From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Newsgroups: gmane.emacs.help Subject: Re: (*) -> 1 Date: Wed, 18 Jan 2023 09:37:26 +0100 Message-ID: References: <87sfg9kuya.fsf@web.de> <87bkmxkpzg.fsf@web.de> <878ri1av5j.fsf@telefonica.net> <87ilh4kgqo.fsf@web.de> <87zgagakh5.fsf@telefonica.net> <87cz7cka06.fsf@web.de> <87v8l49t8w.fsf@telefonica.net> Mime-Version: 1.0 Content-Type: multipart/signed; micalg=pgp-sha1; protocol="application/pgp-signature"; boundary="9eMR0zB1EA46RAj4" Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="1522"; mail-complaints-to="usenet@ciao.gmane.io" To: help-gnu-emacs@gnu.org Original-X-From: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Wed Jan 18 09:38:18 2023 Return-path: Envelope-to: geh-help-gnu-emacs@m.gmane-mx.org Original-Received: from lists.gnu.org ([209.51.188.17]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1pI3xZ-0000BP-Tj for geh-help-gnu-emacs@m.gmane-mx.org; Wed, 18 Jan 2023 09:38:17 +0100 Original-Received: from localhost ([::1] helo=lists1p.gnu.org) by lists.gnu.org with esmtp (Exim 4.90_1) (envelope-from ) id 1pI3wr-0000dz-NL; Wed, 18 Jan 2023 03:37:33 -0500 Original-Received: from eggs.gnu.org ([2001:470:142:3::10]) by lists.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1pI3wp-0000dZ-7o for help-gnu-emacs@gnu.org; Wed, 18 Jan 2023 03:37:31 -0500 Original-Received: from mail.tuxteam.de ([5.199.139.25]) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1pI3wn-0001LS-2b for help-gnu-emacs@gnu.org; Wed, 18 Jan 2023 03:37:31 -0500 DKIM-Signature: v=1; a=rsa-sha256; q=dns/txt; c=relaxed/relaxed; d=tuxteam.de; s=mail; h=From:In-Reply-To:Content-Type:MIME-Version:References:Message-ID: Subject:To:Date:Sender:Reply-To:Cc:Content-Transfer-Encoding:Content-ID: Content-Description:Resent-Date:Resent-From:Resent-Sender:Resent-To:Resent-Cc :Resent-Message-ID:List-Id:List-Help:List-Unsubscribe:List-Subscribe: List-Post:List-Owner:List-Archive; bh=sX+Jn80fcV9xm6F05BNE2Gn6abw7Lkxx/MqMElheQtw=; b=b2M63a60oa02CIRTKKvzvhL5IW AF2flIjBPIgFZtgiaq7/FFggx4aHI/7asIBB/vDT2sv1H3+PMrtsUQV2wKgA5Hbsrth3x8WzZFv04 4HtLXYuqjlVnQAzihwMpxOk4RQ2/j+m2wF9SIzXmeaJXm9j6g0LHg0Q+GNURQF4oDQOybx6z0IETs 5pHUNfqfCiv/I9wPyrJkUP1Ivey8LL8DMWuftYeKCul/T3Vs+vh2RUbD+Cjc/3xiTb5j859kj5PIl CwbPV50D8SffXd2dXO+HZ55q1A2SAAF3nHAvQEjLMZKhKWH66U2QECkJkvY1hwD13WTtvSRNfNfVb IpTbaSHg==; Original-Received: from tomas by mail.tuxteam.de with local (Exim 4.94.2) (envelope-from ) id 1pI3wk-0006Lr-Lv for help-gnu-emacs@gnu.org; Wed, 18 Jan 2023 09:37:26 +0100 Content-Disposition: inline In-Reply-To: <87v8l49t8w.fsf@telefonica.net> Received-SPF: pass client-ip=5.199.139.25; envelope-from=tomas@tuxteam.de; helo=mail.tuxteam.de X-Spam_score_int: -20 X-Spam_score: -2.1 X-Spam_bar: -- X-Spam_report: (-2.1 / 5.0 requ) BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, DKIM_VALID_EF=-0.1, SPF_HELO_NONE=0.001, SPF_PASS=-0.001 autolearn=ham autolearn_force=no X-Spam_action: no action X-BeenThere: help-gnu-emacs@gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Users list for the GNU Emacs text editor List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Original-Sender: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Xref: news.gmane.io gmane.emacs.help:142348 Archived-At: --9eMR0zB1EA46RAj4 Content-Type: text/plain; charset=utf-8 Content-Disposition: inline Content-Transfer-Encoding: quoted-printable On Wed, Jan 18, 2023 at 08:50:07AM +0100, =C3=93scar Fuentes wrote: > Michael Heerdegen writes: >=20 > > =C3=93scar Fuentes writes: > > > >> The languages that use the concept of partially applied function usual= ly > >> have no support for variadic functions, so the duality problem you ref= er > >> to is not an issue. > > > > Interesting. I do not know many other languages. > > > > I see your point now: while I wrote about the procedure of finding an > > interpretation [of the technical or mathematical semantics of a formula] > > in the real world [this is what had been ongoing: Ferraris etc], you > > mention that even the technical/theoretical semantics of a formula like > > (*) can be different. This is an interesting point, especially since > > terms like "right" and "wrong" had been used. > > > > Although I think the "meaning" of the expression (*) in Elisp is clear, > > it describes a mathematical term, so the question, asked specifically > > for Elisp, has to be answered using the mathematical background. In my > > understanding the OP asked specifically about the empty algebraic > > product. >=20 > I was prompted to enter the discussion when I saw your reference to > Mathematics. As almost every other math-related thing in computers, > Elisp's + is a toy representation of Sigma. And then the relevant > characteristics of Sigma for this discussion are a convention among > practitioners, not a proper mathematical fact. This goes a bit deeper: whenever you have an associative operator [i.e. (a + b) + c =3D=3D a + (b + c)], 1. the "variadic extension" is straightforward, since you can leave out the parentheses in (a + (b + (c + ...))) without losing info 2. the extension to zero arguments is also straightforward *provided* you have a neutral element, since 0 + a =3D=3D a. This works for products, logical and, or, set union and intersection, you name it (in mathematical logic, you often see the or/and cousins of Sigma and Pi; in set theory likewise the union/intersection things). > Although it is possible that the implementors were inspired by Sigma, I > think it is more probable that they made + variadic because s-exps like > (+ (+ 1 2) 3) are awkward and then extended the function with support > for 0 and 1 arguments because they are convenient when defining macros. I think a mathematician doesn't really distinguish between "Sigma" and just "sum". Sigma is just a notation. No magic, just maths. Cheers --=20 t --9eMR0zB1EA46RAj4 Content-Type: application/pgp-signature; name="signature.asc" -----BEGIN PGP SIGNATURE----- iF0EABECAB0WIQRp53liolZD6iXhAoIFyCz1etHaRgUCY8evvwAKCRAFyCz1etHa RokkAJ96HyeJSWQuE7qFNzIuFCo7x/fN1gCfX699gKs4w6oyGDc8psAyOoEjgZM= =d9yK -----END PGP SIGNATURE----- --9eMR0zB1EA46RAj4--