NB. Definitions used in the Algorithms Chapter

sum_ones =: monad def 0
if. y. = 0
  do. 0
  else. 1 + sum_ones y. - 1
end.
)

traced_sum_ones =: monad def 0
entering y.
if. y. = 0
  do. leaving 0
  else. leaving 1 + traced_sum_ones y. - 1
end.
)

sum_ones1 =: monad def 'sum_ones_iter y. , 0 1'

sum_ones_iter =: monad def 0
('n' ; 'acc' ; 'i') =. y.
if. i > n
  do. acc
  else. sum_ones_iter n , (acc + 1) , i + 1
end.
)

traced_sum_ones1 =: monad def 'traced_sum_ones_iter y. , 0 1'

traced_sum_ones_iter =: monad def 0
entering y.
('n' ; 'acc' ; 'i') =. y.
if. i > n
  do. leaving acc
  else. traced_sum_ones_iter n , (acc + 1) , i + 1
end.
)

sum =: monad def 0
if. y. = 0
  do. 0
  else. y. + sum y. - 1
end.
)

traced_sum =: monad def 0
entering y.
if. y. = 0
  do. leaving 0
  else. leaving y. + traced_sum y. - 1
end.
)

sum1 =: monad def 'sum_iter y. , 0 1'

sum_iter =: monad def 0
('n' ; 'acc' ; 'i') =. y.
if. i > n
  do. acc
  else. sum_iter n , (acc + i) , i + 1
end.
)

traced_sum1 =: monad def 'traced_sum_iter y. , 0 1'

traced_sum_iter =: monad def 0
entering y.
('n' ; 'acc' ; 'i') =. y.
if. i > n
  do. leaving acc
  else. traced_sum_iter n , (acc + i) , i + 1
end.
)

fact =: monad def 0
if. y. < 2
  do. 1
  else. y. * fact y. - 1
end.
)

traced_fact =: monad def 0
entering y.
if. y. < 2
  do. leaving 1
  else. leaving y. * traced_fact y. - 1
end.
)

fact1 =: monad def 'fact_iter y. , 1 1'

fact_iter =: monad def 0
('n' ; 'acc' ; 'i') =. y.
if. i > n
  do. acc
  else. fact_iter n , (i * acc) , i + 1
end.
)

traced_fact1 =: monad def 'traced_fact_iter y. , 1 1'

traced_fact_iter =: monad def 0
entering y.
('n' ; 'acc' ; 'i') =. y.
if. i > n
  do. leaving acc
  else. traced_fact_iter n , (i * acc) , i + 1
end.
)

fibonacci =: monad def 0
if. y. < 2 
  do. y.
  else. (fibonacci y. - 1) + fibonacci y. - 2
end.
)

traced_fibonacci =: monad def 0
entering y.
if. y. < 2
  do. leaving y.
  else. leaving (traced_fibonacci y. - 1) + traced_fibonacci y. -2
end.
)

fib_work =: monad def 0
if. y. < 2
  do. 1
  else. 1 + (fib_work y. - 1) + fib_work y. - 2
end.
)

fibonacci1 =: monad def 'fib_iter 1 0 , y.'

fib_iter =: monad def 0
('a' ; 'b' ; 'count') =. y.
if. count = 0
  do. b
  else. fib_iter (a + b) , a , count - 1
end.
)

traced_fibonacci1 =: monad def 'traced_fib_iter 1 0 , y.'

traced_fib_iter =: monad def 0
entering y.
('a' ; 'b' ; 'count') =. y.
if. count = 0
  do. leaving b
  else. leaving traced_fib_iter (a + b) , a , count - 1
end.
)