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We study five extensions of the polymorphically typed lambda-calculus (system
) by type constructs intended to model fixed-points of monotone
operators. Building on work by Geuvers
concerning the relation between term
rewrite systems for least pre-fixed-points and greatest post-fixed-points of
positive type schemes (, non-nested positive inductive and coinductive
types) and so-called
retract types, we show that there are
reduction-preserving
embeddings even between systems of monotone (co)inductive...
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