Summary: Mixed Inductive/Coinductive Types and
Andreas Abel #
Department of Computer Science, University of Munich
Oettingenstr. 67, D80538 M˜unchen, Germany
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 equiinductive 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
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