## 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