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I'm currently trying to write an SMT script using define-fun-rec. I've tested with both Z3, version 4.4.2, and CVC4, version 1.4. As far as I can tell, these are the most recent versions of both, and both support the feature*. However, both do not seem to recognize the command.

(I made some changes to this based on Nikolaj's reply. It still gives the error messages.) Specifically, given:

(define-fun-rec 
    fac ((x Int)) Int
    (
        ite (<= x 1) 
            1 
            (* x (fac (- x 1)))
    )
)

(assert (= (fac 4) 24))

(check-sat)

Z3 outputs:

unsupported
; define-fun-rec
(error "line 10 column 17: unknown function/constant fac")
sat

And CVC4 outputs:

(error "Parse Error: fac.smt2:1.15: expected SMT-LIBv2 command, got `define-fun-rec'.

  (define-fun-rec 
   ^
")

My best guess is that there is some sort of flag I need to set or I need to be using some specific logic, but I've had a lot of trouble finding any sort of detailed instructions or examples with define-fun-rec. Any advice would be appreciated. Thanks!

*Z3 has support: How to deal with recursive function in Z3?

CVC4 has support: http://lara.epfl.ch/~reynolds/pres-smt15.pdf

Community
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Bill
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2 Answers2

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The latest version of CVC4 can be downloaded under "Development versions" (on the right hand side) of: http://cvc4.cs.nyu.edu/downloads/

The latest development version has support for recursive function definitions. You can use the cvc4 command line option "--fmf-fun" to enable a technique that finds small models for problems involving recursive function applications, assuming definitions are admissible.

(Although, unfortunately your example with factorial also requires non-linear arithmetic, which CVC4 does not yet support.)

Andrew Reynolds
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  1. Don't set the logic to LIA. This is not in the LIA fragment and Z3 will use the wrong tactic to solve the problem.Just remove the set-logic line.
  2. It helps to not use an undefined function "f" inside the definition of "fib".
  3. I would suggest that you call the function "fac" and not "fib" since you are defining a factorial function.

Thus,

(define-fun-rec 
   fac ((x Int)) Int
   (
    ite (<= x 1) 
        1 
        (* x (fac (- x 1)))
   )
)

(assert (= (fac 4) 24))

(check-sat)

z3 -version

Z3 version 4.4.2

z3 fac.smt2

sat

If you change 24 to 25 you get unsat.

Nikolaj Bjorner
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  • I feel silly about (1) and (2)- I originally called the function f, then figured I'd make the name more descriptive for others benefit on here- obviously I had fibonacci rather than factorial on the mind for some reason, so two misfires there... Unfortunately, even after making the "f" consistent again and removing the set-logic line, I'm still getting the exact same errors. I also tried copy and pasting the formula you posted, and it gives me the same errors as well. "z3 -version" does output "Z3 version 4.4.2" for me. – Bill Jul 26 '16 at 00:07
  • It turns out that apparently there are some versions of z3 that report there version number as 4.4.2 but do not support this... I just pulled from github and tried building again, and it worked. Thanks for your pointers on the other topics Nikolaj! – Bill Jul 26 '16 at 05:07
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    4.4.2 is not officially released yet (the latest official release is 4.4.1: https://github.com/Z3Prover/z3/releases); all the development versions that are currently being worked on report their version as 4.4.2. Ideally we should always report the current githash when referring to these, but we don't always remember. Also, the output of -version didn't report them, but I've added that now. – Christoph Wintersteiger Jul 26 '16 at 18:23