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Set-based Operators and Fixed-Points by Support Andreas Abel

Summary: Set-based Operators and Fixed-Points by Support
Andreas Abel
April 22, 2004
In Abel and Altenkirch's article A Predicative Analysis of Structural Recur-
sion [AA02] one finds on page 34 a definition of the semantics [[]] of a strictly
positive inductive type . This definition (5.1) is itself a strictly-positive induc-
tive definition on the meta-level. In the following we exhibit its correspondence
to the algorithmic construction of a least fixed-point as found in Pierce's book
Types and Programming Languages [Pie02] on pages 290≠295.
First we give a simplified version of the definition restricted to a single type
Definition 5.1. For Ty(X) and a closed type let
[[]] : P (Val
) P Val()
be a monotone operator with a urelement relation
◊ Val()
such that for all v Val()
and u Val


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


Collections: Computer Technologies and Information Sciences