Abstract
We present a definition of untyped λ-terms using a heterogeneous datatype, i.e. an inductively defined operator. This operator can be extended to a Kleisli triple, which is a concise way to verify the substitution laws for λ-calculus. We also observe that repetitions in the definition of the monad as well as in the proofs can be avoided by using well-founded recursion and induction instead of structural induction. We extend the construction to the simply typed λ-calculus using dependent types, and show that this is an instance of a generalization of Kleisli triples. The proofs for the untyped case have been checked using the LEGO system.
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Altenkirch, T., Reus, B. (1999). Monadic Presentations of Lambda Terms Using Generalized Inductive Types. In: Flum, J., Rodriguez-Artalejo, M. (eds) Computer Science Logic. CSL 1999. Lecture Notes in Computer Science, vol 1683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48168-0_32
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DOI: https://doi.org/10.1007/3-540-48168-0_32
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