Single-threaded polymorphic lambda calculus

Assignments for applicative languages

“…This reflects the requirement that manipulations of state should be performed in a sequential fashion, similar in spirit to the proposal of single-threaded lambda calculus [GH90]. Even though it is possible to express functions which accept more than one observer, the state manipulations of such observers have to be eventually sequentialized because there are no multiary primitives on observers.…”

“…Guzman and Hudak [GH90] propose a typed extension of functional languages called single threaded lambda calculus that can express the sequencing constraints required for the in-place update of array-like data structures. Wadler [Wad90b] proposes a similar solution using types motivated by Girard's Linear Logic and, later, shows the two approaches to be equivalent [Wad91].…”

“…In contrast, one models dynamic data in functional languages by representing the state explicitly or, possibly, by creating streams of states. Compilation techniques and language notations have been proposed to permit explicit state manipulation to be implemented efficiently [HB85,GH90,Wad90b,Wad90a]. Unfortunately, these methods do not achieve all the effects of true dynamic data.…”

Uniqueness Typing Redefined

“…Finally, G u z m a n 's Single-T hreaded Polym orphic L am bda C alculus [24] has sim ilar goals to uniqueness typing, b u t is considerably m ore com plicated. M uch of th is com plexity comes from try in g to su p p o rt a "stric t let" co n stru ct where unique (or "sin gle-threaded" ) term s can be used m ultiple tim es a t a non-unique (m ultiple-threaded) type.…”

Assignments for Applicative Languages

“…This is achieved by a type system that sequentializes access to regions of the state, much as in effect systems [GL86] and the languages based on linear logic [GH90,Wad90b,Wad91].…”