Self-applicable online partial evaluation of the pure lambda calculus

Mogensen, Torben Ægidius

doi:10.1145/215465.215469

Cited by 28 publications

(23 citation statements)

References 6 publications

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“…They show that their ai-based approach is more powerful than Mogensen's approach [25] which is more powerful than Gomard's [14] approach. In view of the current work, the latter is not surprising because more terms are typable in the presence of recursive types.…”

Section: Comparison Of the Equational And Inclusion-based Btasmentioning

confidence: 99%

“…Henglein's algorithm [18] performs the entire reconstruction for this system in almost-linear time. Strictly speaking, we are discussing Mogensen's system [25] because Gomard and Henglein disallow recursive types. Hence, the inclusion-based BTA builds on an extension of the equational flow-type system with subtyping, _L, and T types.…”

Section: Another Variation Of Equational Btamentioning

confidence: 99%

“…Here, we only discuss additional work that has not been discussed in the body of the paper. Mogensen [25] was the first one to consider BTA based on recursive types. His motivation was typing Y in order to unfold fixpoints statically.…”

Section: Comparison Of the Equational And Inclusion-based Btasmentioning

confidence: 99%

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A unified framework for binding-time analysis

Thiemann

1997

TAPSOFT '97: Theory and Practice of Software Development

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Abstract. Binding-time analysis is a crucial part of o~ine partial evaluation. It is often specified as a non-standard type system. Many typebased binding-time analyses are reminiscent of simple type systems with additional features like recursive types. We make this connection explicit by expressing binding-time analysis with annotated type systems that separate the concerns of type inference from those of binding-time annotation. The separation enables us to explore a design space for bindingtime analysis by varying the underlying type system and the annotation strategy independently. The result is a classification of different monova~iant binding-time analyses which allows us to compare their relative power. Due to the systematic approach we uncover some novel analyses.A partial evaluator separates the computation of a source program into two or more stages [7,20]. Using the (static) input of the first stage it transforms a source program into a specialized residual program. Application of the residual program to the (dynamic) input of the second stage yields the same answer as application of the source program to the entire input. The binding time of an input is the information whether it is static or dynamic.Binding-time analysis (BTA) is a prepass of a partial evaluator that annotates each expression in the source program with the earliest (static is earlier than dynamic) time at which it can be evaluated. The actual specializer is a mere interpreter of annotated programs that executes the static expressions and generates code for the remaining ones.Binding-time analyses come in two flavors: A monovariant BTA computes a single mapping of program points to binding-times, whereas a polyvariant BTA allows for several such mappings. Both alternatives have their merits. Monovariant BTAs are simple and efficient to implement [4,14,15,18,20]. However, in some applications static and dynamic values flow through the same program points, which forces a monovariant BTA to annotate the program points as dynamic. A polyvariant BTA [5,6] yields better results in these cases, but is also considerably more expensive.In the current work we concentrate on monovariant BTAs for the lambda calculus as they are used in many partial evaluators I4, 14,15,18]. Our analyses achieve some degree of polyvariance because we admit liberal binding-time coercions and rely on a more precise inclusion-based flow analysis framework.BTA is often presented as a monolithic analysis which makes it unnecessarily hard to understand and to reason about [2,3,14,18,21]. Recent work has shown the possibility to modularize BTA into several stages [4,12,13]. All of these

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Section: Comparison Of the Equational And Inclusion-based Btasmentioning

confidence: 99%

Section: Another Variation Of Equational Btamentioning

confidence: 99%

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A unified framework for binding-time analysis

Thiemann

1997

TAPSOFT '97: Theory and Practice of Software Development

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“…Hence, we delay the recursion until the right-hand side has been reduced. A similar trick was used in [4]:…”

Section: Comparing Different Number Basesmentioning

confidence: 99%

An Investigation of Compact and Efficient Number Representations in the Pure Lambda Calculus

Mogensen

2001

Lecture Notes in Computer Science

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“…Palsberg presents a generalization of Gomard and Jones criteria [7] for consistent binding-time annotations. Wand studies Mogensen's self-applicable partial evaluator [18] for the pure λ-calculus. His binding-time analysis is essentially the same as Gomard and Jones's as well the one presented here.…”

Section: Related Workmentioning

confidence: 99%

Mechanically verifying the correctness of an offline partial evaluator

Hatcliff¹

1995

Programming Languages: Implementations, Logics and Programs

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Abstract. We show that using deductive systems to specify an offline partial evaluator allows one to specify, prototype, and mechanically verify correctness via meta-programming -all within a single framework. For a λ-mix-style partial evaluator, we specify binding-time constraints using a natural-deduction logic, and the associated program specializer using natural (aka "deductive") semantics. These deductive systems can be directly encoded in the Elf programming language -a logic programming language based on the LF logical framework. The specifications are then executable as logic programs. This provides a prototype implementation of the partial evaluator. Moreover, since deductive system proofs are accessible as objects in Elf, many aspects of the partial evaluator correctness proofs (e.g., the correctness of binding-time analysis) can be coded in Elf and mechanically checked.

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Self-applicable online partial evaluation of the pure lambda calculus

Cited by 28 publications

References 6 publications

A unified framework for binding-time analysis

A unified framework for binding-time analysis

An Investigation of Compact and Efficient Number Representations in the Pure Lambda Calculus

Mechanically verifying the correctness of an offline partial evaluator

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