A Congruence Relation for Restructuring Classical Terms

We present a congruence relation on sequent-style classical proofs which identifies proofs up to trivial rule permutation. The study is performed in the framework of ∗X calculus which provides a CurryHoward correspondence for classical logic (with explicit structural rules) ensuring that proofs can be seen as terms and proof transformation as computation. Congruence equations provide an explicit account for classifying proofs (terms) which are syntactically different but essentially the same. We are able to prove that there is always a representative of a congruence class which enables computation at the top level.