Hi all, after some more experiments, I found out that there is another difference between explicit typeclass annotations and lemmas in the context: the former theorems are included in instantiations but are not included in interpretations. This usually does not make a difference, since there is usually a single order on a type.
Instead, I introduced an additional typeclass to the hierarchy. The change was successfully tested on testboard (mercurial diff <http://isabelle.in.tum.de/repos/testboard/rev/18f26b6779ad>, status <https://ci.isabelle.systems/jenkins/job/testboard/117/>), and does not need any AFP change. Does someone have an opinion on this change? Mathias > On 04 Jul 2016, at 14:20, Mathias Fleury <mathias.fle...@ens-rennes.fr> wrote: > > Hi Johannes, > > > the multiset ordering (contrary to the subset ordering) does not have this > property: > > lemma "{#0#} <= {#Suc 0#}” > unfolding Multiset_Order.le_multiset⇩H⇩O by auto > > (the actual notation is #⊆# and not <=). > > > I tried locally to apply the changes of my previous email this week-end. > Except some proofs inside the typeclass definitions (i.e. in the files > Groups.thy, Rings.thy, and Missing_Ring.thy), no other changes were needed in > Isabelle or the AFP. > > > Thanks for your answer, > Mathias > > >> On 04 Jul 2016, at 13:22, Johannes Hölzl <hoe...@in.tum.de >> <mailto:hoe...@in.tum.de>> wrote: >> >> Hi Mathias, >> >> there is at least the type class 'canonically_ordered_monoid' which has >> the property a <= b <--> ?c. a + c = b which implies 0 <= a for all a. >> Are the multisets already in this typeclass? >> >> - Johannes >> >> >> Am Dienstag, den 28.06.2016, 10:04 +0100 schrieb Mathias Fleury: >>> Dear type-classes and simplifier experts, >>> >>> in the plan of instantiating multisets with the multiset ordering, I >>> am trying to instantiate the multisets with additional typeclasses to >>> get specific simplification theorems. The aim is to mimic the >>> simplifier’s behaviour of other types like natural numbers. One of my >>> problems can be nicely illustrated by the following lemma: “M <= M + >>> N <-> 0 <= N”. >>> >>> >>> Analog simplification rules already exist for rings (e.g., natural >>> numbers*) and ordered groups too: >>> thm >>> Rings.linordered_semiring_class.less_eq_add_cancel_left_greater_eq_ze >>> ro >>> thm Groups.ordered_ab_group_add_class.le_add_same_cancel1 >>> Both rules are stating that “M <= M + N <—> 0 <= N” and are marked as >>> [simp]. >>> >>> >>> However, the multisets are neither a group (no inverse for the law >>> “+”) nor a ring (no multiplication). I could duplicate the theorems, >>> but I noticed that the proofs of the theorems do only rely on the >>> fact it is a monoid_add (for the zero element) and an >>> ordered_ab_semigroup_add_imp_le (for the order). The following >>> theorem would work too and is general enough to include the multiset >>> case: >>> >>> lemma le_add_same_cancel1 [simp]: >>> “(a :: 'a :: {monoid_add, ordered_ab_semigroup_add_imp_le}) ≤ a + b >>> ⟷ 0 ≤ b” >>> using add_le_cancel_left [of a 0] by simp >>> >>> >>> Are there any obvious differences between this more general version >>> with explicit type class annotations >>> and Groups.ordered_ab_group_add_class.le_add_same_cancel1? If no, >>> would it make sense to use this version in Isabelle? >>> >>> >>> >>> Thanks in advance, >>> Mathias Fleury >>> >>> >>> >>> >>> * for natural numbers, the simproc >>> Numeral_Simprocs.natle_cancel_numerals is able to do it too. >>> _______________________________________________ >>> isabelle-dev mailing list >>> isabelle-...@in.tum.de <mailto:isabelle-...@in.tum.de> >>> https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabel >>> le-dev >> _______________________________________________ >> isabelle-dev mailing list >> isabelle-...@in.tum.de <mailto:isabelle-...@in.tum.de> >> https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev > > _______________________________________________ > isabelle-dev mailing list > isabelle-...@in.tum.de > https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev
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