 
Summary: Setbased Operators and FixedPoints 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 strictlypositive induc
tive definition on the metalevel. In the following we exhibit its correspondence
to the algorithmic construction of a least fixedpoint as found in Pierce's book
Types and Programming Languages [Pie02] on pages 290295.
First we give a simplified version of the definition restricted to a single type
variable.
Definition 5.1. For Ty(X) and a closed type let
[[]] : P (Val
) P Val()
be a monotone operator with a urelement relation
U
Val
× Val()
such that for all v Val()
and u Val
