An Operational Foundation for Delimited Continuations in the CPS Hierarchy

We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in continuation-passing style (CPS); the reduction semantics (i.e., a small-step operational semantics with an explicit representation of evaluation contexts) is constructed from the abstract machine; and the control operators are the shift and reset family. At level n of the CPS hierarchy, programs can use the control operators shift_i and reset_i for

An Operational Foundation for Delimited Continuations in the CPS Hierarchy

We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in continuation-passing style (CPS); the reduction semantics (i.e., a small-step operational semantics with an explicit representation of evaluation contexts) is constructed from the abstract machine; and the control operators are the shift and reset family. At level n of the CPS hierarchy, programs can use the control operators shift_i and reset_i for

An Operational Foundation for Delimited Continuations in the CPS Hierarchy

We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in continuation-passing style (CPS); the reduction semantics (i.e., a small-step operational semantics with an explicit representation of evaluation contexts) is constructed from the abstract machine; and the control operators are the shift and reset family. At level n of the CPS hierarchy, programs can use the control operators shift_i and reset_i for

An Operational Foundation for Delimited Continuations in<br><br> the<br><br><br> CPS<br><br> Hierarchy

We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in continuation-passing style (CPS); the reduction semantics (i.e., a small-step operational semantics with an explicit representation of evaluation contexts) is constructed from the abstract machine; and the control operators are the shift and reset family. We also present new applications of delimited continuations in the CPS hierarchy: finding list prefixes and normalization by evaluation for a hierarchical language of units and products.Comment: 39 page

Logical relations for coherence of effect subtyping

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing

An Operational Foundation for Delimited Continuations

We derive an abstract machine that corresponds to a definitional interpreter for the control operators shift and reset. Based on this abstract machine, we construct a syntactic theory of delimited continuations. Both the derivation and the construction scale to the family of control operators shift_n and reset_n. The definitional interpreter for shift_n and reset_n has n + 1 layers of continuations, the corresponding abstract machine has n + 1 layers of control stacks, and the corresponding syntactic theory has n + 1 layers of evaluation contexts.See also BRICS-RS-05-24

Proving termination of evaluation for System F with control operators

We present new proofs of termination of evaluation in reduction semantics (i.e., a small-step operational semantics with explicit representation of evaluation contexts) for System F with control operators. We introduce a modified version of Girard's proof method based on reducibility candidates, where the reducibility predicates are defined on values and on evaluation contexts as prescribed by the reduction semantics format. We address both abortive control operators (callcc) and delimited-control operators (shift and reset) for which we introduce novel polymorphic type systems, and we consider both the call-by-value and call-by-name evaluation strategies.Comment: In Proceedings COS 2013, arXiv:1309.092

A Rational Deconstruction of Landin's SECD Machine with the J Operator

Landin's SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin's J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continu-ation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke's double-barrelled continuations and to Felleisen's encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. These reduction semantics mechanically correspond to the modernized versions of the SECD machine and to the best of our knowledge, they provide the first syntactic theories of applicative expressions with the J operator

A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations

We present a new abstract machine that accounts for dynamic delimited continuations. We prove the correctness of this new abstract machine with respect to a pre-existing, definitional abstract machine. Unlike this definitional abstract machine, the new abstract machine is in defunctionalized form, which makes it possible to state the corresponding higher-order evaluator. This evaluator is in continuation+state passing style and threads a trail of delimited continuations and a meta-continuation. Since this style accounts for dynamic delimited continuations, we refer to it as `dynamic continuation-passing style.' We show that the new machine operates more efficiently than the definitional one and that the notion of computation induced by the corresponding evaluator takes the form of a monad. We also present new examples and a new simulation of dynamic delimited continuations in terms of static ones