Unary PCF is Decidable

Sequentiality in Bounded Biorders

We study a notion of bounded stable biorder, showing that the monotone and stable functions on such biorders are sequential. We construct bounded biorder models of a range of sequential, higher-order functional calculi, including unary PCF, (typed and untyped) call-by-value and lazy λ-calculi, and non-deterministic SPCF. We prove universality and full abstraction results for these models by red...

Decidable Discriminator Varieties from Unary Varieties

We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

Relative Definability and Models of Unary PCF

Universality and Almost Decidability

We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a decidable and generic (i.e. a set of natural density one) set whose intersection with S is decidable. Every decidable set is almost decidable, but the conve...

On Berry's conjectures about the stable order in PCF

PCF is a sequential simply typed lambda calculus language. There is a unique order-extensional fully abstract cpo-model of PCF, built up from equivalence classes of terms. In 1979, Gérard Berry defined the stable order in this model and proved that the extensional and the stable order together form a bicpo. He made the following two conjectures: 1) “Extensional and stable order form not only a ...