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; Mon, 5 Jun 1995 16:21:37 +0100 Received: by leopard.cs.byu.edu (1.37.109.15/16.2) id AA087972955; Mon, 5 Jun 1995 08:35:55 -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 AA082142380; Mon, 5 Jun 1995 08:26:20 -0600 Received: from Q.icl.co.uk by flow.pipex.net with SMTP (PP); Mon, 5 Jun 1995 15:24:54 +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 AA01135; Mon, 5 Jun 95 16:18:46 BST From: Rob Arthan Date: Mon, 5 Jun 95 10:37:30 BST Message-Id: <9506050937.16882.0@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 wrote (a while ago) > By far the simplest, abstract characterization of infinite+finite sequences > (over A) is as the final coalgebra of the functor 1 + (A * -), that is, the > functor F such that F(Z) = 1 + (A*Z) for all Z. and I quibbled, because I thought such a thing would have to be a greatest fixed point for F. However, greatest fixed point or no, the characterisation as a final coalgebra is, I now see, correct (and captures precisely the sequences which have an initial segment of the natural numbers as indices). Sorry for being obtuse. Rob Arthan (rda@win.icl.co.uk)