declare-fun and define-fun in Z3 can't work together?

Question

I need to model length of array. So I declare a function

(declare-fun LEN ((Array Int Int)) Int)

At the same time, I want to define some macros using define-fun.

However, as I tested a little bit on Z3, it seems that define-fun and declare-fun can't exist at the same source file?

This code like following works fine:

(define-fun mymax ((a Int) (b Int)) Int
  (ite (> a b) a b))

(assert (= (mymax 100 7) 100))
(check-sat)

(src: http://rise4fun.com/Z3/jRzs)

But the following, no matter where the LEN inserted, there will be errors:

;(declare-fun LEN ((Array Int Int) Int) 
;unknown sort 'assert'  
(define-fun mymax ((a Int) (b Int)) Int
  (ite (> a b) a b))
; (declare-fun LEN ((Array Int Int) Int) 
;unknown sort 'assert'
(assert (= (mymax 4 7) 7))
; (declare-fun LEN ((Array Int Int) Int) 
;;unknown sort 'check-assert'
(check-sat)
;(declare-fun LEN ((Array Int Int) Int) 
 ;invalid sort, symbol, '_' or '(' expected

(src: http://rise4fun.com/Z3/HdEy)

Does anybody know how to work around this?

Answer 1

declare-fun and define-fun can be used together. The problem is that you have a missing parenthesis. It should be

(declare-fun LEN ((Array Int Int)) Int) 

instead of

(declare-fun LEN ((Array Int Int) Int) 

Because of the missing parenthesis, the second is actually declaring a function LEN with two arguments (array and integer), then Z3 generates an error when it can find the resulting sort for this declaration.

Here is a link to the complete example: http://rise4fun.com/Z3/TjNS