Implementation of the typed call-by-value λ-calculus using a stack of regions

Abstract

We present a translation scheme for the polymorphically typed call-by-value λ-calculus. All runtime values, including function closures, are put into regions. The store consists of a stack of regions. Region inference and effect inference are used to infer where regions can be allocated and de-allocated. Recursive functions are handled using a limited form of polymorphic recursion. The translation is proved correct with respect to a store semantics, which models a regionbased run-time system. Experimental results suggest that regions tend to be small, that region allocation is frequent and that overall memory demands are usually modest, even without garbage collection.

Region-Based Memory Management for a Dynamically-Typed Language

“…An expression let f = fix(f, Λ˜ . (λx.e 1 at ρ)) at ρ in e 2 stores in region ρ a recursive, region-polymorphic [19] function f that takes regions and a value as an argument, binds them to˜ and x, and evaluates e; It then binds f to the function and evaluates e 2 . An expression f [ρ] applies the region-polymorphic function f toρ.…”

“…Tofte et al [19] proposed a static memory management scheme called region inference. In this scheme, heap space is divided into abstract memory spaces called regions.…”

“…Given the source program above, a compiler can infer that integer 2 is used only in that expression, so that it inserts letregion ρ 2 in · · · end. This transformation (which inserts letregion ρ · · · and at ρ) is called region inference [19].…”

Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time

“…Tofte uses, with good practical performance, the "trick" of restarting at the last computed result of a loop [16] in his inference algorithm for region-based storage management [17]. In the area of transformational programming Cai and Paige describe efficient incremental recomputation of fixed points; our Lemma 12 is a variation on theirs [2].…”

“…His algorithm basically works by iterating algorithm W. It later turned out that the type inference problem associated with Mycroft's type system is undecidable, see [10]. The extension is, however, desirable both in the context of standard typing and program analysis [14,7,17].…”