Interface talk:Example of abbreviation which tries to introduce a variable

Legality of new RHS variables in abbreviations
Actually, new RHS variables in abbreviation will remain legal for proof modules. Proof modules are never imported anywhere, so no dummy variables are required. The extra variables are simply dragged along silently. This is quite practical for an abbreviation of an expression appearing multiple times in one or more proofs in the same proof module (just as you would abbreviate a common subexpression with a letter or (*) in a regular paper). In interface modules, of course, such an abbreviation should generate an error.--GrafZahl (talk) 14:25, 20 December 2011 (UTC)


 * Hmm. The first question that springs to mind is what happens if I then try to export to an interface which has a  matching the left hand side? But aside from that, let me try to figure out what is being proposed here. In an example like User:GrafZahl/unsound-def.gh, but where   would be changed to , is the idea that   would then be treated the same as   would be (and thus require a   distinct variable constraint)? There's also the question of the appeal of this feature, compared with explicitly specifing the variables in the abbreviation (as is done in   in Nicod's reduction of Principia Mathematica). There are plenty of cases where specifying variables seems natural, for example   in First-order_logic or   in Out lines. But I guess the use case for this sort of abbreviation is something like the Nicod one, or perhaps the repetitive hypotheses in places like Connectivity for betweenness or, to pick a less intimidating example, a geometry proof like   in Triangle_congruence. Kingdon 04:52, 21 December 2011 (UTC)


 * Yes,  would be treated exactly as   everywhere, possibly triggering dv constraint checks. The Nicod case is precisely what I had in mind when introducing the definition feature into JHilbert in the first place (compare with Nicod's original paper, where he doesn't specify variables in π). For   and , you have to specify all variables, otherwise the definition/abbreviation does not do what you want.   is indeed a possible use case, where you would explain your hypotheses (or your antecedent) once, and then use something like  , a phrase you will also find in many textbooks. That being said, it's quite possible to confuse users if you overdo it with abbreviations, so, as an author, you have the responsibility to choose your abbreviations wisely.--GrafZahl (talk) 12:13, 21 December 2011 (UTC)