## A type theory for probabilistic $$\lambda$$-calculus.(English)Zbl 1440.68043

Di Pierro, Alessandra (ed.) et al., From lambda calculus to cybersecurity through program analysis. Essays dedicated to Chris Hankin on the occasion of his retirement. Cham: Springer. Lect. Notes Comput. Sci. 12065, 86-102 (2020).
Summary: We present a theory of types where formulas may contain a choice constructor. This constructor allows for the selection of a particular type among a finite set of options, each corresponding to a given probabilistic term. We show that this theory induces a type assignment system for the probabilistic $$\lambda$$-calculus introduced in an earlier work by Chris Hankin, Herbert Wiklicky and the author, where probabilistic terms represent probability distributions on classical terms of the simply typed $$\lambda$$-calculus. We prove the soundness of the type assignment with respect to a probabilistic term reduction and a normalization property of the latter.
For the entire collection see [Zbl 1435.68026].

### MSC:

 68N18 Functional programming and lambda calculus 03B40 Combinatory logic and lambda calculus

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### References:

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