Editing Setoid (section)

==Proof theory==
In proof theory, particularly the proof theory of [[constructive mathematics]] based on the [[Curry–Howard correspondence]], one often identifies a mathematical [[Proposition (mathematics)|proposition]] with its set of [[proof (mathematics)|proof]]s (if any). A given proposition may have many proofs, of course; according to the principle of proof irrelevance, normally only the truth of the proposition matters, not which proof was used. However, the Curry–Howard correspondence can turn proofs into [[algorithm]]s, and differences between algorithms are often important. So proof theorists may prefer to identify a proposition with a ''setoid'' of proofs, considering proofs equivalent if they can be converted into one another through [[beta conversion]] or the like.