Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
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
An Implementation of LF with Coercive Subtyping & Universes
Journal of Automated Reasoning
A Unifying Theory of Dependent Types: The Schematic Approach
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
Mathematical Vernacular and Conceptual Well-Formedness in Mathematical Language
LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Some Algorithmic and Proof-Theoretical Aspects of Coercive Subtyping
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
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In the context of Plastic, a proof assistant for a variant of Martin-Löf's Logical Framework LF with explicitly typed λ-abstractions, we outline the technique used for implementing inductive types from their declarations. This form of inductive types gives rise to a problem of non-linear pattern matching; we propose this match can be ignored in well-typed terms, and outline a proof of this. The paper then explains how the inductive types are realised inside the reduction mechanisms of Plastic, and briefly considers optimisations for inductive types.