Type Theory with First-Order Data Types and Size-Change Termination

Author: David Wahlstedt; Chalmers Tekniska Högskola.; Chalmers University Of Technology.; [2004]

Keywords: TEKNIKVETENSKAP; TECHNOLOGY; Type Theory; Dependent types; Lambda-calculus; Normalization; Size-Change Termination; Type system; Logical Framework; Reducibility; Pattern-matching; Term rewriting.;

Abstract: We prove normalization for a dependently typed lambda-calculus extended with first-order data types and computation schemata for first-order size-change terminating recursive functions. Size-change termination, introduced by C.S. Lee, N.D. Jones and A.M. Ben-Amram, can be seen as a generalized form of structural induction, which allows inductive computations and proofs to be defined in a straight-forward manner. The language can be used as a proof system---an extension of Martin-Löf's Logical Framework.

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