Set-theoretic types: inference of patterns and guards

[josevalim]

The goal of this issue is to track the main tasks for the first milestone of set theoretic types: type inference of patterns and guards, followed by body checking.

Typing description:

• Non-divisible types (integer, floats, pids, etc)
• Dynamic
• Atoms
• Maps
  • Domain key-types
  • map_fetch
  • map_put
  • map_delete
  • map_keys
  • map_values
• Tuples
  • Generalize :open / :closed
  • tuple_fetch
  • tuple_insert
  • tuple_delete
  • tuple_values
• Lists
  • list_hd
  • list_tl
• Functions
  • apply/2 and fun.(args...)
  • fn ... -> ... end
  • Capture
  • Unions of closures

Type inference and checking:

• Tracking of variables
• Type inference of patterns
• Type inference of guards
• Type inference of return types
• Map and struct updates
• Checking of all inlined functions from Kernel
• Checking of all inlined conversion functions
• Checking of __STACKTRACE__ and raising functions
• Tuple module
• Map module
• Storing of inferred types in .beam files
• Support for local calls
• Support for remote calls

These are additional features not required for the first milestone:

• Support for __info__, module_info, and behaviour_info
• Typing of :erlang inlined functions
• for comprehensions
• with comprehensions
• Detect never matching clauses and patterns (cond, case, receive, try)
• Detect overlapping clauses (case, receive, try)
• Exhaustiveness checks
• Unused clauses in private functions
• Tracking of mismatches in equality operators
• Tracking of structs in ordered comparison operators
• Support for macros
• Move compile.protocols to parallel compiler
• Type check private (local?) functions against the union of all call types

For the second and third milestones, see #13881.