Executable higher-order algebraic specifications

  • Jean-Pierre Jouannaud
Invited Lectures

DOI: 10.1007/BFb0020784

Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)
Cite this paper as:
Jouannaud JP. (1991) Executable higher-order algebraic specifications. In: Choffrut C., Jantzen M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg


Conventional algebraic specifications are first-order. Using higher-order equations in combination with first-order ones raises several fundamental model-theoretic and proof-theoretic questions. The model theory of higher-order equations is well understood (see [20] for a survey of algebraic specifications). The proof theory of higher-order equations is equally well understood, it requires higher- order matching, and higher-order rewriting therefore providing with a simple execution model. Higher-order variables may be instantiated by functions described by λ-expressions, bringing in λ-calculus, whose execution model is again rewriting (β-redexes). Hence rewriting is at the heart of all three execution models, which makes their combination quite simple on the operational side. The main question reviewed in this paper is whether the Church-Rosser and termination properties of these three execution models are preserved within their combination. We will see that the answer is to a large extent positive.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Jean-Pierre Jouannaud
    • 1
  1. 1.Laboratoire de Recherche en Informatique Bat. 490Orsay CedexFrance

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