Re: [isabelle] extending well-founded partial orders to total well-founded orders
>> I guess since Isabelle2013 this is now "~~/src/HOL/Cardinals/", right?
>> Could you elaborate on the mentioned finite recursion combinator and how it is used?
The worec combinator,
worec :: "(('a => 'b) => 'a => 'b) => 'a => 'b"
(defined in the context of a fixed wellorder r on 'a)
is just a slightly more convenient version of wfrec.
It is used to define a function f :: 'a => 'b by specifying,
for each x :: 'a, the value of f on x in terms of the values of f
on all elements less than x w.r.t. r, i.e., in my notation, all
elements of underS x. This would ideally employ an operator
Prod x : 'a. (underS x => 'b) => 'b
In HOL, the same is achieved by an
"admissible" operator of a less informative type.
The only relevant facts are below:
adm_wo :: "(('a => 'b) => 'a => 'b) => bool"
"adm_wo H ≡ ∀f g x. (∀y ∈ underS x. f y = g y) --> H f x = H g x"
assumes "adm_wo H"
shows "worec H = H (worec H)"
--- On Mon, 2/18/13, Christian Sternagel <c.sternagel at gmail.com> wrote:
From: Christian Sternagel <c.sternagel at gmail.com>
Subject: Re: [isabelle] extending well-founded partial orders to total well-founded orders
To: "Andrei Popescu" <uuomul at yahoo.com>
Cc: cl-isabelle-users at lists.cam.ac.uk
Date: Monday, February 18, 2013, 8:32 AM
finally deadlines are over for the time being and I found your email again ;)
On 01/19/2013 12:22 AM, Andrei Popescu wrote:
> My AFP formalization ordinals
I guess since Isabelle2013 this is now "~~/src/HOL/Cardinals/", right?
> (hopefully) provides the necessary ingredients: Initial segments in
> Wellorder_Embedding, ordinal sum in theory Constructions_on_Wellorders,
> and a transfinite recursion combinator (a small adaptation of the
> wellfounded combinator) in theory Wellorder_Relation.
Could you elaborate on the mentioned finite recursion combinator and how it is used?
thanks in advance,
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