Toward a general theory of names: binding and scope

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Toward a general theory of names: binding and scope (2005)

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by James Cheney

Venue:	In MERLIN ’05: Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized
Citations:	6 - 0 self

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@INPROCEEDINGS{Cheney05towarda,
    author = {James Cheney},
    title = {Toward a general theory of names: binding and scope},
    booktitle = {In MERLIN ’05: Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized},
    year = {2005},
    pages = {33--40},
    publisher = {ACM Press}
}

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Abstract

High-level formalisms for reasoning about names and binding such as de Bruijn indices, various flavors of higher-order abstract syntax, the Theory of Contexts, and nominal abstract syntax address only one relatively restrictive form of scoping: namely, unary lexical scoping, in which the scope of a (single) bound name is a subtree of the abstract syntax tree (possibly with other subtrees removed due to shadowing). Many languages exhibit binding or renaming structure that does not fit this mold. Examples include binding transitions in the pi-calculus; unique identifiers in contexts, mem-ory heaps, and XML documents; declaration scoping in modules and namespaces; anonymous identifiers in automata, type schemes, and Horn clauses; and pattern matching and mutual recursion con-structs in functional languages. In these cases, it appears necessary to either rearrange the abstract syntax so that lexical scoping can be used, or revert to first-order techniques. The purpose of this paper is to catalogue these “exotic ” binding, renaming, and structural congruence situations; to argue that lexical scoping-based syntax techniques are sometimes either inappropri-ate or incapable of assisting in such situations; and to outline tech-niques for formalizing and proving properties of languages with more general forms of renaming and other structural congruences.

Keyphrases

general theory abstract syntax bruijn index unique identifier declaration scoping restrictive form first-order technique lexical scoping-based syntax technique structural congruence situation exotic binding horn clause high-level formalism mem-ory heap anonymous identifier lexical scoping unary lexical scoping functional language various flavor general form structural congruence nominal abstract syntax address type scheme higher-order abstract syntax bound name xml document many language mutual recursion con-structs abstract syntax tree

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