eyeprolog

List collections

How do you work with a whole list as one value?

A list is an ordinary term, so a fact can hold a complete list. This small example stores two lists and asks the basic questions: how long is it, what is in it, what do you get by extending it, and what are its head and tail.

Run it in the playground · Source

The question

Given a list of numbers and a list of letters: how many numbers are there, which numbers are members, what does the letter list look like with c added at the end, and what are its first element and its remaining elements?

The facts

collection(numbers, [1, 2, 3]).
collection(letters, [a, b]).

Each list is kept whole, as the second argument of one fact, instead of being spread over separate item facts.

The rules

collectionLength(numbers, N) :-
  collection(numbers, List),
  length(List, N).

collectionMember(numbers, X) :-
  collection(numbers, List),
  member(X, List).

collectionAppend(letters, Extended) :-
  collection(letters, List),
  append(List, [c], Extended).

head(letters, Head) :-
  collection(letters, [Head|_tail]).

tail(letters, Tail) :-
  collection(letters, [_head|Tail]).

length/2, member/2, and append/3 come from library(lists). The last two rules need no library at all: the pattern [Head|Tail] splits a list by unification.

The answer

eyeprolog examples/list-collection.pl

collectionLength(numbers, 3).
collectionMember(numbers, 1).
collectionMember(numbers, 2).
collectionMember(numbers, 3).
collectionAppend(letters, "abc").
head(letters, a).
tail(letters, "b").

member/2 gives one answer per element. A list of one-character atoms such as [a, b, c] is printed in double-quote notation, "abc": with the default double_quotes(chars) flag that is the same term, written more compactly.

The reason

eyeprolog --proof examples/list-collection.pl

step(collectionAppend(letters, "abc"),
     rule(5),
     ['Extended' = "abc", 'List' = "ab"],
     [collection(letters, "ab"), append("ab", "c", "abc")]).
step(tail(letters, "b"), rule(7), ['Tail' = "b"], [collection(letters, "ab")]).

The extended list comes from rule 5: the stored letters "ab", appended with "c". The tail needs only the stored fact, matched against [_head|Tail].

The check

condition('C1', resolution, ok, 9).
condition('C5', re_decision, ok, 5).
recomputed(5).
trusted(0).
verdict(checked).

Nine rule and fact steps replay against the program, and the five library calls (length/2, three member/2 calls, append/3) are recomputed by the checker on its own. Nothing is taken on trust.

Try it

Change the numbers to the empty list []. The length becomes 0 and the member answers disappear.
Add last(letters, X) :- collection(letters, L), last(L, X). and run it.
Use append/3 the other way round to split [a, b] into every prefix and suffix.

Learn more in The Art of EyeProlog, Chapter 5.

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