Reference counting with frame limited reuse

The recently introduced _Perceus_ algorithm can automatically insert reference count instructions such that the resulting (cycle-free) program is _garbage free_: objects are freed at the very moment they can no longer be referenced. An important extension is reuse analysis. This optimization pairs objects of known size with fresh allocations of the same size and tries to reuse the object in-place at runtime if it happens to be unique. Unfortunately, current implementations of reuse analysis are fragile with respect to small program transformations, or can cause an arbitrary increase in the peak heap usage. We present a novel _drop-guided_ reuse algorithm that is simpler and more robust than previous approaches. Moreover, we generalize the linear resource calculus to precisely characterize garbage-free and frame-limited evaluations. On each function call, a frame-limited evaluation may hold on to memory longer if the size is bounded by a constant factor. Using this framework we show that our drop-guided reuse _is_ frame-limited and find that an implementation of our new reuse approach in Koka can provide significant speedups.

Reference counting with frame limited reuse

Lorenzen

Leijen

2022

Tail Recursion Modulo Context: An Equational Approach

Leijen

Lorenzen

2023

The tail-recursion modulo cons transformation can rewrite functions that are not quite tail-recursive into a tail-recursive form that can be executed efficiently. In this article we generalize tail recursion modulo cons (TRMc) to modulo contexts (TRMC), and calculate a general TRMC algorithm from its specification. We can instantiate our general algorithm by providing an implementation of application and composition on abstract contexts, and showing that our context laws_ hold. We provide some known instantiations of TRMC, namely modulo evaluation contexts (CPS), and associative operations , and further instantiantions not so commonly associated with TRMC, such as defunctionalized evaluation contexts, monoids , semirings , exponents , and cons products . We study the modulo cons instantiation in particular and prove that an instantiation using Minamide’s hole calculus is sound. We also calculate a second instantiation in terms of the Perceus heap semantics to precisely reason about the soundness of in-place update. While all previous approaches to TRMc fail in the presence of non-linear control (for example induced by call/cc, shift/reset or algebraic effect handlers), we can elegantly extend the heap semantics to a hybrid approach which dynamically adapts to non-linear control flow. We have a full implementation of hybrid TRMc in the Koka language and our benchmark shows the TRMc transformed functions are always as fast or faster than using manual alternatives.

FP²: Fully in-Place Functional Programming

Lorenzen,

Leijen,

Swierstra

2023

As functional programmers we always face a dilemma: should we write purely functional code, or sacrifice purity for efficiency and resort to in-place updates? This paper identifies precisely when we can have the best of both worlds: a wide class of purely functional programs can be executed safely using in-place updates without requiring allocation, provided their arguments are not shared elsewhere. We describe a linear _fully in-place_ (FIP) calculus where we prove that we can always execute such functions in a way that requires no (de)allocation and uses constant stack space. Of course, such a calculus is only relevant if we can express interesting algorithms; we provide numerous examples of in-place functions on datastructures such as splay trees or finger trees, together with in-place versions of merge sort and quick sort. We also show how we can generically derive a map function over _any_ polynomial data type that is fully in-place. Finally, we have implemented the rules of the FIP calculus in the Koka language. Using the Perceus reference counting garbage collection, this implementation dynamically executes FIP functions in-place whenever possible.