Models and recursive functions

Question

As previously asked Z3 can not provide a model for recursive functions. However, is it possible to tell Z3 (preferably via the Java API) that a model without a definition for recursive functions is sufficient (or indeed choose the functions I am interested in, essentially I do not need a model for non-constant functions)? Obviously, that might lead to queries that return sat although some functions do not have a model. Basically, the user then has to ensure that these functions do have some model. However, I would assume this is not really realizable the way Z3 or SMT solvers work, i.e., I would assume Z3 needs a (partial) model of recursive functions to evalutate expressions.

Answer 1

The MBQI implementation for quantifiers doesn't really work nicely with recursive functions. There is one thing that might do the trick for you: replace recursive function definitions by bounded-recursive functions. You add an extra argument that counts the number of unfoldings you are willing to explore of the function. Whenever you apply the recursive function in the rest of the input, set the depth parameter. You can use either algebraic data-type Peano numbers or integers. The symbolic automata toolkit uses this approach, for example.

Answer 2

I found one paper that explores the idea given in Nikolaj Bjorner's answer further: "Computing with an SMT solver" by Amin, Leino and Rompf (2014).

Furthermore, I found "Satisfiability Modulo Recursive Programs" by Suter, Köksal and Kuncak (2011) which unfolds calls to recursive functions successively until the satisfiability can be decided.