In this paper the complexity of provability of polarized additive, multiplicative, and exponential formulas in the (initial) Cockett-Seely polarized game logic is discussed. The complexity is ultimately based on the complexity of finding a strategy in a formula which is, for polarized additive formulas, in the worst case linear in their size. Having a proof of a sequent is equivalent to having ...

namely 90 a M0 a M! a M1 a Yset : set !Mset: We recall from [8] or [9] that a locally small category B is said to be total (abbreviating totally cocomplete) if Y : B !MB has a left adjoint, X: Considerable motivation for the terminology is given in either reference. Examples include categories of algebras, categories of spaces and categories of sheaves on a Grothendieck site. The reader is advi...

model of Idealized Algol raises signi cant problems over and above those associated with the full abstraction problem for PCF [20, 29]. In a previous paper [5, 6], we gave the rst fully abstract model of Idealized Algol with active, i.e. possibly side-e ecting, expressions. It is signi cantly harder to capture the \pure" version of Idealized Algol originally proposed by Reynolds, in which a sha...