Either

Either types are the well-known sum types, otherwise known as tagged unions.

They defined a finite number of variants, each with a different name and a payload. A value of an either type is one of its variants.

type StringOrNumber = either {
  .string String,
  .number Int,
}

def Str: StringOrNumber = .string "Hello!"
def Num: StringOrNumber = .number 42,

An either type is spelled with the keyword either, followed by curly braces enclosing a comma-separated list of variants.

Each variant has a lower-case name prefixed by a period and followed by a single, obligatory payload type:

either {
  .variant1 Payload1,
  .variant2 Payload2,
  .variant3 Payload3,
}

Since each payload must be a single type, units, pairs, and other types are used to define composite payloads. For example:

type MaybeBoth<a, b> = either {
  .neither!,
  .left a,
  .right b,
  .both(a, b)!,
}

Either types are frequently used together with recursive types to define finite tree-like structures.

type BinaryTree<a> = recursive either {
  .empty!,
  .node(a, self, self)!,
}

The pre-defined List<a> type is a combination of recursive and either:

type List<a> = recursive either {
  .end!,
  .item(a) self,
}

Construction

Values of either types are constructed starting with .name — the name of one of the variants in the type — followed by an expression of the corresponding payload type.

Here are some examples of constructions for an either type that demonstrates many possible payloads:

type Varied = either {
  .unit!,                        // payload is `!`
  .string String,                // payload is `String`
  .number Int,                   // payload is `Int`
  .pair(Int) String,             // payload is `(Int) String`
  .symmetricPair(Int, String)!,  // payload is `(Int, String)!`
  .nested either {               // payload is another either type
    .left!,
    .right!,
  },
  .nested2(String) either {      // payload is a pair of `String` and another either
    .left!,
    .right!,
  }
}

def Example1: Varied = .unit!
def Example2: Varied = .string "Hello!"
def Example3: Varied = .number 42
def Example4: Varied = .pair(42) "Hello!"
def Example5: Varied = .symmetricPair(42, "Hello!")!
def Example6: Varied = .nested.left!
def Example7: Varied = .nested.right!
def Example8: Varied = .nested2("Hello!").left!
def Example9: Varied = .nested2("Hello!").right!

Pairs are frequently used in payloads of either types, both in their symmetric and sequential styles. The sequential style makes chaining either types with attached payloads very natural, like in the .nested2 variant.

Destruction

Values of either types can be deconstructed using .case expressions, similar to pattern-matching in other languages.

A .case expression starts with the value to be destructed, followed by .case, and a list of comma-separated branches enclosed in curly braces, one per each variant.

value.case {
  // branches
}

Each branch consists of the name of its variant, a pattern to assign the payload to, then a => followed by an expression computing the result for that branch. All branches must evaluate to the same type.

// branch
.name pattern => expression,

The patterns to assign the payloads are the same as can appear on the left side of let assignments:

• variable matches the whole value.
• ! matches units.
• (pattern1, ...) patternN matches pairs.

For a small example, we analyze the Str and Num values of the StringOrNumber type from above:

// evaluates to "Hello!"
def ResultForStr = Str.case {
  .string s => s,
  .number n => Int.ToString(n),
}

// evaluates to "42"
def ResultForNum = Num.case {
  .string s => s,
  .number n => Int.ToString(n),
}

For a comprehensive example, here’s a big function converting the above Varied type to a String:

dec VariedToString : [Varied] String
def VariedToString = [varied] varied.case {
  .unit! => ".unit!",

  .string s => String.Builder.add(".string ").add(String.Quote(s)).build,

  .number n => String.Builder.add(".number ").add(Int.ToString(n)).build,

  .pair(n) s =>
    String.Builder
      .add(".pair(")
      .add(Int.ToString(n))
      .add(") ")
      .add(String.Quote(s))
      .build,

  .symmetricPair(n, s)! =>
    String.Builder
      .add(".symmetricPair(")
      .add(Int.ToString(n))
      .add(", ")
      .add(String.Quote(s))
      .add(")!")
      .build,

  .nested inside => String.Builder.add(".nested").add(inside.case {
    .left! => ".left!",
    .right! => ".right!",
  }).build,

  .nested2(s) inside =>
    String.Builder
      .add(".nested2(")
      .add(String.Quote(s))
      .add(")")
      .add(inside.case {
        .left! => ".left!",
        .right! => ".right!",
      }).build,
}