My class constraint is ignored in a type synonym definition: for

type_synonym 'value myTypeOperator = "'value::group_add"

I get

Ignoring sort constraints in type variables(s): "'value"
in type abbreviation "myTypeOperator"

The examples I have found in the codebase were using such constraints on the right hand side:

Isabelle2022/src/HOL/Isar_Examples/Hoare_Ex.thy:type_synonym 'a time = "\<lparr>time :: nat, \<dots> :: 'a\<rparr>"
Isabelle2022/src/HOL/TLA/Intensional.thy:type_synonym ('w,'a) expr = "'w \<Rightarrow> 'a"   (* intention: 'w::world, 'a::type *)
afp-2023-03-16/thys/Binomial-Heaps/BinomialHeap.thy:type_synonym ('e, 'a) BinomialQueue_inv = "('e, 'a::linorder) BinomialTree list"
afp-2023-03-16/thys/Binomial-Heaps/SkewBinomialHeap.thy:type_synonym ('e, 'a) SkewBinomialQueue = "('e, 'a::linorder) SkewBinomialTree list"
afp-2023-03-16/thys/Locally-Nameless-Sigma/preliminary/FMap.thy:type_synonym ('a, 'b) fmap = "('a :: finite) \<rightharpoonup> 'b" (infixl "-~>" 50)
afp-2023-03-16/thys/Strong_Security/Types.thy:type_synonym ('id, 'd) DomainAssignment = "'id \<Rightarrow> 'd::order"
afp-2023-03-16/thys/Differential_Dynamic_Logic/Denotational_Semantics.thy:type_synonym 'a Rvec = "real^('a::finite)"

so I wonder what the problem is here.

Section 5.12.2 of the Isabelle/Isar Reference Manual says that

Unlike the semantic type definitions in Isabelle/HOL, type synonyms are merely syntactic abbreviations without any logical significance.

I guess this is the cause it does not pay attention to type class constraints.

What is a semantic type definition in Isabelle/HOL then? Should I use datatype for this?


1 Answer 1


Yes, datatype is adequate for this:

datatype ('v::group_add) myTypeOperator = MyTyOp 'v

datatype ('v) myTypeOperator2 = MyTyOp2 "'v::group_add"

Type class prescription works on both sides of the defining equation.

  • $\begingroup$ Caveat: I do not see if this has an effect on later definitions. I had to use the type class prescription again when defining a function on this type. $\endgroup$
    – Gergely
    Commented Aug 4, 2023 at 15:06

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