Directly reflective meta-programming

Stump, Aaron

doi:10.1007/s10990-007-9022-0

Cited by 13 publications

(3 citation statements)

References 35 publications

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“…The axiomatic semantics of HGMP is explored in [2]. Some original approaches towards the foundations of run-time HGMP are: M-LISP [26] which provides an operational semantics for a simplified Lisp variant with eval but without macros; Archon [34], which is based on the untyped λ-calculus but without an explicit representation of code; the two-level λ-calculus [15] which is based on nominal techniques; and the ρ-calculus [25] which combines ideas from Conway games and π-calculus.…”

Section: :20mentioning

confidence: 99%

Program Logics for Homogeneous Generative Run-Time Meta-Programming

Berger

Tratt

2015

Logical Methods in Computer Science

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Abstract. This paper provides the first program logic for homogeneous generative runtime meta-programming-using a variant of MiniML e by Davies and Pfenning as its underlying meta-programming language. We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics.Dedicated to the memory of Kohei Honda.

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Section: :20mentioning

confidence: 99%

Program Logics for Homogeneous Generative Run-Time Meta-Programming

Berger

Tratt

2015

Logical Methods in Computer Science

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“…To gain some insight into the construction defined above, one can observe that it is related to an encoding of data attributed to Scott 3 (and thus commonly referred to in the literature as the Scott encoding), which has subsequently been developed by others (e.g. [30,27,16,31]). In the more familiar 'standard' encoding of functions, a fixed-point combinator is used to solve any recursion in the definition.…”

Section: T K Beginning With T I ;mentioning

confidence: 99%

Encoding the Factorisation Calculus

Rowe

2015

Electron. Proc. Theor. Comput. Sci.

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Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the internal structure of its first argument. The calculus is significant in that as well as being combinatorially complete it also exhibits the property of structural completeness, i.e. it is able to represent any function on terms definable using pattern matching on arbitrary normal forms. In particular, it admits a term that can decide the structural equality of any two arbitrary normal forms. Since SF-calculus is combinatorially complete, it is clearly at least as powerful as the more familiar and paradigmatic Turing-powerful computational models of Lambda Calculus and Combinatory Logic. Its relationship to these models in the converse direction is less obvious, however. Jay and Given-Wilson have suggested that SF-calculus is strictly more powerful than the aforementioned models, but a detailed study of the connections between these models is yet to be undertaken. This paper begins to bridge that gap by presenting a faithful encoding of the Factorisation Calculus into the Lambda Calculus preserving both reduction and strong normalisation. The existence of such an encoding is a new result. It also suggests that there is, in some sense, an equivalence between the former model and the latter. We discuss to what extent our result constitutes an equivalence by considering it in the context of some previously defined frameworks for comparing computational power and expressiveness.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634

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“…This encoding is relatively unknown, and independently (re)discovered by several authors (e.g. [9,8,10] and the author of this paper [6]), but originally attributed to Scott in an unpublished lecture which is cited in Curry, Hindley and Seldin ( [4] 1 We will therefore call it the Scott encoding. The encoding results in a representation that is very close to algebraic data types as they are used in most functional programming languages.…”

Section: The Church and Scott Encodings For Algebraic Data Typesmentioning

confidence: 99%

Programming in the λ-Calculus: From Church to Scott and Back

Jansen

2013

Lecture Notes in Computer Science

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Abstract. Although the λ-calculus is well known as a universal programming language, it is seldom used for actual programming or expressing algorithms. Here we demonstrate that it is possible to use the λ-calculus as a comprehensive formalism for programming by showing how to convert programs written in functional programming languages like Clean and Haskell to closed λ-expressions. The transformation is based on using the Scott-encoding for Algebraic Data Types instead of the more common Church encoding. In this way we not only obtain an encoding that is better comprehensible but that is also more efficient. As a proof of the pudding we provide an implementation of Eratosthenes' prime sieve algorithm as a self-contained, 143 character length, λ-expression.

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Directly reflective meta-programming

Cited by 13 publications

References 35 publications

Program Logics for Homogeneous Generative Run-Time Meta-Programming

Program Logics for Homogeneous Generative Run-Time Meta-Programming

Encoding the Factorisation Calculus

Programming in the λ-Calculus: From Church to Scott and Back

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