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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 nds on page 34 a de nition of the semantics [[]] of a strictly
positive inductive type . This de nition (5.1) is itself a strictly-positive induc-
tive de nition on the meta-level. In the following we exhibit its correspondence
to the algorithmic construction of a least xed-point as found in Pierce's book
Types and Programming Languages [Pie02] on pages 290{295.
First we give a simpli ed version of the de nition restricted to a single type
variable.
De nition 5.1. For  2 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 2 Val () and u 2 Val  :
v 2 [[]](V ) u U  v

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

 

Collections: Computer Technologies and Information Sciences