Kenichi Asai

Polymorphic delimited continuations

This paper presents a polymorphic type system for a language with delimited control operators, shift and reset. Based on the monomorphic type system by Danvy and Filinski, the proposed type system allows pure expressions to be polymorphic. Thanks to the explicit presence of answer types, our type system satisfies various important properties, including strong type soundness, existence of principal types and an inference algorithm, and strong normalization. Relationship to CPS translation as well as extensions to impredicative polymorphism are also discussed. These technical results establish the foundation of polymorphic delimited continuations.

On typing delimited continuations: three new solutions to the printf problem

In “Functional Unparsing” (J. Funct. Program. 8(6):621–625, 1998), Danvy presented a type-safe printf function using continuations and an accumulator to achieve the effect of dependent types. The key technique employed in Danvy’s solution is the non-standard use of continuations: not all of its calls are tail calls, i.e., it uses delimited continuations. Against this backdrop, we present three new solutions to the printf problem: a simpler one that also uses delimited continuations but that does not use an accumulator, and the corresponding two in direct style with the delimited-control operators, shift and reset. These two solutions are the direct-style counterparts of the two continuation-based ones. The last solution pinpoints the essence of Danvy’s solution: shift is used to change the answer type of delimited continuations. Besides providing a new application of shift and reset, the solutions in direct style raise a key issue in the typing of first-class delimited continuations and require Danvy and Filinski’s original type system. The resulting types precisely account for the behavior of printf.

Duplication and partial evaluation: for a better understanding of reflective languages

This paper presents a general implementation framework for reflective languages. It allows us to systematically build reflective languages which have the following favorable properties: (1) user programs are allowed to access and change (parts of) metalevel interpreters, (2) reflective facilities are available at every level, (hence there exists conceptually an infinite tower of interpreters), and (3) the interpreter runs as efficiently as the conventional (directly implemented) metacircular interpreter when reflection is not used. Our scheme is divided into three stages. First, we define interpreters which give the operational semantics of each level, and conceptually construct the infinite tower of these interpreters. They are thenduplicated to obtain directly executed interpreters, while introducing double interpretation to maintain redefinability of interpreters. Finally, partial evaluation is employed to collapse the double interpretation into single interpretation. We illustrate our scheme by implementing a particular reflective language calledBlack in Scheme, but it is general enough to be applied to other reflective languages. The paper gives the complete Scheme implementation of Black and demonstrates some examples. We also show how a system with the delta abstraction introduced by Blond can be constructed in our framework.

Binding-Time Analysis for Both Static and Dynamic Expressions

This paper presents a specializer and a binding-time analyzer for a functional language where expressions are allowed to be used as both static and dynamic. With both static and dynamic expressions, we can statically access data structures while residualizing them at the same time. Previously, such data structures were treated as completely dynamic, which prevented us from accessing their components statically. The technique presented in this paper effectively allows us to lift data structures which was prohibited in the conventional partial evaluators. The binding-time analysis is formalized as a type system and the solution is obtained by solving constraints generated by the type system. We prove the correctness of the constraint solving algorithm and show that the algorithm runs efficiently in almost linear time.

Offline partial evaluation for shift and reset

This paper presents an offline partial evaluator for the λ-calculus with the delimited continuation constructs shift and reset. Based on Danvy and Filinskis type system for shift and reset, we first present a type system that specifies well-annotated terms. We then show a specializer that receives an annotated term and produces the output in continuation-passing style (CPS). The correctness of our partial evaluator is established using the technique of logical relations. Thanks to the explicit reference to the type of continuations, we can establish the correctness using the standard proof technique of structural induction, despite the fact that the specializer itself is written in CPS. The paper also shows an efficient constraint-based binding-time analysis as well as how to extend the present work to richer language constructs, such as recursion and conditionals.

Partial evaluation of call-by-value λ-calculus with side-effects

We present a framework of an online partial evaluator for a call-by-value l-calculus with destructive updates of data structures. It properly and correctly specializes expressions that contain side-effects, while preserving pointer equality, which is an important property for programs using updates. Our partial evaluator uses a side-effect analysis to extract immutable data structures and then performs an online specialization using preactions. Once mutable and immutable data structures are separated, partial evaluation is done in such a way that accesses to immutable ones are performed at specialization time, while accesses to mutable ones are residualized. For the correct residualization of side-effecting operations, preactions are used to solve various issues, including code elimination, code duplication, and execution order preservation. The preaction mechanism also enables us to reduce expressions that were residualized when the conventional let-expression approach of Similix was used. The resulting partial evaluator is simple enough to prove its correctness. Based on the framework, we have constructed a partial evaluator for Scheme, which is powerful enough to specialize fairly complicated programs with side-effects, such as an interpreter.

An Embedded Type Debugger

This paper presents how to build a type debugger without implementing any dedicated type inferencer. Previous type debuggers required their own type inferencers apart from the compiler’s type inferencer. The advantage of our approach is threefold. First, by not implementing a type inferencer, it is guaranteed that the debugger’s type inference never disagrees with the compiler’s type inference. Secondly, we can avoid the pointless reproduction of a type inferencer that should work precisely as the compiler’s type inferencer. Thirdly, our approach is robust to updates of the underlying language. The key observation of our approach is that the interactive type debugging, as proposed by Chitil, does not require a type inference tree but only a tree with a certain simple property. We identify the property and present how to construct a tree that satisfies this property using the compiler’s type inferencer. The property guides us how to build a type debugger for various language constructs. In this paper, we describe our idea and first apply it to the simply-typed lambda calculus. After that, we extend it with let-polymorphism and objects to see how our technique scales.

Binding-time analysis for both static and dynamic expressions

This paper presents a specializer and a binding-time analyzer for a functional language where expressions are allowed to be used as both static and dynamic. With both static and dynamic expressions, data structures can be statically accessed while they are residualized at the same time. Previously, such data structures were treated as completely dynamic, which prevented their components from being accessed statically. The technique presented in this paper effectively allows data structures to be lifted which was prohibited in the conventional partial evaluators. The binding-time analysis is formalized as a type system and the solution is obtained by solving constraints generated by the type system. We prove the correctness of the constraint solving algorithm and show that the algorithm runs efficiently in almost linear time.

Compiling a reflective language using MetaOCaml

A reflective language makes the language semantics open to user programs and allows them to access, extend, and modify it from within the same language framework. Because of its high flexibility and expressiveness, it can be an ideal platform for programming language research as well as practical applications in dynamic environments. However, efficient implementation of a reflective language is extremely difficult. Under the circumstance where the language semantics can change, a partial evaluator is required for compilation. This paper reports on the experience of using MetaOCaml as a compiler for a reflective language. With staging annotations, MetaOCaml achieves the same effect as using a partial evaluator. Unlike the standard partial evaluator, the run mechanism of MetaOCaml enables us to use the specialized (compiled) code in the current runtime environment. On the other hand, the lack of a binding-time analysis in MetaOCaml prohibits us from compiling a user program under modified compiled semantics.

Reflection in direct style

A reflective language enables us to access, inspect, and/or modify the language semantics from within the same language framework. Although the degree of semantics exposure differs from one language to another, the most powerful approach, referred to as the behavioral reflection, exposes the entire language semantics (or the language interpreter) that defines behavior of user programs for user inspection/modification. In this paper, we deal with the behavioral reflection in the context of a functional language Scheme. In particular, we show how to construct a reflective interpreter where user programs are interpreted by the tower of metacircular interpreters and have the ability to change any parts of the interpreters during execution. Its distinctive feature compared to the previous work is that the metalevel interpreters observed by users are written in direct style. Based on the past attempt of the present author, the current work solves the level-shifting anomaly by defunctionalizing and inspecting the top of the continuation frames. The resulting system enables us to freely go up and down the levels and access/modify the direct-style metalevel interpreter. This is in contrast to the previous system where metalevel interpreters were written in continuation-passing style (CPS) and only CPS functions could be exposed to users for modification.