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