GenPoly provides evidence that an instance of Gen[T] exists for some concrete but unknown type T. Subtypes of GenPoly provide additional constraints on the type of T, such as that an instance of Ordering[T] or Numeric[T] exists. Users can also extend GenPoly to add their own constraints.

This allows construction of polymorphic generators where the the type is known to satisfy certain constraints even though the type itself is unknown.

For instance, consider the following generalized algebraic data type:

sealed trait Expr[+A] extends Product with Serializable

final case class Value[+A](value: A) extends Expr[A]
final case class Mapping[A, +B](expr: Expr[A], f: A => B) extends Expr[B]

We would like to test that for any expression we can fuse two mappings. We want to create instances of Expr that reflect the full range of values that an Expr can take, including multiple layers of nested mappings and mappings between different types.

Since we do not need any constraints on the generated types we can simply use GenPoly. GenPoly includes a convenient generator in its companion object, genPoly, that generates instances of 40 different types including primitive types and various collections.

Using it we can define polymorphic generators for expressions:

def genValue(t: GenPoly): Gen[Any, Expr[t.T]] =
  t.genT.map(Value(_))

def genMapping(t: GenPoly): Gen[Any, Expr[t.T]] =
  Gen.suspend {
    GenPoly.genPoly.flatMap { t0 =>
      genExpr(t0).flatMap { expr =>
        val genFunction: Gen[Any, t0.T => t.T] = Gen.function(t.genT)
        val genExpr1: Gen[Any, Expr[t.T]]      = genFunction.map(f => Mapping(expr, f))
        genExpr1
      }
    }
  }

def genExpr(t: GenPoly): Gen[Any, Expr[t.T]] =
  Gen.oneOf(genMapping(t), genValue(t))

Finally, we can test our property:

test("map fusion") {
  check(GenPoly.genPoly.flatMap(genExpr(_))) { expr =>
    assert(eval(fuse(expr)))(equalTo(eval(expr)))
  }
}

This will generate expressions with multiple levels of nesting and polymorphic mappings between different types, making sure that the types line up for each mapping. This provides a higher level of confidence in properties than testing with a monomorphic value.

Inspired by Erik Osheim's presentation "Galaxy Brain: type-dependence and state-dependence in property-based testing" http://plastic-idolatry.com/erik/oslo2019.pdf.