Expressiveness via intensionality and concurrency

Abstract

Computation can be considered by taking into account two dimensions: extensional versus intensional, and sequential versus concurrent. Traditionally sequential extensional computation can be captured by the λ-calculus. However, recent work shows that there are more expressive intensional calculi such as S F-calculus. Traditionally process calculi capture computation by encoding the λ-calculus, such as in the π-calculus. Following this increased expressiveness via intensionality, other recent work has shown that concurrent pattern calculus is more expressive than π-calculus. This paper formalises the relative expressiveness of all four of these calculi by placing them on a square whose edges are irreversible encodings. This square is representative of a more general result: that expressiveness increases with both intensionality and concurrency.