types in Plastic
TYPES '99 Selected papers from the International Workshop on Types for Proofs and Programs
Type Isomorphisms and Proof Reuse in Dependent Type Theory
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
PAL+: a lambda-free logical framework
Journal of Functional Programming
Transitivity in coercive subtyping
Information and Computation
A computational view of implicit coercions in type theory
Mathematical Structures in Computer Science
Coercive Subtyping via Mappings of Reduction Behaviour
Electronic Notes in Theoretical Computer Science (ENTCS)
Coercions in a polymorphic type system
Mathematical Structures in Computer Science
Manifest Fields and Module Mechanisms in Intensional Type Theory
Types for Proofs and Programs
Coercive subtyping in lambda-free logical frameworks
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
Weyl's predicative classical mathematics as a logic-enriched type theory
ACM Transactions on Computational Logic (TOCL)
Transitivity in coercive subtyping
Information and Computation
Weak transitivity in coercive subtyping
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
A type-theoretic framework for formal reasoning with different logical foundations
ASIAN'06 Proceedings of the 11th Asian computing science conference on Advances in computer science: secure software and related issues
Weyl's predicative classical mathematics as a logic-enriched type theory
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Contextual analysis of word meanings in type-theoretical semantics
LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics
Dot-types and their implementation
LACL'12 Proceedings of the 7th international conference on Logical Aspects of Computational Linguistics
Coercive subtyping: Theory and implementation
Information and Computation
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We present ‘Plastic’, an implementation of LF with Coercive Subtyping, and focus on its implementation of Universes. LF is a variant of Martin-Löf's logical framework, with explicitly typed λ-abstractions. We outline the system of LF with its extensions of inductive types and coercions. Plastic is the first implementation of this extended system; we discuss motivations and basic architecture and give examples of its use. LF is used to specify type theories. The theory UTT includes a hierarchy of universes that is specified in Tarski style. We outline the theory of these universes and explain how they are implemented in Plastic. Of particular interest is the relationship between universes and inductive types, and the relationship between universes and coercive subtyping. We claim that the combination of Tarski-style universes together with coercive subtyping provides an ideal formulation of universes that is both semantically clear and practical to use.