Definition. Normalizing Horn clauses [0059]

  • December 19, 2025

Something of note when dealing with weakets preconditions in terms of horn clauses is that we have to first normalize them to ensure they are in the correct horn format, which is to say we commonly have some horn clause in the form

\[ p(e_1, e_2) \land \ldots \land \phi \to H(e_3) \]

where \(e_i\) represents an expression, to normalize these clauses we lift the expressions out of the parameters for the predicates and into the list of conjuncts, i.e.:

\[ p(x_1, x_2) \land x_1 = e_1 \land x_2 = e_2 \land x_3 = e_3 \land \ldots \land \phi \to H(x_3) \]

So we create fresh variables \(x_1, x_2, x_3\) and assign these to the respective expressions then use them in place of the expressions themselves.