Abstract: In the Equivalent Transformation (ET) computation
model, a program is constructed by the successive accumulation of
ET rules. A method by meta-computation by which a correct ET
rule is generated has been proposed. Although the method covers a
broad range in the generation of ET rules, all important ET rules
are not necessarily generated. Generation of more ET rules can be
achieved by supplementing generation methods which are specialized
for important ET rules. A Specialization-by-Equation (Speq) rule is
one of those important rules. A Speq rule describes a procedure in
which two variables included in an atom conjunction are equalized
due to predicate constraints. In this paper, we propose an algorithm
that systematically and recursively generate Speq rules and discuss
its effectiveness in the synthesis of ET programs. A Speq rule is
generated based on proof of a logical formula consisting of given
atom set and dis-equality. The proof is carried out by utilizing some
ET rules and the ultimately obtained rules in generating Speq rules.