Bindings as bounded natural functors

We present a general framework for specifying and reasoning about syntax with bindings. Abstract binder types are modeled using a universe of functors on sets, subject to a number of operations that can be used to construct complex binding patterns and binding-aware datatypes, including non-well-fou...

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Bibliographic Details
Published inProceedings of ACM on programming languages Vol. 3; no. POPL; pp. 1 - 34
Main Authors Blanchette, Jasmin Christian, Gheri, Lorenzo, Popescu, Andrei, Traytel, Dmitriy
Format Journal Article
LanguageEnglish
Published New York, NY, USA ACM 02.01.2019
Subjects
Computer Science
Higher order logic
Logic
Logic and verification
Logic in Computer Science
Program constructs
Semantics and reasoning
Theory of computation
Type structures
syntax with bindings
proof assistants
inductive and coinductive datatypes
Type struc-tures
Theory of computation → Logic and verification
Higher order logic
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Summary:We present a general framework for specifying and reasoning about syntax with bindings. Abstract binder types are modeled using a universe of functors on sets, subject to a number of operations that can be used to construct complex binding patterns and binding-aware datatypes, including non-well-founded and infinitely branching types, in a modular fashion. Despite not committing to any syntactic format, the framework is ``concrete'' enough to provide definitions of the fundamental operators on terms (free variables, alpha-equivalence, and capture-avoiding substitution) and reasoning and definition principles. This work is compatible with classical higher-order logic and has been formalized in the proof assistant Isabelle/HOL.
ISSN:2475-1421
2475-1421
DOI:10.1145/3290335