Compositional Coinduction with Sized Types

Abstract : Proofs by induction on some inductively defined structure, e. g., finitely-branching trees, may appeal to the induction hypothesis at any point in the proof, provided the induction hypothesis is only used for immediate substructures, e. g., the subtrees of the node we are currently considering in the proof. The basic principle of structural induction can be relaxed to course-of-value induction, which allows application of the induction hypothesis also to non-immediate substructures, like any proper subtree of the current tree. If course-of-value induction is not sufficient yet, we can resort to define a well-founded relation on the considered structure and use the induction hypothesis for any substructure which is strictly smaller with regard to the constructed relation.
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Andreas Abel. Compositional Coinduction with Sized Types. 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2016, Eindhoven, Netherlands. pp.5-10, ⟨10.1007/978-3-319-40370-0_2⟩. ⟨hal-01446030⟩

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