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Finally tagless observable recursion for an abstract grammar model

Part of: JFP Research Articles

Published online by Cambridge University Press:  10 July 2012

DOMINIQUE DEVRIESE  and
FRANK PIESSENS
DOMINIQUE DEVRIESE
Affiliation:
IBBT-Distrinet, KU Leuven, Belgium (e-mail: dominique.devriese@cs.kuleuven.be, frank.piessens@cs.kuleuven.be)
FRANK PIESSENS
Affiliation:
IBBT-Distrinet, KU Leuven, Belgium (e-mail: dominique.devriese@cs.kuleuven.be, frank.piessens@cs.kuleuven.be)
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Abstract

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We define a finally tagless, shallow embedding of a typed grammar language. In order to avoid the limitations of traditional parser combinator libraries (no bottom-up parsing, no full grammar analysis or transformation), we require object-language recursion to be observable in the meta-language. Since existing proposals for recursive constructs are not fully satisfactory, we propose new finally tagless primitive recursive constructs to solve the problem. To do this in a well-typed way, we require considerable infrastructure, for which we reuse techniques from the multirec generic programming library. Our infrastructure allows a precise model of the complex interaction between a grammar, a parsing algorithm and a set of semantic actions. On the flip side, our approach requires the grammar author to provide a type- and value-level encoding of the grammar's domain and we can provide only a limited form of constructs like many. We demonstrate five meta-language grammar algorithms exploiting our model, including a grammar pretty-printer, a reachability analysis, a translation of quantified recursive constructs to the standard one and an implementation of the left-corner grammar transform. The work we present forms the basis of the grammar-combinators parsing library1, which is the first to work with a precise, shallow model of abstract context-free grammars in a classical (not dependently typed) functional language and which supports a wide range of grammar manipulation primitives. From a more general point of view, our work shows a solution to the well-studied problem of observable sharing in shallowly embedded domain-specific languages and specifically in finally tagless domain-specific languages.

Type
Articles
Information
Journal of Functional Programming , Volume 22 , Issue 6 , November 2012 , pp. 757 - 796
Copyright
Copyright © Cambridge University Press 2012

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