Doug Gregor 3c69f6a305 [Constraint solver] Introduce one-way constraints. ...

Introduce the notion of "one-way" binding constraints of the form

  $T0 one-way bind to $T1

which treats the type variables $T0 and $T1 as independent up until
the point where $T1 simplifies down to a concrete type, at which point
$T0 will be bound to that concrete type. $T0 won't be bound in any
other way, so type information ends up being propagated right-to-left,
only. This allows a constraint system to be broken up in more
components that are solved independently. Specifically, the connected
components algorithm now proceeds as follows:

1. Compute connected components, excluding one-way constraints from
consideration.
2. Compute a directed graph amongst the components using only the
one-way constraints, where an edge A -> B indicates that the type
variables in component A need to be solved before those in component
B.
3. Using the directed graph, compute the set of components that need
to be solved before a given component.

To utilize this, implement a new kind of solver step that handles the
propagation of partial solutions across one-way constraints. This
introduces a new kind of "split" within a connected component, where
we collect each combination of partial solutions for the input
components and (separately) try to solve the constraints in this
component. Any correct solution from any of these attempts will then
be recorded as a (partial) solution for this component.

For example, consider:

  let _: Int8 = b ? Builtin.one_way(int8Or16(17)) :
  Builtin.one_way(int8Or16(42\
))

where int8Or16 is overloaded with types `(Int8) -> Int8` and
`(Int16) -> Int16`. There are two one-way components (`int8Or16(17)`)
and (`int8Or16(42)`), each of which can produce a value of type `Int8`
or `Int16`. Those two components will be solved independently, and the
partial solutions for each will be fed into the component that
evaluates the ternary operator. There are four ways to attempt that
evaluation:

```
  [Int8, Int8]
  [Int8, Int16]
  [Int16, Int8]
  [Int16, Int16]

To test this, introduce a new expression builtin `Builtin.one_way(x)` that
introduces a one-way expression constraint binding the result of the
expression 'x'. The builtin is meant to be used for testing purposes,
and the one-way constraint expression itself can be synthesized by the
type checker to introduce one-way constraints later on.

Of these two, there are only two (partial) solutions that can work at
all, because the types in the ternary operator need a common
supertype:

  [Int8, Int8]
  [Int16, Int16]

Therefore, these are the partial solutions that will be considered the
results of the component containing the ternary expression. Note that
only one of them meets the final constraint (convertibility to
`Int8`), so the expression is well-formed.

Part of rdar://problem/50150793.

2019-08-13 11:48:42 -07:00

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