Effect system

An effect system is a formal system which describes the computational effects of computer programs, such as side effects. An effect system can be used to provide a compile-time checking of the possible effects of the program.

The effect system extends the notion of type to have an "effect" component, which comprises an effect kind and a region. The effect kind describes what is being done, and the region describes with what it is being done.

An effect system is typically an extension of a type system. The term "type and effect system" is sometimes used in this case. Often, a type of a value is denoted together with its effect as type ! effect, where both the type component and the effect component mention certain regions (for example, a type of a mutable memory cell is parameterized by the label of the memory region in which the cell resides).

Some examples of the behaviors that can be described by effect systems include:

• Reading, writing or allocating memory: the effect kind is read, write, allocate or free, and the region is the point of the program where allocation was performed (i.e., each program point where allocation is performed is assigned a unique label, and region information is statically propagated along the dataflow). Most functions working with memory will actually be polymorphic in the region variable: for example, a function that swaps two locations in memory will have type forall r1 r2, unit ! {read r1, read r2, write r1, write r2}.
• Working with resources, such as files: for example, the effect kind may be open, read and close, and again, the region is the point of the program where the resource is opened.
• Control transfers with continuations and long jumps: the effect kind may be goto (i.e. the piece of code may perform a jump) and comefrom (i.e. the piece of code may be the target of a jump), and the region denotes the point of the program from which or to which the jump may be performed.
• Java's checked exceptions are an example of an effect system: the effect kind is throws and the region is the type of the exception being thrown.

Effect systems may be used to prove the external purity of certain internally impure definitions: for example, if a function internally allocates and modifies a region of memory, but the function's type does not mention the region, then the corresponding effect may be erased from the function's effect.

References

• Hankin, Chris; Nielson, Flemming; Nielson, Hanne Riis (1999). Principles of Program Analysis. Berlin: Springer. ISBN 3-540-65410-0. 
• Gifford, David; Turbak, Franklyn A.; Sheldon, Mark A. (2008). "16". Design Concepts in Programming Languages. Cambridge, Mass: MIT Press. ISBN 0-262-20175-5. 

Further reading

• Marino, Daniel; Millstein, Todd (2008). "A Generic Type and Effect System". Proceedings of the 4th international workshop on Types In Language Design And Implementation (ACM): 39. doi:10.1145/1481861.1481868. http://www.cs.ucla.edu/~todd/research/tldi09.pdf. 
• Lucassen, John M.; Gifford, David K. (1988). "Polymorphic Effect Systems". Proceedings of the 15th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (ACM): 47–57. doi:10.1145/73560.73564. http://scholar.google.com/scholar?cluster=4860658690557317521.