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We present a probabilistic version of PCF, a well-known simply typeduniversal functional language. The type hierarchy is based on a single groundtype of natural numbers. Even if the language is globally call-by-name, weallow a call-by-value evaluation for ground type arguments in order to providethe language with a suitable algorithmic expressiveness. We describe adenotational semantics based on probabilistic coherence spaces, a model ofclassical Linear Logic developed in previous works. We prove an adequacy and anequational full abstraction theorem showing that equality in the modelcoincides with a natural notion of observational equivalence.

Full abstraction for probabilistic PCF