# Re: [isabelle] Notation issues trying to make Multiset more convenient

Nice idea to add this syntax to Multisets, I'm also tired writing
{#a#}+{#b#}+...

I can only partially reproduce your error.
The problem seems to be the predefined syntax for the single-function
"{#_#}" in Multiset.thy.

The following works for me (at least in one direction):

In Multiset.thy, replace:

-  single :: "'a => 'a multiset"    ("{#_#}")

+   single :: "'a => 'a multiset"

syntax

"@multiset" :: "args => 'a multiset" ("{#(_)#}")

translations

"{# x, xs #}" == "single x + {#xs#}" (* Note that xs seems to be the syntactic rest of the argument list, not yet translated *)

"{# x #}" == "single x"

This works as far as "{# a,b,c #}" is correctly parsed as
"{#a#}+({#b#}+{#c#})", but the backward translations seems not to work, i.e.
{# a,b,c #} is output as "{#a#}+({#b#}+{#c#})", although it should be
output as "{# a,b,c #}". Any ideas ?

Regards,
Peter

Rafal Kolanski wrote:
> Hi,
>
> As you know, {a,b,c} works for sets, and [a,b,c] works for lists.
> I'm in need of this sort of thing for Multisets, but I just can't get
> it to work.
>
> Firstly, syntax issues ... anything along the lines of:
>     translations
>       "{# x, xs #}" == "{# x #} + {# xs #}"
> fails due to a parse error, even if I replace # with any non-bracket
> symbol.
>
> On the other hand, bracket symbols work:
>     translations
>       "[{x, xs}]" == "{# x #} + {# xs #}"
> but this redefines the "one set in a list" syntax.
>
> What I can do is specify some unary operator for multiset_of and pass
> in a list:
>     notation
>       multiset_of ("\<kappa> _" [40] 40)
> but then I lose the nice simplification of:
>     lemma "a :# ({# b #} + {# a #})" by simp
> as this won't work:
>     lemma "a #\<in> \<kappa>[b, a, c]" by simp
>
> I am not sure how to proceed from here. Could you offer any advice?
>
> Sincerely,
>
> Rafal Kolanski.
>

--
Peter Lammich, Institut für Informatik
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