doc/guide/src/EqualityType.adoc

   1 EqualityType
   2 ============
   3
   4 An equality type is a type to which <:PolymorphicEquality:> can be
   5 applied.  The <:DefinitionOfStandardML:Definition> and the
   6 <:BasisLibrary:Basis Library> precisely spell out which types are
   7 equality types.
   8
   9 * `bool`, `char`, `IntInf.int`, ++Int__<N>__.int++, `string`, and ++Word__<N>__.word++ are equality types.
  10
  11 * for any `t`, both `t array` and `t ref` are equality types.
  12
  13 * if `t` is an equality type, then `t list`, and `t vector` are equality types.
  14
  15 * if `t1`, ..., `tn` are equality types, then `t1 * ... * tn` and `{l1: t1, ..., ln: tn}` are equality types.
  16
  17 * if `t1`, ..., `tn` are equality types and `t` <:AdmitsEquality:>, then `(t1, ..., tn) t` is an equality type.
  18
  19 To check that a type t is an equality type, use the following idiom.
  20 [source,sml]
  21 ----
  22 structure S: sig eqtype t end =
  23    struct
  24       type t = ...
  25    end
  26 ----
  27
  28 Notably, `exn` and `real` are not equality types.  Neither is `t1 -> t2`, for any `t1` and `t2`.
  29
  30 Equality on arrays and ref cells is by identity, not structure.
  31 For example, `ref 13 = ref 13` is `false`.
  32 On the other hand, equality for lists, strings, and vectors is by
  33 structure, not identity.  For example, the following equalities hold.
  34
  35 [source,sml]
  36 ----
  37 val _ = [1, 2, 3] = 1 :: [2, 3]
  38 val _ = "foo" = concat ["f", "o", "o"]
  39 val _ = Vector.fromList [1, 2, 3] = Vector.tabulate (3, fn i => i + 1)
  40 ----