Accumulators
Compare the following two definitions of the
list-length predicate. Do a trace to see how the
result is computed.
list_length1([],0).
list_length1([_|Tail],Length) :-
list_length1(Tail,TailLength),
Length is TailLength + 1.
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list_length2(List,Length) :- list_length2(List,0,Length).
list_length2([],Length,Length).
list_length2([_|Tail],Accumulator,Length) :-
NewAcc is Accumulator + 1,
list_length2(Tail,NewAcc,Length).
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The main difference that you can observe when doing a trace is
that list_length1 computes the result when coming
out of the recursion, while list_length2 computes
the result while going into the recursion. At the time where the
bottom of the recursion (the empty list) has been reached, the
length of the list has already been established. To be able to
do this, list_length2 uses an accumulator,
i.e., an argument for storing intermediate results. In the
beginning, the accumulator is instantiated with 0. In each
recursive call, the accumulator argument is increased by one (to
indicate that one more list element has been processed). By the
time the empty list is reached, the accumulator argument
contains a number corresponding to the length of the list.
The accumulator adds an extra argument to the predicate which has to be instantiated when the predicate is first called. We use a wrapper predicate to do this automatically:
list_length2(List,Length) :- list_length2(List,0,Length).
Define an accumulator version of the predicate
max/2 that you had to define in this exercise.
Hint
Define a predicate mirror(+InList,?OutList) which
takes a list as argument and turns it around. For example, the
query mirror([a,b,c,d],L) should yield the answer
L = [d,c,b,a]. Use an accumulator and don't use
append, such that the result is ready when the
empty list is reached.
Hint
Define an accumulator version of the flattening predicate
defined in this exercise.
Hint