Formulas as programs

We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the emph{formulas themselves are emph{programs. This contrasts with the so-called emph{formulas as types approach in which the proofs of the formulas are typed terms that can be taken as programs. This view of computing is inspired by logic programming and constraint logic programming but differs from them in a number of crucial aspects. Formulas as programs is argued to yield a realistic approach to programming that has been realized in the implemented programming language almazero{ citeasnoun{ABPS98a that combines the advantages of imperative and logic programming. The work here reported can also be used to reason about the correctness of non-recursive almazero{ programs that do not include destructive assignment