wp@iddth.id.dk (Wiesiek Pawlowski (900415#)) (01/25/91)
Maybe somebody could give me some references to the literature or give me some advise. I have problems in proving decidability of a sequent calculus formalizing subtype-relation. The system looks as follows: Type ::= Nat | Type-set | T + T | N N - type name (an identifier) Subtype Calculus formulae are of the form: T1 < T2 sequents are of the form: A |- f ,where f is a formula and A is a set of formulae. inference rules: A |- T < T T1 < T2,A |- T1 < T2 A |- T1 < T2 ==> A |- T1-set < T2-set A |- T < T1 ==> A |- T < T1+T2 A |- T < T2 ==> A |- T < T1+T2 A |- T1 < T & A |- T2 < T ==> A |- T1+T2 < T n < T2,A |- T1 < T2 ==> A |- n < T2 ,where n=T1 is a type definition A |- T1 < T2 & A |- T2 < T3 ==> A |- T1 < T3 It is the last rule - the rule of transitivity which causes problems. In a sence some form of "transitivity-elimination" theorem should be proved. In a reacher type system with more constants and some specific axioms it would mean that for a given proof tree we are able to "push-down" all the occurrences of the transitivity rule up to the axioms. But I do not know how to prove it. Perhaps there exists some well-known strategy of proving decidability of similar systems? Maybe the system as stated is undecidable?! Wiesiek Pawlowski my e-mail address is wp@id.dth.dk