Lazy Evaluation and Delimited Control

The call-by-need lambda calculus provides an equational framework for reasoning syntactically about lazy evaluation. This paper examines its operational characteristics. By a series of reasoning steps, we systematically unpack the standard-order reduction relation of the calculus and discover a novel abstract machine definition which, like the calculus, goes "under lambdas." We prove that machine evaluation is equivalent to standard-order evaluation. Unlike traditional abstract machines, delimited control plays a significant role in the machine's behavior. In particular, the machine replaces the manipulation of a heap using store-based effects with disciplined management of the evaluation stack using control-based effects. In short, state is replaced with control. To further articulate this observation, we present a simulation of call-by-need in a call-by-value language using delimited control operations

No value restriction is needed for algebraic effects and handlers

We present a straightforward, sound Hindley-Milner polymorphic type system for algebraic effects and handlers in a call-by-value calculus, which allows type variable generalisation of arbitrary computations, not just values. This result is surprising. On the one hand, the soundness of unrestricted call-by-value Hindley-Milner polymorphism is known to fail in the presence of computational effects such as reference cells and continuations. On the other hand, many programming examples can be recast to use effect handlers instead of these effects. Analysing the expressive power of effect handlers with respect to state effects, we claim handlers cannot express reference cells, and show they can simulate dynamically scoped state

Tabling as a Library with Delimited Control

Tabling is probably the most widely studied extension of Prolog. But despite its importance and practicality, tabling is not implemented by most Prolog systems. Existing approaches require substantial changes to the Prolog engine, which is an investment out of reach of most systems. To enable more widespread adoption, we present a new implementation of tabling in under 600 lines of Prolog code. Our lightweight approach relies on delimited control and provides reasonable performance.Comment: 15 pages. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201