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paper available
The following report is available by anonymous ftp from the University
of Cambridge.
Larry Paulson
Set Theory for Verification: II. Induction and Recursion
A theory of recursive definitions has been mechanized in Isabelle's
Zermelo-Fraenkel (ZF) set theory. The objective is to support the
formalization of particular recursive definitions for use in
verification, semantics proofs and other computational reasoning.
Inductively defined sets are expressed as least fixedpoints,
applying the Knaster-Tarski Theorem over a suitable set. Recursive
functions are defined by well-founded recursion and its derivatives,
such as transfinite recursion. Recursive data structures are
expressed by applying the Knaster-Tarski Theorem to a set that
is closed under Cartesian product and disjoint sum.
Worked examples include the transitive closure of a relation, lists,
variable-branching trees and mutually recursive trees and forests.
The Schr\"oder-Bernstein Theorem and the soundness of
propositional logic are proved in Isabelle sessions.
FTP Instructions:
* Connect to host ftp.cl.cam.ac.uk [128.232.0.56]
* Use login id "ftp" with your internet address as password
* put ftp in BINARY MODE ("binary")
* go to directory reports (by typing "cd reports")
* "get" the file TR312-lcp-set-II.ps.gz from that directory.
TR312-lcp-set-II.ps.gz is a gzip'ed Postscript file, and should be
unpacked using the Gnu utility gunzip.
Part I of the report is available as TR271-lcp-set-theory.dvi.Z from
the same directory, but the final version is on directory ml (not
reports) and consists of two files: set-I.dvi.Z (text only) and
set-I.fig.ps.Z (figures).