Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.
To see that, it is enough to take any enumeration (a 1, ..., an) ofµ 0, and to consider the program: P:= if(x̸=a 1)(⋆)( if (x̸=a 2)(⋆)(if....)))
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Interpreting De Finetti's theorem in the Category of Integrable Cones (long version)
Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.