doc-src/Tutorial/Misc/Ackermann.thy

proof by cases and induction on types and sets (used to be specific for HOL);

Ackermann = WF_Rel +
consts ack :: "nat * nat => nat"
recdef ack "measure(%m. m) ** measure(%n. n)"
"ack(0,n)         = Suc n"
"ack(Suc m,0)     = ack(m, 1)"
"ack(Suc m,Suc n) = ack(m,ack(Suc m,n))"
end