Return-Path: Delivery-Date: Received: from leopard.cs.byu.edu (no rfc931) by swan.cl.cam.ac.uk with SMTP (PP-6.5) outside ac.uk; Fri, 26 May 1995 17:56:49 +0100 Received: by leopard.cs.byu.edu (1.37.109.15/16.2) id AA152714753; Fri, 26 May 1995 10:12:33 -0600 Sender: info-hol-request@lal.cs.byu.edu Errors-To: info-hol-request@lal.cs.byu.edu Precedence: list Received: from relay1.pipex.net by leopard.cs.byu.edu with SMTP (1.37.109.15/16.2) id AA152274682; Fri, 26 May 1995 10:11:22 -0600 Received: from Q.icl.co.uk by flow.pipex.net with SMTP (PP); Fri, 26 May 1995 17:11:31 +0100 Received: from norman.win.icl.co.uk (norman.win01.icl.co.uk) by Q.icl.co.uk (4.1/icl-2.12-server) id AA01769; Fri, 26 May 95 18:05:54 BST From: Rob Arthan Date: Wed, 24 May 95 21:15:33 BST Message-Id: <9505242015.20242.0@win.icl.co.uk> To: Larry.Paulson@cl.cam.ac.uk Subject: Re: Finite+Infinite Sequences Cc: info-hol@leopard.cs.byu.edu Larry Paulson writes: > There are natural constructions such that the final coalgebra of the functor > is just its greatest fixed point. But the functor in question, F(Z) = 1 + A*Z, has no greatest fixed point in ZF, does it? (If I'm wrong, please, tell me more about the cardinality of such a fixed point). Forgive me for replying before rereading the references you mention, but doesn't your work on codatatypes require a set which is closed under the functor in question to be supplied as part of the data when the codatatype is introduced? If so, I can't see how to derive a characterisation of an HOL polymorphic type with the desired properties from it. Rob Arthan (rda@win.icl.co.uk)