An Infinitary Lambda Calculus with Global Trace Condition (Extended Abstract) (opens in new tab)

We consider an extension of the infinitary lambda calculus by Kennaway et al., with zero, successor, and conditional, and a type system akin to Goedel's system T. For terms that can be typed in this system, we define the Global Trace Condition (GTC), adapting the concept from Brotherston and Simpson's Cyclic Proofs, and show that any infinite reduction of a well-typed term satisfying the GTC is strongly convergent. As a corollary, we obtain the ...