Do (static) type systems exist which attempt to formalize the performance characteristics of programs? I cannot find seem to find such attempts.Since type systems are (one of) the most powerful tools in the programmer's arsenal to make statements about programs, and since there are many instances in which performance is critical, it would not seem to be far-fetched to imagine attempts had been undertaken to create a type system which attempts to make at least some statements about the storage and runtime characteristics of programs.
Type system for performance
language design