# How to Average in Prolog

If I had to average a list of numbers, I would probably do it like this:

```
averagelist(List, Avg) :-
length(List, N), sumlist(List, Sum),
Avg is Sum / N.
```

This resembles the actual mathematical definition. Then you *could* just make a list of numbers and average that. @lurker is right, this is a terrible way to go, but it would work:

```
average(N, Avg) :-
findall(I, between(1, N, I), Is),
averagelist(Is, Avg).
```

This is building up abstraction. But of course, this is for a class and the important thing is to not use Prolog or learn declarative programming or solve actual problems but rather to perform meaningless inductive calisthenics to prove you understand recursion. So a "better" (i.e. worse but likelier to be accepted by a clueless professor) solution is to take the procedural code:

```
average(list) ::=
sum := 0
count := 0
repeat with i ∈ list
sum := sum + i
count := count + 1
return sum / count
```

and convert it into equivalent Prolog code:

```
average(List, Result) :- average(List, 0, 0, Result).
average([], Sum, Count, Result) :- Result is Sum / Count.
average([X|Xs], Sum, Count, Result) :-
Sum1 is Sum + X,
succ(Count, Count1),
average(Xs, Sum1, Count1, Result).
```

The list result of my `findall/3`

must be delicately hand-assembled using only tools available in the 18th century lest anyone develop a sense that Prolog can be used effectively in fewer than 40 lines of code:

```
iota(N, Result) :- iota(1, N, Result).
iota(X, Y, [X|Result]) :- X < Y, succ(X,X1), iota(X1, Y, Result).
iota(X, X, [X]).
```

Then you could build `averagelist/2`

without the taint of library code (of course, you'll have to write `length/2`

and `sumlist/2`

, and probably `member/2`

even though it isn't used, but just because it's clever and useful and it sort of seems like it should be in the source file next to all this other stuff we might need), but it would look generally like this:

```
average(N, Avg) :-
iota(N, List),
averagelist(List, Avg).
```

Now, of course, it will be pointed out that the introduction of additional predicates that are not directly answers to the take home assignment are illegitimate and will be penalized as doing such leads to readability, maintainability, breaking problems down into manageable pieces and other things that are not directly related to the goal of the assignment (to make Prolog appear tedious yet opaque) so we could now look at this and realize that if we want to flatten these two predicates together we ought to be able to by just smushing together their state variables and doing all the work of both, like this:

```
average(N, Avg) :- average(1, N, 0, 0, Avg).
average(X, Y, Sum, Count, Avg) :-
X < Y,
Sum1 is Sum + X,
succ(Count, Count1),
succ(X, X1),
average(X1, Y, Sum1, Count1, Avg).
average(X, X, Sum, Count, Avg) :-
Sum1 is Sum + X,
succ(Count, Count1),
Avg is Sum1 / Count1.
```

Now this is starting to look like Professor of Programming Languages code! We went from basically four little readable lines to 9 or 10 repetitive lines and a lot of book-keeping and state! I think we're on the right track now, let's review how it works:

`average/2`

is just a call to`average/5`

with our state initialized (no sum, no count, starting value = 1).`average/5`

has two cases: a base case where the count-up-to value and the current-count value are equal, and an inductive case where the current-count is less.- add up the blah blah blah you get the point

The key takeaways here are: 1) Prolog has a terse, high-level, readable and comprehensible standard library, which you are prohibited from using in school, and 2) any procedural loop can be made working Prolog by creating a recursive helper predicate and moving the code around.