CS195Y Lecture 29

4/17/16

Announcement: There are will be two visitors coming to class in the next couple lectures. One on Friday and one on next Wednesday.

Rosette(1)

Problems with what we've been using:

Alloy ints
Spin ints
Floating Point
Visualizations
Functions
Error Messages
Longer traces

This week we are transitioning to SMT solvers. SMT stands for satisfiablity modulo theory. The solver we'll use today (Rosette) is built on Racket.

(define-symbolic p boolean?)
  (define-symbolic q boolean?)
  (solve(assert(or p q)))

And we get p as #f and q as #t, which we know would satistfy p or q. Can we make this model give us a different result?


  (solve (assert(or p q)
         (assert(or p (not q))))

  (solve (assert(or p q))
         (assert(or p (not q)))
         (assert(or (not p) q))))

Q: this seems really cumbersome A; you're not wrong. but we're going to build on this and it'll get better

Getting into some more interesting stuff

(define-symbolic a integer?)
(define-symbolic b integer?)
(define-symbolic f (-> integer? integer?))
(solve (assert (> b a))
       (assert (< (f b) (f a))))


(solve (assert (> b a))
       (assert (< (f b) (f a)))
       (assert (> a 20)))

It's taking a really long time... What might that happen? We have a really big search space and it's taking a long time to go through the whole thing. How about some debugging? Let's try 10.


(solve (assert (> b a))
       (assert (< (f b) (f a)))
       (assert (> a 10)))

It works! By why? Tim said that these were real integers but they're not really. They are Alloy style integers. We can fix this by setting bitwidth to false.


(current-bitwidth #f)

Once we do that we can run the version with 20 no problem.

Next Example


(define-symbolic x integer?)
(define-symbolic root1 integer?)
(define-symbolic root2 integer?)
(solve (assert (forall(x integer?)(= (* (+ x root1) (+ x root2)) (+(* x x) (* x -198) -39483)))))