Cryptol

It appears that all we have done so far is to write a Cryptol program to recognize whether a given solution to the n-Queens problem is valid.

Planet Haskell Levent Erkok 2010

Without further ado, here is how we solve n-Queens in Cryptol, without writing any additional code on top of what we have already seen:

Planet Haskell Levent Erkok 2010

(Note that we do not have to check for negative numbers since all Cryptol numbers are non-negative.)

Planet Haskell Levent Erkok 2010

Having done the heavy-lifting above, we can now write the predicate that recognizes a valid n-Queens solution in Cryptol: type Solution (n) = [n]

Planet Haskell Levent Erkok 2010

The first command puts Cryptol in the sbv mode, which allows for the use of SAT/SMT solvers.

Planet Haskell Levent Erkok 2010

We would be remiss if we didn't mention some of the actual uses of the satisfiability checker in the Cryptol tool chain.

Planet Haskell Levent Erkok 2010

We can test this function in Cryptol, by providing sample input:

Planet Haskell Levent Erkok 2010

Having described how we will recognize an alleged solution, let us now consider how we can code this in Cryptol.

Planet Haskell Levent Erkok 2010

Given any predicate (like nQueens above), Cryptol can find inputs that will satisfy it automatically, at the push of a button!

Planet Haskell Levent Erkok 2010

The second command tells Cryptol to print results in base 10.

Planet Haskell Levent Erkok 2010