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Assignability & inference

Assignability is the load-bearing operation of a type system. pcore.IsAssignable(a, b) answers is b a subtype of a — is every instance of b also an instance of a?

a, _ := pcore.Parse("Integer[0,10]")
b, _ := pcore.Parse("Integer[2,5]")
pcore.IsAssignable(a, b) // true

The lattice

  • Any is the top: everything is assignable to it.
  • Scalar ⊇ ScalarData ⊇ Numeric ⊇ Integer / Float, and String ⊇ Enum / Pattern.
  • Data is Variant[ScalarData, Undef, Array[Data], Hash[String, Data]], checked structurally and recursively.
  • Collection accepts any Array, Hash, Tuple or Struct within its size range.
  • Numeric and string ranges use containment: Integer[0,10] accepts Integer[2,5]; String[1,3] accepts Enum['a','bb'] (each value's length is in range).
  • Variant distributes: b is assignable when every member of b's union is assignable, and a (a Variant) accepts b when some branch does.
  • Optional[T] is Variant[Undef, T]; NotUndef[T] accepts a non-undef type assignable to T.
  • Struct is closed: assignability checks every required key is present and compatible, with no extra keys.

The assignability arms are covered exhaustively by the test suite.

Inference

Infer(v) returns the most specific type of a value; ranges collapse to the observed value:

pcore.Infer(int64(5))                       // Integer[5, 5]
pcore.Infer("hello")                        // String[5, 5]
pcore.Infer([]pcore.Value{int64(1), "x"})   // Array[ScalarData, 2, 2]

Generalize widens a type by dropping range/size constraints; CommonType returns the narrowest single supertype of two types:

pcore.Generalize(pcore.Infer(int64(5)))     // Integer
i1, _ := pcore.Parse("Integer[1,3]")
i2, _ := pcore.Parse("Integer[5,7]")
pcore.CommonType(i1, i2)                     // Integer[1, 7]