What does Prolog assert/1 do with the term it is passed? - prolog

I'm trying to understand what assert and retract do with the term they are passed. If I run the following:
?- assertz(item(first)).
true.
?- assertz(item(second)).
true.
?- assertz((item(Y) :- =(Y, third), writeln(Y))).
true.
?- retract(item(X)).
X = first ;
X = second ;
false.
retract/1 removes all of the items but my writeln/1 is never called, so it appears retract is not actually resolving the term it is passed. It looks like it is doing some special operation where it:
Unifies the term with only facts (i.e. rules with no tail) in the database
Retracts each one after applying the substitution from unification
Is this right? Or is something else happening here?
Said another way: If I write my own single argument rule, Prolog does not automatically unify item(X) with the database and iterate through all facts that are item/1. It just gives me item(X). How is retract doing its magic?
?- assertz((myRule(X) :- writeln(X))).
true.
? myRule(item(X)).
item(_2556)
true.
Answer with further clarification:
Based on the answer by User9213, it appears that the answer is "retract (but not assert!) has a funny behavior where it does a simple unification of its term before it does something to the database". I'm left wondering why other built-in functions that I've seen (like atom/1 and writeln/1) don't appear to do this. Maybe it is more common than I've experienced?
For consistency, it seems like retract should have required ground terms and if the user wanted to do something like my above example, they could have done this:
?- (item(X), retract(item(X))).
It all makes me think I'm missing something or maybe these built in functions were just inconsistently designed? Any clarification that would explain that would be great.

To add my voice to the chorus, yes, all these predicates (assert*, retract*) manipulate the Prolog database of facts and rules; they do not evaluate their arguments as if they were facts or rules. Yes, they just do "syntactic" unification between their argument and the facts and rules in the database.
Prolog is a homoiconic language. The program can be manipulated as if it was data; the data structures can be interpreted as if they were the program. Most importantly: whether a certain structure is data or program depends only on the context.
You seem to understand this, but for the next poor soul that stumbles across your question and this answer, here is a toy example to demonstrate.
There is a built-in predicate atom/1 that succeeds if its argument is, well, an atom:
?- atom(foo).
true.
?- atom(Bar). % Bar is a free variable, which is not an atom
false.
?- atom(atom(bar)). % atom(bar) is a compound term, which is not an atom
false.
But atom(bar) is just a compound term in the last query. It is a compound term with a functor atom/1. Its only argument is an atom. So if you now queried it:
?- atom(bar).
true.
There is also this really nice predicate called call. It makes it even easier to blur the lines between program and data. The following three queries are identical in meaning:
?- atom(bar).
true.
?- call(atom, bar).
true.
?- call(atom(bar)).
true.
In addition, you can dynamically (at run-time) create a data structure and evaluate it as program. Here is a naive implementation of call/2 that can evaluate predicates, provided a predicate name and a list of arguments. It constructs the compound term using "univ" and evaluates it by just placing it in a slot where a subgoal is supposed to be. I'll call it my_call/2 and I will add it to the database using assertz:
?- assertz((my_call(Name, Args) :- Goal =.. [Name|Args], Goal)).
true.
?- my_call(between, [1, 3, X]).
X = 1 ;
X = 2 ;
X = 3.
Do you see what is going on? (Note: it seems that call is a relatively new addition to Prolog. Before call was widely available, you had to do this trick if you wanted to meta-call predicates. I don't know this from experience, just educated guessing based on things I've read or heard and can't be bothered to cite right now.)
So, let's try that again. In reality things are more complicated, but very simplified:
A Prolog program is a set of predicates. Not ordered!
Each predicate is a list of clauses. It is a list because a predicate may have 0 or more clauses, and they have order.
A clause can be a fact or a rule.
A rule is a compound term with functor :-/2. Yes, this is right. To see what I mean:
?- assertz(:-(foo(X), between(1, 3, X))).
true.
?- listing(foo/1).
:- dynamic foo/1.
foo(A) :-
between(1, 3, A).
true.
This is just another way to write it. It is more conventional.
So indeed, these two are very different:
foo(X). % a fact
foo(X) :- between(1, 3, X). % a rule
You cannot unify the one with the other. This is why, if you want to retract foo(X) :- between(1, 3, X), you cannot just pass foo(X) as the argument to retract. Or, to complete your example:
?- assertz(item(first)).
true.
?- assertz(item(second)).
true.
?- assertz((item(Y) :- =(Y, third), writeln(Y))).
true.
?- retract(item(X)).
X = first ;
X = second ;
false.
?- retract((item(X) :- X = Y, writeln(X))).
Y = third.
Do you see it now?

I had a vague memory of there being a retractall/1 that lives alongside retract/1 and it turns out the reason for it is situations like this. retract/1 accepts a Prolog term, as the documentation states:
retract(+Term)
When Term is an atom or a term it is unified with the first unifying fact or clause in the database. The fact or clause is removed from the database.
Emphasis added by me.
This is illustrated by the following:
?- asserta(foo(X) :- X = 2 ; X = 4).
true.
?- foo(X).
X = 2 ;
X = 4.
?- retract(foo(X)).
false.
?- foo(X).
X = 2 ;
X = 4.
?- retract(foo(X) :- X = 2 ; X = 4).
true.
?- foo(X).
false.
Note that if you furnish the complete clause you gave to asserta/1, it will be retracted. As #CapelliC points out below, you can also furnish a clause with a variable as a parameter to retract things with bodies:
retract(foo(X) :- Y).
However, if you do want to retract things that match a pattern, you can use retractall/1, which the documentation states:
retractall(+Head)
All facts or clauses in the database for which the head unifies with Head are removed.
This is illustrated by the following:
?- asserta(foo(X) :- X = 2 ; X = 4).
true.
?- foo(X).
X = 2 ;
X = 4.
?- retractall(foo(X)).
true.
?- foo(X).
false.
Another important difference between these two is that retract/1 will remove one thing at a time, and it will unify those things:
?- asserta(foo(X) :- X = 2).
true.
?- asserta(foo(X) :- X = 4).
true.
?- retract(foo(X) :- Y).
Y = (X=4) ;
Y = (X=2) .
This is in contrast to retractall/1 which will remove everything that matches the pattern, without unifying anything:
?- asserta(foo(X) :- X=2).
true.
?- asserta(foo(X) :- X=4).
true.
?- foo(X).
X = 4 ;
X = 2.
?- retractall(foo(X)).
true.
?- foo(X).
false.
So, retract/1 is really for doing one-at-a-time retractions but expects something shaped like the term you asserted, whereas retractall/1 only wants a head, treats it as a pattern, and will remove as many things as match the pattern.
This certainly helped me improve my understanding of Prolog, so I hope it helps you as well!

The definition of assert in swi-prolog is:
Assert a clause (fact or rule) into the database. The predicate asserta/1 asserts the clause as first clause of the predicate while assertz/1 assert the clause as last clause. The deprecated assert/1 is equivalent to assertz/1. If the program space for the target module is limited (see set_module/1), asserta/1 can raise a resource_error(program_space) exception. The example below adds two facts and a rule. Note the double parentheses around the rule.
Hence, it does not call or infer anything! It's just an assertion for the fact and the rule into the active memory.

Related

Proper subsumes_term/2 in SWI-Prolog?

Lets assume SICStus Prolog is the benchmark for the
implementation of certain predicates, even ISO core standard
predicates. Especially in connection with attributed variables.
I then find these examples here. It's from SICStus 4 and not only SICStus 3:
?- when(nonvar(X), X=a), subsumes_term(X, b), X = a.
X = a ?
yes
?- when(nonvar(X), X=a), subsumes_term(X, b), X = b.
no
When doing the same in SWI-Prolog I get different results:
?- when(nonvar(X), X=a), subsumes_term(X, b), X = a.
false.
?- when(nonvar(X), X=a), subsumes_term(X, b), X = b.
false.
How would one implement a workaround in SWI-Prolog? ROKs METUTL.PL probably doesn't help, since it uses normal unification.
Here is a suggestion (not actually tested in SWI-prolog):
subsumes_term_sicstus(X, Y):-
copy_term(X-Y, XC-YC, _),
subsumes_term(XC, YC).
The idea is simply to copy the two structures then use the original predicate on the copies, which do not have attributes or frozen goals attached.
According to the documentation, it appears that copy_term/2 copies the attributes of attributed variables in SWI-prolog (but not in SICStus), so I am using copy_term/3 instead here. I see that there is also a copy_term_nat/2, which might be used instead.

Checking all Members Of List

Let's say that I have the following list in my prolog:
L=[10,11,2,3,5]
Is there a way that we can check all the members of a list L to make sure that each member is less than 5?
We can make use of maplist/2 here. This is a predicate that:
maplist(:Goal, ?List)
True if Goal can successfully be applied on all elements of List. Arguments are reordered to gain performance as well as to make the predicate deterministic under normal circumstances.
So we can here check the elements with:
all_less_five(L) :-
maplist(>(5), L).
Here for every element x ∈ L, it will thus call >(5, x), or in inline form 5 > x. So if all these elements are less than five, the the all_less_five/1 predicate will succeed.
For example:
?- all_less_five([10,11,2,3,5]).
false.
?- all_less_five([2,3,5]).
false.
?- all_less_five([2,3]).
true.
Here goes another solution without using any built-in function:
all_less_five([]).
all_less_five([X|L]):-
X < 5,
all_less_five(L).
This solution uses the typical recursion over lists. The predicate stands true for the empty list, and then we only call the recursion over the tail if the head is less than five.
Here are some questions over the predicate:
?- all_less_five([10,11,2]).
false.
?- all_less_five([2,3,6,5]).
false.
?- all_less_five([1,2,3,4]).
true.
Now it should be easy to implement it to any given X. Try it!

prolog doesn't give me a solution when one exists

I am working through Seven Languages in Seven Weeks, but there is something I don't understand about prolog. I have the following program (based on their wallace and grommit program):
/* teams.pl */
onTeam(a, aTeam).
onTeam(b, aTeam).
onTeam(b, superTeam).
onTeam(c, superTeam).
teamMate(X, Y) :- \+(X = Y), onTeam(X, Z), onTeam(Y, Z).
and load it like this
?- ['teams.pl'].
true.
but it doesn't give me any solutions to the following
?- teamMate(a, X).
false.
it can solve simpler stuff (which is shown in the book):
?- onTeam(b, X).
X = aTeam ;
X = superTeam.
and there are solutions:
?- teamMate(a, b).
true ;
false.
What am I missing? I have tried with both gnu prolog and swipl.
...AND THERE IS MORE...
when you move the "can't be your own teammate" restriction to then end:
/* teams.pl */
onTeam(a, aTeam).
onTeam(b, aTeam).
onTeam(b, superTeam).
onTeam(c, superTeam).
teamMate(X, Y) :- onTeam(X, Z), onTeam(Y, Z), \+(X = Y).
it gives me the solutions I would expect:
?- ['teams.pl'].
true.
?- teamMate(a, X).
X = b.
?- teamMate(b, X).
X = a ;
X = c.
What gives?
You have made a very good observation! In fact, the situation is even worse, because even the most general query fails:
?- teamMate(X, Y).
false.
Declaratively, this means "there are no solutions whatsoever", which is obviously wrong and not how we expect relations to behave: If there are solutions, then more general queries must not fail.
The reason you get this strange and logically incorrect behaviour is that (\+)/1 is only sound if its arguments are sufficiently instantiated.
To express disequality of terms in a more general way, which works correctly no matter if the arguments are instantiated or not, use dif/2, or, if your Prolog system does not provide it, the safe approximation iso_dif/2 which you can find in the prolog-dif tag.
For example, in your case (note_that_I_am_using_underscores_for_readability instead of tuckingTheNamesTogetherWhichMakesThemHarderToRead):
team_mate(X, Y) :- dif(X, Y), on_team(X, Z), on_team(Y, Z).
Your query now works exactly as expected:
?- team_mate(a, X).
X = b.
The most general query of course also works correctly:
?- team_mate(X, Y).
X = a,
Y = b ;
X = b,
Y = a ;
X = b,
Y = c ;
etc.
Thus, using dif/2 to express disequality preserves logical-purity of your relations: The system now no longer simply says false even though there are solutions. Instead, you get the answer you expect! Note that, in contrast to before, this also works no matter where you place the call!
The answer by mat gives you some high-level considerations and a solution. My answer is a more about the underlying reasons, which might or might not be interesting to you.
(By the way, while learning Prolog, I asked pretty much the same question and got a very similar answer by the same user. Great.)
The proof tree
You have a question:
Are two players team mates?
To get an answer from Prolog, you formulate a query:
?- team_mate(X, Y).
where both X and Y can be free variables or bound.
Based on your database of predicates (facts and rules), Prolog tries to find a proof and gives you solutions. Prolog searches for a proof by doing a depth-first traversal of a proof tree.
In your first implementation, \+ (X = Y) comes before anything else, so it at the root node of the tree, and will be evaluated before the following goals. And if either X or Y is a free variable, X = Y must succeed, which means that \+ (X = Y) must fail. So the query must fail.
On the other hand, if either X or Y is a free variable, dif(X, Y) will succeed, but a later attempt to unify them with each other must fail. At that point, Prolog will have to look for a proof down another branch of the proof tree, if there are any left.
(With the proof tree in mind, try to figure out a way of implementing dif/2: do you think it is possible without either a) adding some kind of state to the arguments of dif/2 or b) changing the resolution strategy?)
And finally, if you put \+ (X = Y) at the very end, and take care that both X and Y are ground by the time it is evaluated, then the unification becomes more like a simple comparison, and it can fail, so that the negation can succeed.

Prolog and List Unification

I'm trying to further my understanding of Prolog, and how it handles unification. In this case, how it handles unification with lists.
This is my knowledgebase;
member(X, [X|_]).
member(X, [_|T]):- member(X, T).
If I'm understanding the process correctly. If member(X, [X|_]) is not true, then it moves into the recursive rule, and if X is in list T, then [_|T] is unified with T.
So what happens to the anonymous variable in my recursive predicate? Does it get discarded? I'm having difficulty understanding the exact unification process with lists, as [_|T] is two variables, rather than one. I'm just trying to figure out how the unification process works precisely with lists.
Assume that _ is Y
member(X, [Y|T]):- member(X, T).
Then this is True regardless Y. Now you are "returning" member(X, T). In other words, you are discarding Y and "returning" member(X, T).
_ means, whatever it is, ignore that variable.
The _ is just like any other variable, except that each one you see is
treated as a different variable and Prolog won't show you what it
unifies with. There's no special behavior there; if it confuses you
about the behavior, just invent a completely new variable and put it
in there to see what it does.
In your case, your function check if a given element exists on a list, so, you take first element of the list, check if is equal, if not, you discard that element and moves on.
I think your primary question of how lists are represented as variables has been adequately answered, but I sense there are some other aspects to Prolog that need clarification.
To understand Prolog predicates and clauses, it's a good idea not to think of them as "functions" that "return" things, even metaphorically. It can lead you down the dark path of imperative thinking in Prolog. :)
In considering the predicate:
(1) member(X, [X|_]).
(2) member(X, [_|T]) :- member(X, T).
Think of member/2 as a relation which describes when element X is a member of the list L, and the clauses are the rules for determining when it is true.
I'll assume that you already know about how lists are represented in Prolog based upon other answers (e.g., Will Ness' detailed answer).
The first clause says:
(1) X is a member of [X|_] regardless of what the tail of the list [X|_] is
In that notation, the variable _ represents the tail of list [X|_] and X represents the first element of that list. It's trivially true that X is a member of this list, so member(X, [X|_]). is a fact. It's true regardless of what the tail of the list is, so we just use _ (an anonymous variable) since this rule doesn't need the information. Prolog doesn't technically "throw the value away" but the programmer throws it away because the programmer isn't using it. If we had, instead, said, member(X, [X|T]). that would work fine, but we're not using T. Prolog might instantiate it, but it wouldn't be used. It's like assigning x = 3 in C but not using it's value. In this case, Prolog will indicate a warning about a "singleton" variable. Watch for those, because it often means you misspelled something or forgot something. :)
The next rule is recursive. It says:
(2) X is a member of list [_|T] if X is a member of the tail (T) of that list, regardless of what the first element of the list is
Here we're considering the less trivial case where the first element in the list may not be a match to X, so the truth value of member(X, L) depends, in this rule, upon the truth value of member(X, T) where T is the tail (everything but the first element) of L. The rule does not unify member(X, [_|T]) with member(X, T), so it does not unify T with [_|T] as you might suppose. The :- operator defines a rule or implication (note the if in the rule description). [N.B., If you were to unify these terms, it would be done with with the unification operator, =/2: member(X, [_|T]) = member(X, T)].
On the recursive query member(X, T), Prolog goes back to the top, the first rule, and attempts to unify the first argument X with the head of the second argument (which is the original list minus its first element, or head) and, if it doesn't match, goes to rule #2 again, continually checking the tail as well, until it can unify. If it gets to the point where the tail is empty ([]) and hasn't been able to unify X with any elements, the predicate fails because there are no facts or rules that match member(X, []). However, if it does unify X with an element, it succeeds (it does not "return a value* in the sense that a function would in other languages) and reveals the values of any variables it instantiated in the arguments in the process, or simply will succeed if all the arguments passed are already instantiated. If there are more rules to check after succeeding (there was what's called a choice point), it will (if you tell it to) go back and check for more solutions and, if it finds them, display them as well. Or display no or false if there are no more.
Looking at an example query, is b a member of [a,b,c]?
member(b, [a,b,c]).
Prolog will first try to unify the query with a fact or the head of a predicate. The first one it finds is:
member(X, [X|_]).
In attempting to unify, X = b, but [a,b,c] (or, [a|[b,c]] in the head-tail notation) doesn't unify with [b|_](note the head elementsaandb` mismatch). Prolog then moves on to the next clause:
member(X, [_|T]) :- member(X, T).
In unifying member(b, [a,b,c]) with the head, it comes up with:
member(b, [_|[b,c]]) :- member(b, [b,c]).
It now has the recursive query to chase down: member(b, [b,c]). Since it's a new query, it starts at the top again and attempts to unify this with member(X, [X|_]). Now, it's successful, because member(b, [b,c]) (or, member(b, [b|[c]])) matches this pattern: member(b, [b|_]).
Therefore, the member(b, [a,b,c]). succeeds and Prolog will return "true". However, it's not done yet because it left what's called a choice point. Even though it matched member(b, [b,c]) with the first clause, it will still want to go back and find more cases that make it succeed, and there's still another clause to pursue. So, Prolog will go back and try member(b, [b,c]) against the second clause, matching member(b, [b|[c]]) to member(b, [_|[c]]) and doing another recursive query, member(b, [c]) and so on until it ultimately fails to find another solution. This is why the query looks something like this:
| ?- member(b, [a,b,c]).
true ? ;
no
| ?-
It first succeeds, but then we ask for more (with ;) and it then fails (no). This confuses some Prolog beginners, but it's because we've asked Prolog to get another solution, and it said there are none.
Because Prolog continues to try to find solutions (upon request), you can also use a variable in the query:
member(E, [a,b,c]).
This query runs the same way as the prior example, but now I have a variable as the first argument. Prolog will successfully match this to the first clause: member(E, [a,b,c]) unifies with member(X, [X|_]) via E = a. So you'll see something like:
| ?- member(E, [a,b,c]).
E = a ?
If we now ask for more solutions with ;, Prolog goes back and attempts the second clause, unifying member(E, [a|[b,c]]) with member(X, [_|T]) yielding _ = a (which is ignored in the predicate) and T = [b,c]. It then recursively queries, member(E, [b,c]) and, since it's a new query, goes back to the top and matches member(X, [X|_]) again, this time with E = b. So we see:
| ?- member(E, [a,b,c]).
E = a ? ;
E = b ?
And so on. member(E, [a,b,c]) will find all the values of E which make member(E, [a,b,c]) true and then finally fail after exhausting all the elements of [a,b,c]).
[A|B] represents a list where A is the Head element and B is the whole rest list.
So to explain you the algorithm shortly:
Clause: If X is the first element of the list the predicate succeeds.
Clause: If that's not the case, we try to find X in the tail of the list. Therefore, we call member recursively but instead of passing the whole list we now pass the list EXCEPT the head element. In other words, we walk through the list step by step always looking at the head element first. If that is not our element, we dig further.
Think of the anonymous variable _ just as a variable you do not need later. The algorithm would also work, if you replaced _ by a capital letter, however it would give you a warning that you named a variable that you never use.
A list is just a compound term with the '.' functor:
1 ?- [_|T] = .(_,T).
true.
2 ?- [_|T] =.. X.
X = ['.', _G2393, T].
The usual process of structural unification of compound terms apply:
3 ?- [A|T] = .(B,R).
A = B,
T = R.
[A|T] is really .(A,T) so the functors (.) and the arities (both terms are binary, of arity 2) match, so the respective constituents are matched as well.
Yes, the anonymous variable _ is ignored for the purposes of reporting the unification results. Otherwise it is just a fresh uniquely named variable.
it moves into the recursive rule, and if X is in list T, then [_|T] is unified with T.
Not quite. The unification happens before the "moving on", as part of the clause selection. To unify a list L with [_|T] is to select its "tail" and have T referring to it. E.g.
4 ?- L = [1,2,3], L = [_|T].
L = [1, 2, 3],
T = [2, 3].
(_ is 1 but is not reported).

Prolog: Error out of global stack with what looks like ONE level of recursion to me

I am quite rusty in prolog, but I am not sure why things like this fail:
frack(3).
frack(X) :- frack(X-1).
So, if I evaluate frack(4). from the interactive prompt with the above facts defined, I expect that it should not have to endlessly recurse, since 4-1 = 3. But I get this error in SWI-Prolog:
ERROR: Out of global stack
Try it:
?- 4-1 = 3.
false.
Why? Because 4-1 = -(4, 1), which clearly is not a number but a compound term.
To reason about integers in Prolog, use clpfd constraints, for example (using GNU Prolog or B-Prolog):
| ?- 4-1 #= X.
X = 3
In SWI-Prolog, the graphical tracer may be useful for you to see what happens:
?- gtrace, frack(4).
For more complex debugging, I recommend failure-slice as shown in false's answer.
Here is the reason for this non-termination. Your query does not terminate, because there is a failure-slice of your program that does not terminate:
?- frack(4).
frack(3) :- false.
frack(X) :-
frack(X-1), false.
You can fix this only by modifying something in the visible part. Three SO-answers suggest to use (is)/2. But this will not remove non-termination! In fact, using (is)/2 leads to essentially the same fragment:
?- frack(4).
frack(3) :- false.
frack(X) :-
Y is X - 1,
frack(Y), false.
At least, frack(4) now succeeds, but it will loop on backtracking. You have to change something in the visible part, like some test for X, in order to avoid non-termination. See failure-slice for more.
frack(X) :- frack(X-1).
should be
frack(X) :- Y is X - 1, frack(Y).
The way you wrote it, X-1 expression of the first level unifies with X variable at the next level, never going for the frack(3) fact.
Prolog doesn't do arithmetic unless you use the is operator:
frack(X) :- X1 is X-1, frack(X1).

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