Inferring Algebraic Effects

We present a complete polymorphic effect inference algorithm for an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references and many others. Our main aim is to offer the programmer a useful insight into the effectful behaviour of programs. Handlers help here by cutting down possible effects and the resulting lengthy output that often plagues precise effect systems. Additionally, we present a set of methods that further simplify the displayed types, some even by deliberately hiding inferred information from the programmer. Though Haskell [10] fans may not think it is better to write impure programs in ML [18], they do agree it is easier. You can insert a harmless printout without rewriting the rest of the program, and you can combine multiple effects without a monad transformer. This flexibility comes at a cost, though —ML types offer no insight into what effects may happen. The suggested solution is to use an effect system [16, 29, 4, 31, 33, 3, 27], which enriches existing types with information about effects. An effect system can play two roles: it can be descriptive and inform about potential effects, and it can be prescriptive and limit the allowed ones. In this paper, we focus on the former. It turns out that striking a balance between expressiveness and simplicity of a descriptive effect system is hard. One of the bigger problems is that effects tend to pile up, and if the effect system takes them all into account, we are often left with a lengthy output listing every single effect there is. In this paper, we present a complete inference algorithm for an expressive and simple descriptive polymorphic effect system of Eff [2] (freely available at http://eff-lang.org), an ML-style language with handlers of not only exceptions, but of any other algebraic effect [22] such as input & output, non-determinism, mutable references and many others [23, 2]. Handlers prove to be extremely versatile and can express stream redirection, transactional memory, backtracking, cooperative multi-threading, delimited continuations, and, like monads, give programmers a way to define their own. And as handlers eliminate effects, they make the effect system non-monotone, which helps with the above issue of a snowballing output. 2012 ACM CCS: [Theory of computation]: Semantics and reasoning—Program reasoning—Program analysis.