#lang rosette

(define (check-spec-len prop pre spec xs)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (car (spec xs)))))

(define (check-spec-is-empty prop pre spec xs)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (car (spec xs)))))

(define (check-spec-first prop pre spec xs)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (car (spec xs)))))

(define (check-spec-last prop pre spec xs)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (car (spec xs)))))

(define (check-spec-contains prop pre spec xs x)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (car (spec xs x)))))

(define (check-spec-insert prop pre spec xs x)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (spec xs x))))

(define (check-spec-remove prop pre spec xs x)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (car (spec xs x)))))

(define (check-spec-clear prop pre spec xs)
  (assume (and (prop xs) (pre xs)))
  (assert (prop (spec xs))))

(define (check-not-contradict prop pre xs)
  (assert (and (prop xs) (pre xs) (> (length xs) 1))))

(define (check prop pres specs xs x . rest)
  (cond 
    [(or (unsat? (solve (check-not-contradict prop (first pres) xs)))
         (unsat? (solve (check-not-contradict prop (second pres) xs)))
         (unsat? (solve (check-not-contradict prop (third pres) xs)))
         (unsat? (solve (check-not-contradict prop (fourth pres) xs)))
         (unsat? (solve (check-not-contradict prop (fifth pres) xs)))
         (unsat? (solve (check-not-contradict prop (sixth pres) xs)))
         ) #f]
    [else (and (unsat? (verify (check-spec-clear prop (first pres) (first specs) xs)))
               (unsat? (verify (check-spec-contains prop (second pres) (second specs) xs x)))
               (unsat? (verify (check-spec-insert prop (third pres) (third specs) xs x)))
               (unsat? (verify (check-spec-is-empty prop (fourth pres) (fourth specs) xs)))
               (unsat? (verify (check-spec-len prop (fifth pres) (fifth specs) xs)))
               (unsat? (verify (check-spec-remove prop (sixth pres) (sixth specs) xs x)))
               )]))

(provide check)