Is there a way to add syntax for a custom datatype in Isabelle?

Question

So I have two custom datatypes:

datatype ('a, 't) action = ACTION (name: "'a") (args: "'t list") ("⌈_ _⌋")

and

datatype ('a, 't) multiaction = MULTIACTION "('a, 't) action multiset" ("⟨(_)⟩")

Both of them work with their given notations, however whenever I want to use these data structures in their pretty-printed format, it looks a little redundant. For example:

value "⟨{#⌈a b⌋, ⌈c d⌋#}⟩"

What I'd like to do is have the above typed without the multiset brackets, so that it looks like this:

value "⟨⌈a b⌋, ⌈c d⌋⟩"

What I've tried is using syntax:

syntax
  "_maction" :: "args ⇒ ('a, 't) multiaction" ("⟨_⟩" [0] 60)
translations
  "⟨x⟩" == "CONST MULTIACTION {#x#}"

But when I try it out with some datatypes:

value "⟨⌈''x'' [1,2,3::int]⌋⟩"

But I get a wellsortedness error, which I have no idea why it occurs. Can I please have some help with this?

Thanks in advance!

Answer 1

Perhaps, you are looking to lift the multiset syntax to multiaction ? In this case, you may also wish to lift the relevant definitions for the multiset (as noted in the comments, ideally, you will wish to use the datatype / lift_definition infrastructure for this):

datatype ('a, 't) action = ACTION (name: "'a") (args: "'t list") ("⌈_ _⌋")
datatype ('a, 't) multiaction = MULTIACTION "('a, 't) action multiset"

(*this should not be lifted manually: use the integration of
the datatype and lifting infrastructure*)
fun add_multiaction :: 
  "('a, 'b) action ⇒ ('a, 'b) multiaction ⇒ ('a, 'b) multiaction"
  where "add_multiaction x (MULTIACTION xs) = MULTIACTION (add_mset x xs)"

abbreviation MAempty :: "('a, 't) multiaction" ("⟨#⟩") where
  "MAempty ≡ MULTIACTION {#}"

syntax
  "_multiaction" :: "args ⇒ ('a, 't) multiaction" ("⟨(_)⟩")
translations
  "⟨x, xs⟩" == "CONST add_multiaction x ⟨xs⟩"
  "⟨x⟩" == "CONST add_multiaction x ⟨#⟩"

value "⟨⌈''x'' [1,2,3::int]⌋, ⌈''x'' [1,2,3::int]⌋⟩"

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I have to admit I am not entirely certain if I fully understood what exactly you are trying to achieve: I am providing the first idea that came to my mind based on not-very-thorough understanding of the question.

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Isabelle version: Isabelle2021-RC6