Abstract
We give a coalgebraic account of context-free languages using the functor \({\mathcal D}(X) = 2 \times X^A\) for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing context-free grammars as \({\mathcal D}\)-coalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. \({\mathcal D}\)) for which the unique solutions are precisely the context-free languages; and (iii) as the \({\mathcal D}\)-coalgebra of generalized regular expressions in which the Kleene star is replaced by a unique fixed point operator. In all cases, semantics is defined by the unique homomorphism into the final coalgebra of all languages, paving the way for coinductive proofs of context-free language equivalence. Furthermore, the three characterizations can serve as the basis for the definition of a general coalgebraic notion of context-freeness, which we see as the ultimate long-term goal of the present study.
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Winter, J., Bonsangue, M.M., Rutten, J. (2011). Context-Free Languages, Coalgebraically. In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_25
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DOI: https://doi.org/10.1007/978-3-642-22944-2_25
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