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Mixed Inductive/Coinductive Types and Strong Normalization
 

Summary: Mixed Inductive/Coinductive Types and
Strong Normalization
Andreas Abel
Department of Computer Science, University of Munich
Oettingenstr. 67, D-80538 M®unchen, Germany
andreas.abel@ifi.lmu.de
Abstract. We introduce the concept of guarded saturated sets, satu-
rated sets of strongly normalizing terms closed under folding of corecur-
sive functions. Using this tool, we can model equi-inductive and equi-
coinductive types with terminating recursion and corecursion principles.
Two type systems are presented: Mendler (co)iteration and sized types.
As an application we show that we can directly represent the mixed in-
ductive/coinductive type of stream processors with associated recursive
operations.
1 Introduction
Symbolic evaluation, aka evaluation of terms with free variables, is used, amongst
others, for optimization through partial evaluation in compilers and for checking
term equivalence in languages based on dependent types--such as the theorem
provers Agda, Coq, Epigram, and LEGO, founded on intensional type theory. In
these applications, symbolic evaluation is required to terminate. My long term

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen

 

Collections: Computer Technologies and Information Sciences