I'd be interested to learn more about the background of the "Suc 0" issue; this is the first time I've seen it discussed on the mailing list.
What I see as the deeper question is, why is "1 = Suc 0" declared as a simp rule? There are two possible views of type nat: 1) an inductive datatype with values 0, Suc 0, Suc (Suc 0), ... 2) an abstract numeric type with values 0, 1, 2, 3, 4, 5 ... By having "1 = Suc 0" declared [simp], it seems that users are required to take view 1 to a certain extent, whether they want to or not. It is actually difficult to use view 2 (for example, Library/Euclidean_Space.thy tries to use view 2; it has "simp del: One_nat_def" all over the place). Doesn't it make sense to leave it to users to decide which representation they want? Is there really any convincing reason why "1 = Suc 0" needs to be a simp rule? - Brian Quoting Tobias Nipkow <nipkow at in.tum.de>: > This translation is not in there by default because it is bound to > confuse novices and sometimes even experts: they see 1 in their proof > state and 1 in their theorem and wonder why Isabelle refuses to apply > the theorem. And eventually they realise that one of the two 1s is a Suc > 0, whereas the other one is a genuine 1. > > Of course, we avoid the above frustration at the cost of Suc 0. > > This issue comes up again and again, and we are not happy with the > current state either. Thanks for your input. > > Tobias > > Chris Capel schrieb: >> translations >> "1" <= "Suc 0" >> "2" <= "Suc (Suc 0)" >> >> Is there a reason why the above isn't defined by default? Is it a >> matter of preference? Context? As a translation, the above doesn't >> interfere with simplification machinery, so I don't think including it >> by default would do any harm. Of course, not including it would be >> fine too. But in the latter case perhaps the statement could be >> mentioned in documentation instead of the current apology for the >> strangeness of seeing "Suc 0" where one would expect "1". >> >> The 2 translation isn't as important. It seems like I occasionally see >> "Suc (Suc 0)", but I don't think the simplifier will ever leave it. >> >> Chris Capel > _______________________________________________ > Isabelle-dev mailing list > Isabelle-dev at mailbroy.informatik.tu-muenchen.de > https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev > >