Abstract
A generalization of positive inductive and coinductive types to monotone inductive and coinductive constructors of rank 1 and rank 2 is described. The motivation is taken from initial algebras and final coalgebras in a functor category and the Curry-Howard-correspondence. The definition of the system as a λ-calculus requires an appropriate definition of monotonicity to overcome subtle problems, most notably to ensure that the (co-) inductive constructors introduced via monotonicity of the underlying constructor of rank 2 are also monotone as constructors of rank 1. The problem is solved, strong normalization shown, and the notion proven to be wide enough to cover even highly complex datatypes.
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Matthes, R. (2001). Monotone Inductive and Coinductive Constructors of Rank 2. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_42
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DOI: https://doi.org/10.1007/3-540-44802-0_42
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