## MLton 20241230

# EqualityType

An equality type is a type to which PolymorphicEquality can be applied. The Definition and the Basis Library precisely spell out which types are equality types.

- `bool`, `char`, `IntInf.int`, `Int<N>.int`, `string`, and `Word<N>.word` are equality types.

- for any `t`, both `t array` and `t ref` are equality types.

- if `t` is an equality type, then `t list`, and `t vector` are equality types.

- if `t1`, …​, `tn` are equality types, then `t1 * …​ * tn` and `{l1: t1, …​, ln: tn}` are equality types.

- if `t1`, …​, `tn` are equality types and `t` AdmitsEquality, then `(t1, …​, tn) t` is an equality type.

To check that a type t is an equality type, use the following idiom.

    structure S: sig eqtype t end =
       struct
          type t = ...
       end

Notably, `exn` and `real` are not equality types. Neither is `t1 -> t2`, for any `t1` and `t2`.

Equality on arrays and ref cells is by identity, not structure. For example, `ref 13 = ref 13` is `false`. On the other hand, equality for lists, strings, and vectors is by structure, not identity. For example, the following equalities hold.

    val _ = [1, 2, 3] = 1 :: [2, 3]
    val _ = "foo" = concat ["f", "o", "o"]
    val _ = Vector.fromList [1, 2, 3] = Vector.tabulate (3, fn i => i + 1)