Abstract
Inductive type theories, as used in systems like Coq or Lego [11,14,4], provide a systematic approach to program recursive functions over inductive data-structures and to reason about these functions. Recursive computation is described by reduction rules, included in the type system under the name ι-reduction. If t is an element of a recursive type, f is a recursive function over that type and v is the value of f(t), then the equality f(t) = v is a simple tautology, because f(t) and v are equal modulo ι-reduction.
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Balaa, A., Bertot, Y. (2000). Fix-Point Equations for Well-Founded Recursion in Type Theory. In: Aagaard, M., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2000. Lecture Notes in Computer Science, vol 1869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44659-1_1
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DOI: https://doi.org/10.1007/3-540-44659-1_1
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