Abstract
This work describes the proof and uses of a theorem allowing definition of recursive functions over the type of λ-calculus terms, where terms with bound variables are identified up to α-equivalence. The theorem embodies what is effectively a principle of primitive recursion, and the analogues of this theorem for other types with binders are clear. The theorem’s side-conditions require that the putative definition be well-behaved with respect to fresh name generation and name permutation. A number of examples over the type of λ-calculus terms illustrate the use of the new principle.
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References
Ambler, S.J., Crole, R.L., Momigliano, A.: A definitional approach to primitive recursion over higher order abstract syntax. In: Honsell et al. [6], Available at http://doi.acm.org/10.1145/976571.976572
Barendregt, H.P.: The Lambda Calculus: its Syntax and Semantics, revised edn. Studies in Logic and the Foundations of Mathematics, vol. 103. Elsevier, Amsterdam (1984)
Gabbay, M.J.: A Theory of Inductive Definitions with Alpha-Equivalence. PhD thesis, University of Cambridge (2001)
Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax involving binders. In: 14th Annual Symposium on Logic in Computer Science, pp. 214–224. IEEE Computer Society Press, Washington (1999)
Gordon, D., Melham, T.: Five axioms of alpha conversion. In: von Wright, J., Harrison, J., Grundy, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 173–190. Springer, Heidelberg (1996)
Honsell, F., Miculan, M., Momigliano, A. (eds.): Merlin 2003, Proceedings of the Second ACM SIGPLAN Workshop on Mechanized Reasoning about Languages with Variable Binding. ACM Digital Library (2003)
Norrish, M.: Mechanising Hankin and Barendregt using the Gordon-Melham axioms. In: Honsell et al. [6], Available at http://doi.acm.org/10.1145/976571.976577
Schürmann, C., Despeyroux, J., Pfenning, F.: Primitive recursion for higherorder abstract syntax. Theoretical Computer Science 266(1-2), 1–57 (2001)
Washburn, G., Weirich, S.: Boxes go bananas: Encoding higher-order abstract syntax with parametric polymophism. In: ICFP 2003: Proceedings of the Eighth ACM SIGPLAN International Conference on Functional Programming, pp. 249–262. ACM Press, New York (2003)
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Norrish, M. (2004). Recursive Function Definition for Types with Binders. In: Slind, K., Bunker, A., Gopalakrishnan, G. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2004. Lecture Notes in Computer Science, vol 3223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30142-4_18
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DOI: https://doi.org/10.1007/978-3-540-30142-4_18
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