I've written the following predicate:
list_withoutlast([_Last], []). % forget the last element
list_withoutlast([First, Second|List], [First|WithoutLast]) :-
list_withoutlast([Second|List], WithoutLast).
Queries like list_withoutlast(X, [1, 2]). succeed deterministically, but queries like list_withoutlast([1, 2, 3], X) leave behind a choicepoint, even though there's only one answer.
When I trace it seems to be that SWI attempts to match list_withoutlast([3], Var) against both clauses, even though definitely only the first one will ever match!
Is there something else I can do to tell SWI that I want a list with more than one element? Or, if I want to take advantage of first-argument indexing, are my only options "zero-length list" and "non-zero length list"?
Do other Prologs handle this situation any differently?
You can rewrite your predicate to avoid the spurious choice point:
list_withoutlast([Head| Tail], List) :-
list_withoutlast(Tail, Head, List).
list_withoutlast([], _, []).
list_withoutlast([Head| Tail], Previous, [Previous| List]) :-
list_withoutlast(Tail, Head, List).
This definition takes advantage of first-argument indexing, which will distinguish in the list_withoutlast /3 predicate the first clause, which have an atom (the empty list) in the first argument, from the second clause, which have a (non-empty) list in the first argument.
Passing the head and tail of an input list argument as separate arguments to an auxiliary predicate is a common Prolog programming idiom to take advantage of first-argument indexing and avoid spurious choice-points.
Note that most Prolog systems don't apply deep term indexing. In particular, for compound terms, indexing usually only takes into account the name and arity and doesn't take into account the compound term arguments (a list with one element and a list with two or more elements share the same functor).
Related
I want to write a function returning an array whose all subarrays must have a length of two.
For example return will be [[1, 2], [3, 4]].
I define:
(1) subset TArray of Array where { .all ~~ subset :: where [Int, Int] };
and
sub fcn(Int $n) of TArray is export(:fcn) {
[[1, 2], [3, 4]];
}
I find (1) over-complicated. Is there something simpler?
Stepping back first
subset TArray of Array where { .all ~~ subset :: where [Int, Int] };
Is there something simpler?
Before we go there, let's step back. Even ignoring your code's "overly-complicated" nature based on just looking at it, it's also potentially problematic and complicated for various reasons that may not be so obvious. I'll highlight three:
This subset will accept an Array containing Arrays, with each of those arrays containing two Ints. But it doesn't mandate an Array[Array[Int]]. The outer Array's type may be just a generic Array, rather than being an Array[Array] let lone an Array[Array[Int]]. Indeed it will be unless you deliberately introduce strongly typed values. I will cover strong typing in the last section of this answer.
What about an empty Array? Your subset will accept that. Is that your intent? If not, what about requiring at least one pair of Ints?
The outer where clause uses a common Raku idiom of the form .all ~~ ..., with a junction on the left hand side of the ~~ smart match operator. Astonishingly, per an issue I just filed, this may be a problem. What alternatives are there?
Starting simple
Raku does a decent job of keeping simple things simple. If we put aside any artificial desire for strong typing, and focus on simple tools for tightening code up, a simple subset I would have suggested in the past would be:
subset TArray where .all == 2; # BAD despite being idiomatic???
This has all of the problems your original code has, plus in addition it accepts data that has non-integers where integers belong.
But it does have the redeeming qualities that it does a useful check (that the inner arrays each have two elements) and it's significantly simpler than your code.
Now I've reminded myself that I need to view .all on the left hand side of ~~ as possibly a problem, I'll instead write it as:
subset TArray where 2 == .all; # Potentially the new idiomatic.
This version reads more poorly, but, while readability is important, basic correctness is more important.
Still fairly simple, and less problems
Here are two variants I came up with:
subset TArray where all .map: * ~~ (Int,Int);
subset TArray where .elems == .grep: (Int,Int);
These both avoid the junction/smartmatch problem. (The first where expression does have a junction to the left of a smart match, but it's not an example of the problem.)
The second version isn't so obviously correct (think of it as checking that the count of subarrays is the same as the count of subarrays that match (Int,Int)) but it nicely lends itself to fixing the problem of matching if there are zero subarrays, if that were to need fixing:
subset TArray where 0 < .elems == .grep: (Int,Int);
Strong typing solutions
The solutions thus far don't deal with strong typing. Perhaps that's desirable. Perhaps not.
To understand what I mean by this, let's first look at literals:
say WHAT 1; # (Int)
say WHAT [1,2]; # (Array)
say WHAT [[1,2],[3,4]]; # (Array)
These values have types determined by their literal constructors.
The last two are just Arrays, generic over their elements.
(The second is not an Array[Int], which might be expected. Similarly the last one is not an Array[Array[Int]].)
Current built in Raku literal forms for composite types (arrays and hashes) all construct generic Arrays which do not constrain the types of their elements.
See the PR Introduce [1,2,3]:Int syntax #4406 for a proposal/PR regarding element typed composite literals and a related issue I just posted in response to your Q here about an alternative and/or complementary approach to that PR. (There have been discussions over the years about this aspect of the type system but it seems like it's time for Rakoons to look at addressing it.)
What if you wanted to build a strongly typed data structure as the value to return from your routine, and to have the return type check that?
Here's one way one might build such a strongly typed value:
my Array[Array[Int]] $result .= new: Array[Int].new(1,2), Array[Int].new(3,4);
Super verbose! But now you could write the following for your sub's return type check and it'll work:
subset TArray of Array[Array[Int]] where 0 < .elems == .grep: (Int,Int);
sub fcn(Int $n) of TArray is export(:fcn) {
my Array[Array[Int]] $result .= new: Array[Int].new(1,2), Array[Int].new(3,4);
}
Another way to build a strongly typed value is to specify not only the strong typing in a variable's type constraint, but also coercion typing to bridge from a loosely typed value to a strongly typed target.
We keep the exact same subset (that establishes the strongly typed target data structure and adds "refinement typing" checks):
subset TArray of Array[Array[Int]] where 0 < .elems == .grep: (Int,Int);
But instead of using a verbose correct-by-construction initialization value, using full type names and news, we introduce additional coercion typing and then just use ordinary literal syntax:
constant TArrayInitialization = TArray(Array[Array[Int]()]());
sub fcn(Int $n) of TArray is export(:fcn) {
my TArrayInitialization $result = [[1,2],[3,4]];
}
(I could have written the TArrayInitialization declaration as another subset, but it would be a slight overkill to have done so. A constant does the job with less fuss.)
I gather that the aim is to restrict the type of the inner Array to [Int,Int] ... the closest I can get to this is to declare two subsets, one based on the other...
subset IArray where * ~~ [Int, Int];
subset TArray where .all ~~ IArray;
Otherwise, the anonymous subset form you use seems to be the briefest, although as #raiph points out you can drop the 'of Array' piece.
If you wanted to impose this sort of constraint on a function's parameter (rather than its return type) you could do so with something like:
sub fcn(#a where {all .map: * ~~ [Int, Int]}) {...}
As the other answers have mentioned, there currently isn't great syntax for similarly constraining the return type, but there's a proposal to add support for similar syntax for return types. In fact, as mentioned in that issue, someone has volunteered to work on an implementation but hasn't yet made any progress as far as I know. (And I guess I should know, since I was that volunteer… oops)
So, for now, a subset is the best option – but hopefully the future will have even better ways to write that.
This code works:
(3,6...66).contains( 9|21 ).say # OUTPUT: «any(True, True)»
And returns a Junction. It's also tested, but not documented.
The problem is I can't find its implementation anywhere. The Str code, which is also called from Cool, never returns a Junction (it does not take a Junction, either). There are no other methods contain in source.
Since it's autothreaded, it's probably specially defined somewhere. I have no idea where, though. Any help?
TL;DR Junction autothreading is handled by a single central mechanism. I have a go at explaining it below.
(The body of your question starts with you falling into a trap, one I think you documented a year or two back. It seems pretty irrelevant to what you're really asking but I cover that too.)
How junctions get handled
Where is contains( Junction) defined? ... The problem is I can't find [the Junctional] implementation anywhere. ... Since it's autothreaded, it's probably specially defined somewhere.
Yes. There's a generic mechanism that automatically applies autothreading to all P6 routines (methods, operators etc.) that don't have signatures that explicitly control what happens with Junction arguments.
Only a tiny handful of built in routines have these explicit Junction handling signatures -- print is perhaps the most notable. The same is true of user defined routines.
.contains does not have any special handling. So it is handled automatically by the generic mechanism.
Perhaps the section The magic of Junctions of my answer to an earlier SO Filtering elements matching two regexes will be helpful as a high level description of the low level details that follow below. Just substitute your 9|21 for the foo & bar in that SO, and your .contains for the grep, and it hopefully makes sense.
Spelunking the code
I'll focus on methods. Other routines are handled in a similar fashion.
method AUTOTHREAD does the work for full P6 methods.
This is setup in this code that sets up handling for both nqp and full P6 code.
The above linked P6 setup code in turn calls setup_junction_fallback.
When a method call occurs in a user's program, it involves calling find_method (modulo cache hits as explained in the comment above that code; note that the use of the word "fallback" in that comment is about a cache miss -- which is technically unrelated to the other fallback mechanisms evident in this code we're spelunking thru).
The bit of code near the end of this find_method handles (non-cache-miss) fallbacks.
Which arrives at find_method_fallback which starts off with the actual junction handling stuff.
A trap
This code works:
(3,6...66).contains( 9|21 ).say # OUTPUT: «any(True, True)»
It "works" to the degree this does too:
(3,6...66).contains( 2 | '9 1' ).say # OUTPUT: «any(True, True)»
See Lists become strings, so beware .contains() and/or discussion of the underlying issues such as pmichaud's comment.
Routines like print, put, infix ~, and .contains are string routines. That means they coerce their arguments to Str. By default the .Str coercion of a listy value is its elements separated by spaces:
put 3,6...18; # 3 6 9 12 15 18
put (3,6...18).contains: '9 1'; # True
It's also tested
Presumably you mean the two tests with a *.contains argument passed to classify:
my $m := #l.classify: *.contains: any 'a'..'f';
my $s := classify *.contains( any 'a'..'f'), #l;
Routines like classify are list routines. While some list routines do a single operation on their list argument/invocant, eg push, most of them, including classify, iterate over their list doing something with/to each element within the list.
Given a sequence invocant/argument, classify will iterate it and pass each element to the test, in this case a *.contains.
The latter will then coerce individual elements to Str. This is a fundamental difference compared to your example which coerces a sequence to Str in one go.
I'm trying to write an SWI-Prolog predicate that applies numbervars/3 to a term's anonymous variables but preserves the user-supplied names of its non-anonymous variables. I eventually plan on adding some kind of hook to term_expansion (or something like that).
Example of desired output:
?- TestList=[X,Y,Z,_,_].
> TestList=[X,Y,Z,A,B].
This answer to the question Converting Terms to Atoms preserving variable names in YAP prolog shows how to use read_term to obtain as atoms the names of the variables used in a term. This list (in the form [X='X',Y='Y',...]) does not contain the anonymous variables, unlike the variable list obtained by term_variables, making isolation of the anonymous variables fairly straightforward.
However, the usefulness of this great feature is somewhat limited if it can only be applied to terms read directly from the terminal. I noticed that all of the examples in the answer involve direct user input of the term. Is it possible to get (as atoms) the variable names for terms that are not obtained through direct user input? That is, is there some way to 'write' a term (preserving variable names) to some invisible stream and then 'read' it as if it were input from the terminal?
Alternatively... Perhaps this is more of a LaTeX-ish line of thinking, but is there some way to "wrap" variables inside single quotes (thereby atom-ifying them) before Prolog expands/tries to unify them as variables, with the end result that they're treated as atoms that start with uppercase letters rather than as variables?
You can use the ISO core standard variable_names/1 read and write option. Here is some example code, that replaces anonymous variables in a variable name mapping:
% replace_anon(+Map, +Map, -Map)
replace_anon([_=V|M], S, ['_'=V|N]) :- member(_=W, S), W==V, !,
replace_anon(M, S, N).
replace_anon([A=V|M], S, [A=V|N]) :-
replace_anon(M, S, N).
replace_anon([], _, []).
variable_names/1 is ISO core standard. It was always a read option. It then became a write option as well. See also: https://www.complang.tuwien.ac.at/ulrich/iso-prolog/WDCor3
Here is an example run:
Welcome to SWI-Prolog (threaded, 64 bits, version 7.7.25)
?- read_term(X,[variable_names(M),singletons(S)]),
replace_anon(M,S,N),
write_term(X,[variable_names(N)]).
|: p(X,Y,X).
p(X,_,X)
To use the old numbervars/3 is not recommended, since its not compatible with attribute variables. You cannot use it for example in the presence of CLP(FD).
Is it possible to get (as atoms) the variable names for terms that are not obtained through direct user input?
if you want to get variable names from source files you should read them from there.
The easiest way to do so using term expansion.
Solution:
read_term_from_atom(+Atom, -Term, +Options)
Use read_term/3 to read the next term from Atom.
Atom is either an atom or a string object.
It is not required for Atom to end with a full-stop.
Use Atom as input to read_term/2 using the option variable_names and return the read term in Term and the variable bindings in variable_names(Bindings).
Bindings is a list of Name = Var couples, thus providing access to the actual variable names. See also read_term/2.
If Atom has no valid syntax, a syntax_error exception is raised.
write_term( Term ) :-
numbervars(Term, 0, End),
write_canonical(Term), nl.
For an application I'm considering, there would be a large (100,000+) 'database' of trees (think expressions in a programming language, or S-expressions), and I would need to query that database for expressions that match a specific given expression.
Before giving the details of what I'd like to have, note that I'd appreciate any information related to indexing a large set of trees for optimizing lookup by a subtree.
In my specific situation (which would be for a backend to be used by Metamath proof assistants), expressions have the following structure (in Haskell-like notation):
data Expression = Placeholder Id | VarName Id | ConstName Id [Expression]
or as a BNF for an S-expression form:
Expression = '?' Id | Id | '(' Id Expression* ')'
where Id is some kind of identifier.
For example, I could have a database with expressions like
(equiv ?ph ?ps)
(not (in (appl (sqrt) (2)) (Q)))
(equiv (eq ?A ?B) (forall ?x (equiv (in ?x ?A) (in ?x ?B))))
In this context, two expressions match if they can be made equal by substitution of expressions for placeholders. So looking up (equiv (eq A (emptyset)) ?ph) in the above mini-database would result in the first and last expressions.
So again: how would I implement fast lookups in a large set of (expression) trees with placeholders? What kind of index data structure could I use?
I would implement the lookup with a trie. Each key would consist of one of the following:
ConstName Identifier
Variable w/ context info
ConstValue
Placeholder
These should be ordered in some fashion- possibly Placeholder, then all ConstNames (alphabetical), then variables (scope ordering, then argument order), then ConstValues (numerical order). As long as there's a concrete ordering for usage in the trie, you're fine.
Traverse the expression's tree, injecting the appropriate keys into the trie as they are encountered. Do this for all the expressions you want to insert into your data structure. When it comes time to query it, you can traverse the trie in a similar fashion, but with a few new rules.
Everything matches a placeholder node. If it matches some other key as well, then you'll need to explore both branches (easily done via a recursive DFS-like approach).
A placeholder matches everything. This is not equivalent to the previous point- we are talking about placeholders in the query here, the previous bullet is regarding placeholders as trie keys.
Now, this does mean that the search space can somewhat "explode" as you encounter placeholders, but there is one thing you can do to try to mitigate this in practice. Traverse the expression's tree in a breadth-first fashion (both in construction of the trie, and querying). This means if one of the arguments is a placeholder, you won't have to full-depth search every single subtree that matches that expression so far- instead you jump ahead to the next argument- which may not be a placeholder, and will thus greatly prune the search space (compared to matching "everything").
For completeness sake, lets take one of your examples
(not (in (appl (sqrt) (2)) (Q)))
and make a trie entry from that-
not -> in -> apply -> "Q" -> sqrt -> 2
adding (not (in ?ph E)) to this would result in-
not -> in -> apply -> "Q" -> sqrt -> 2
\-> ?ph -> "E"
Continue in this fashion injecting expressions into the trie. Also traverse in this fashion for querying until you reach the ends of your searches into the trie, and return those that matched.
Note- the uniqueness of these entries is based on the assumption you do not have to support variadic functions. If you do, attach to each key some context info (read the next paragraphs for info on how to do this) to distinguish which arguments go to which functions
There is one detail I glossed over- variables. If you only want it to match if they are the exact same variable name, then no work is necessary. But this likely isn't what you want; you probably want it to match generic variables as long as they are "consistent" with each other. The way to do this is to assign each variable an identifier that represents the scope of which it was first defined.
The easiest way to do this is just compose an identifier from the concatenation of the argument ordering of its ancestors. That is, if a variable is first defined as the second argument to a function which is the fifth argument to the root function, then we might label it as (5, 2) or (2, 5), whichever makes more sense intuitively. Either way, this will ensure the variable is given a consistent identifier regardless of other variables / functions elsewhere. Then proceed as normal with this new variable name.
I saw this question and it got me wondering.
Ignoring the fact that pretty much all languages have to be backwards compatible, is there any reason we cannot use operators as both keywords and functions, depending on if it's immediately followed by a parenthesis? Would it make the grammar harder?
I'm thinking mostly of python, but also C-like languages.
Perl does something very similar to this, and the results are sometimes surprising. You'll find warnings about this in many Perl texts; for example, this one comes from the standard distributed Perl documentation (man perlfunc):
Any function in the list below may be used either with or without parentheses around its arguments. (The syntax descriptions omit the parentheses.) If you use parentheses, the simple but occasionally surprising rule is this: It looks like a function, therefore it is a function, and precedence doesn't matter. Otherwise it's a list operator or unary operator, and precedence does matter. Whitespace between the function and left parenthesis doesn't count, so sometimes you need to be careful:
print 1+2+4; # Prints 7.
print(1+2) + 4; # Prints 3.
print (1+2)+4; # Also prints 3!
print +(1+2)+4; # Prints 7.
print ((1+2)+4); # Prints 7.
An even more surprising case, which often bites newcomers:
print
(a % 7 == 0 || a % 7 == 1) ? "good" : "bad";
will print 0 or 1.
In short, it depends on your theory of parsing. Many people believe that parsing should be precise and predictable, even when that results in surprising parses (as in the Python example in the linked question, or even more famously, C++'s most vexing parse). Others lean towards Perl's "Do What I Mean" philosophy, even though the result -- as above -- is sometimes rather different from what the programmer actually meant.
C, C++ and Python all tend towards the "precise and predictable" philosophy, and they are unlikely to change now.
Depending on the language, not() is not defined. If not() is not defined in some language, you can not use it. Why not() is not defined in some language? Because creator of that language probably had not need this type of language construction. Because it is better to let things be simpler.