[Haskell-cafe] Gödel's System T

Petr Pudlak deb at pudlak.name
Wed Nov 10 13:42:00 EST 2010


I was reading the paper "Total Functional Programming" [1]. I 
encountered an interesting note on p. 759 that primitive recursion in a 
higher-order language allows defining much larger set of function than 
classical primitive recursion (which, for example, cannot define 
Ackermann's function). And that this is studied in in Gödel's System T. 
It also states that this larger set of primitive functions includes all 
functions whose totality can be proved in first order logic.

I was searching the Internet but I couldn't find a resource (a paper, a 
book) that would explain this in detail, give proofs etc. I'd be happy 
if someone could give me some directions.


[1] http://www.jucs.org/jucs_10_7/total_functional_programming/jucs_10_07_0751_0768_turner.pdf
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