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
• Tuples
• Lists
• Functions

Type inference and checking:

• Tracking of variables
• Type inference and checking of bitstring syntax
• Type inference of patterns
• Type inference of guards
• Support of every syntax construct
  • structs
  • rescue
  • map updates
  • __CALLER__
  • ...
• Support for __info__
• Support for local calls
• Support for application of Kernel and stdlib functions
• Support for application of Map operations

These are additional features not required for the first milestone:

• Storing of inferred types in .beam files
• Detecting overlapping clauses (cond, case, receive, try)
• Detecting unused clauses (cond, case, receive, try)
• Exhaustiveness checks
• Typing of protocol implementations
• Tracking of mismatches in equality operators
• Tracking of structs in ordered comparison operators
• Support for macros
• Type checking during evaluation

Long term:

• Occurrence typing
• Type variables
• Strong arrows
• Row polymorphism
• Behaviours