NB. Definitions for Program Execution Time

maximum =: monad def 'max_helper (rest y.) ; head y.'

max_helper =: monad define
('ls' ; 'max') =. y.
if. nullp ls
    do. max
  elseif. max < head ls
    do. max_helper (rest ls) ; head ls
  elseif. 1
    do. max_helper (rest ls) ; max
end.
)

traced_maximum =: monad def 'traced_max_helper (rest y.) ; head y.'

traced_max_helper =: monad define
entering y.
('ls' ; 'max') =. y.
if. nullp ls
    do. max
  elseif. max < head ls
    do. leaving traced_max_helper (rest ls) ; head ls
  elseif. 1
    do. leaving traced_max_helper (rest ls) ; max
end.
)

sort_pass =: monad define
NB. stop when we have a list of two items
if. nullp rest rest y.
  do. if. (head y.) < head rest y.
        do. y.
        else. reverse y.
      end.
  else. one =. head y.
        two =. head rest y.
       if. one < two
         do. one append sort_pass rest y.
         else. two append sort_pass one append rest rest y.
       end.
end.
)

traced_sort_pass =: monad define
NB. stop when we have a list of two items
entering y.
if. nullp rest rest y.
  do. if. (head y.) < head rest y.
        do. leaving y.
        else. leaving reverse y.
      end.
  else. one =. head y.
        two =. head rest y.
       if. one < two
         do. leaving one append traced_sort_pass rest y.
         else. leaving two append traced_sort_pass one append rest rest y.
       end.
end.
)

sort =: monad define
NB. stop when we have a list of two items
if. nullp rest rest y.
  do. sort_pass y.
  else. result =. sort_pass y.
        (sort drop_last result) append last result
end.
)

traced_sort =: monad define
NB. stop when we have a list of two items
entering y.
if. nullp rest rest y.
  do. leaving sort_pass y.
  else. result =. sort_pass y.
        leaving (traced_sort drop_last result) append last result
end.
)

show_move =: monad def 'display (0 from y.) , '' -> '' , 1 from y.'

move =: monad define
('n' ; 'src' ; 'dst' ; 'hlp') =. y.
if. n = 1
  do. show_move src , dst
  else. move (n - 1) ; src ; hlp ; dst
        show_move src , dst
        move (n - 1) ; hlp ; dst ; src
end.
)

display_tower_hanoi =: monad def '0$move y. ; ''a'' ; ''c'' ; ''b'''