= Contracts for Haskell =
== Involved ==
* Simon Peyton-Jones
* Dimitrios Vytiniotis
* Koen Claessen
* Charles-Pierre Astolfi
== Overview ==
Contracts, just as types, give a specification of the arguments and return values of a function. For example we can give to head the following contract:
{{{
head ::: {x | not (null x)} -> Ok
}}}
Where Ok means that the result of head is not an error/exception as long as the argument isn't.
Any Haskell boolean expression can be used in a contract, for example
{{{
fac ::: a:Ok -> {x | x >= a}
}}}
is a contract that means that for every a which is an actual integer (not an error), then fac a >= a
We can also use a higher-order contracts:
{{{
map ::: ({x | x >= 0} -> {x | x > 0}) -> {xs | not (null xs)} -> Ok
}}}
This contract means that if we apply map to a non-empty list with a function that takes a non-negative integer and returns an positive integer then map returns a list of values without errors.
For a formal introduction, one can read [1].
== The plan ==
Verifying that a function satisfies a given contract is obviously undecidable, but that does not mean that we can't prove anything interesting. Our plan is to translate Haskell programs to first-order logic (with equality) and then use Koen's automated theorem prover to check contract satisfaction. Given that first-order logic is only semi-decidable, the theorem prover can (and in fact does) hang when fed with contracts that are in contradiction with the function definition.
== Current status ==
The current status is described in [3] and some code and examples can be found in [2]. Note that given it's just a prototype the input syntax is slightly different from Haskell. In the end, we should get a ghc extension for contracts.
== Questions ==
* Do we need cfness predicate anymore? It was important in the POPL paper but is still relevant?
* UNR should be renamed to a less confusing name.
* Hoare logic vs liquid types
* Semantics & domain theory to prove the correctness of the translation
* Unfolding for proving contracts on recursive functions
== References ==
[1] : http://research.microsoft.com/en-us/um/people/simonpj/papers/verify/index.htm [[BR]]
[2] : https://github.com/cpa/haskellcontracts and https://github.com/cpa/haskellcontracts-examples [[BR]]
[3] : https://github.com/cpa/haskellcontracts/blob/master/draft2.pdf