Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Checking algorithms for pure type systems
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Proof by computation in the Coq system
Theoretical Computer Science - Special issue on theories of types and proofs
Pure type systems with judgemental equality
Journal of Functional Programming
Explicit convertibility proofs in pure type systems
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
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The type theory @lP corresponds to the logical framework LF. In this paper we present @lH, a variant of @lP where convertibility is not implemented by means of the customary conversion rule, but instead type conversions are made explicit in the terms. This means that the time to type check a @lH term is proportional to the size of the term itself. We define an erasure map from @lH to @lP, and show that through this map the type theory @lH corresponds exactly to @lP: any @lH judgment will be erased to a @lP judgment, and conversely each @lP judgment can be lifted to a @lH judgment. We also show a version of subject reduction: if two @lH terms are provably convertible then their types are also provably convertible.