[FOM] historical question

Jaap van Oosten jvoosten at math.uu.nl
Thu Dec 15 08:45:15 EST 2005

Who invented partial combinatory algebras?

I know that Schönfinkel (and later Curry) invented
total combinatory algebras, that Feferman in his
paper "A language and axioms for explicit mathematics"
works with a partial application (but what he defines
there is now called a "typed partial combinatory algebra",
and that usually Beeson's book (1985) is credited with
the definition (also by Beeson himself, in a recent
paper "Lambda Logic").
But the definition appears in the Ph.D. thesis of Andy
Pitts (1980), 5 years earlier. Is this the first
appearance in print of this definition?

Jaap van Oosten 

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