Prolog find all paths Implementation - multithreading

I've been tasked to implement a version of findall in Prolog without using any Prolog built-ins except for not and cut - so basically in pure Prolog.
I'm trying to search a tree for all direct descendants and return the results in a list
parent(a, b).
parent(b, c).
parent(b, d).
parent(e, d).
What I have so far is:
find(X, L) :- find2(X, [], L).
find2(X, Acc, L) :- parent(Y, X), find2(Y, [Y|Acc], L).
find2(_, Acc, Acc).
What I want to be getting when I enter for example:
find(a,X).
would be:
X = [b, c, d]
(Order not important)
However instead I am getting:
X = [b, c] ;
X = [b, d] ;
X = [b] ;
X = [].
I'm new to Prolog so any help on this would be much appreciated.
Thanks

Besides asserting data as you go, you can also use an extra-logical predicate such as nb_setarg/3. Then once a parent is found, you fail back past nb_setarg and find another parent. All previously found solutions should stay in the term you did nb_setarg on, then after all results are exhausted, the nb_setarg term is the answer. The SWI-Prolog example is good, but its just a counter. Try doing it with a list (or better yet: difference list) that builds as you go.

Take a look at this solution.
Note that this solution uses dynamic predicate named queue in order to cache all solutions until all possibilities are exhausted. Once no more solution exists, implementation retracts all facts and composes the list.
This is of course a bit simplified solution, imagine what would happen if two findall would be active at the same time. It is also a bit fragile on exact semantics of assert and retract if particular prolog implementation

Thanks for you help everyone. I managed to solve it in the end by adding a predicate which checked each item against the current list, and failed if it was already present:
find(X, Loa) :- find(X, [], Loa), !.
find(X, Acc, Loa) :- dec(X, Y), uList(Y, Acc, AccNew), find(X, AccNew, Loa).
find(_, Acc, Acc).
dec(X,Y) :- parent(X,Y).
dec(X,Y) :- parent(X,Z), dec(Z,Y).
uList(X, [], [X]) :- !.
uList(H, [H|_], _) :- !, fail.
uList(X, [H|T], L) :- uList(X, T, Rtn), L = [H|Rtn].

Related

Prolog String manipulation, replacing part of string

What i am trying to do
?- string_manipulation(1\2\3,Z).
Z = 1/2/3.
?- string_manipulation(s/t/a/c/k,Z).
Z = s\t\a\c\k.
What i have tried so far
sign(/,\).
string_manipulation(Forward,Back):-
sign(Forward,_\),
; sign(/,Back).
I will be honest with you. I know this code is rubbish. I am kinda lost with this one. Just started learning Prolog, watched some videos and read some documentation but could not just find something similar to that from internet in the first look. Maybe someone could point me in some direction so i could learn the string manipulation with this one.
From the post title, and the predicate name (so called functor), seems you're looking for something like DCGs, but as an exercise in manipulation of structured terms, and operators, here is a solution for your probem:
string_manipulation(Xs, Ys) :-
member(( Xo , Yo ), [ ( / , \ ), ( \ , / ) ]),
Xs =.. [Xo, H, Xt],
Ys =.. [Yo, T, Yt],
string_manipulation(H, T),
string_manipulation(Xt, Yt).
string_manipulation(S, S) :-
atomic(S).
In SWI-Prolog, we need this preliminary declaration:
?- op(400,yfx,\).
true.
since by default
?- current_op(X,Y,/).
X = 400,
Y = yfx.
and
?- current_op(X,Y,\).
X = 200,
Y = fy.
Declaring the same precedence and associativity helps to keep things clearer.
Edit
The valuable suggestion by #mat:
string_manipulation(Xs, Ys) :-
op_replacement(Xo, Yo),
Xs =.. [Xo, H, Xt],
...
and
op_replacement(/, \).
op_replacement(\, /).
Looks like you want to replace an atom in an atom by another atom. But you would need to place quotes around the arguments, like for example '1\2\3' instead 1\2\3, otherwise the argument is not an atom but a term.
If your Prolog system has atom_split/3, you can bootstrap atom_replace/4 from it. atom_split/3 is part of Prolog Commons, and you need a bidrectional version of it. Namely you can then define:
atom_replace(Source, Old, New, Target) :-
atom_split(Source, Old, List),
atom_split(Target, New, List).
Here are some example runs. Don't worry about the backslash backslash, that is just needed to input an atom that contains a backslash. The second example using write/1 shows that it will not enter the atom:
Jekejeke Prolog 3, Runtime Library 1.3.6
?- atom_replace('1\\2\\3', '\\', '/', X).
X = '1/2/3'
?- atom_replace('s/t/a/c/k', '/', '\\', X), write(X), nl.
s\t\a\c\k
X = 's\\t\\a\\c\\k'

Haskell # type annotation [duplicate]

I've come across a piece of Haskell code that looks like this:
ps#(p:pt)
What does the # symbol mean in this context? I can't seem to find any info on Google (it's unfortunately hard to search for symbols on Google), and I can't find the function in the Prelude documentation, so I imagine it must be some sort of syntactic sugar instead.
Yes, it's just syntactic sugar, with # read aloud as "as". ps#(p:pt) gives you names for
the list: ps
the list's head : p
the list's tail: pt
Without the #, you'd have to choose between (1) or (2):(3).
This syntax actually works for any constructor; if you have data Tree a = Tree a [Tree a], then t#(Tree _ kids) gives you access to both the tree and its children.
The # Symbol is used to both give a name to a parameter and match that parameter against a pattern that follows the #. It's not specific to lists and can also be used with other data structures.
This is useful if you want to "decompose" a parameter into it's parts while still needing the parameter as a whole somewhere in your function. One example where this is the case is the tails function from the standard library:
tails :: [a] -> [[a]]
tails [] = [[]]
tails xxs#(_:xs) = xxs : tails xs
I want to add that # works at all levels, meaning you can do this:
let a#(b#(Just c), Just d) = (Just 1, Just 2) in (a, b, c, d)
Which will then produce this: ((Just 1, Just 2), Just 1, 1, 2)
So basically it's a way for you to bind a pattern to a value. This also means that it works with any kind of pattern, not just lists, as demonstrated above. This is a very useful thing to know, as it means you can use it in many more cases.
In this case, a is the entire Maybe Tuple, b is just the first Just in the tuple, and c and d are the values contained in the first and second Just in the tuple respectively
To add to what the other people have said, they are called as-patterns (in ML the syntax uses the keyword "as"), and are described in the section of the Haskell Report on patterns.

G-machine, (non-)strict contexts - why case expressions need special treatment

I'm currently reading Implementing functional languages: a tutorial by SPJ and the (sub)chapter I'll be referring to in this question is 3.8.7 (page 136).
The first remark there is that a reader following the tutorial has not yet implemented C scheme compilation (that is, of expressions appearing in non-strict contexts) of ECase expressions.
The solution proposed is to transform a Core program so that ECase expressions simply never appear in non-strict contexts. Specifically, each such occurrence creates a new supercombinator with exactly one variable which body corresponds to the original ECase expression, and the occurrence itself is replaced with a call to that supercombinator.
Below I present a (slightly modified) example of such transformation from 1
t a b = Pack{2,1} ;
f x = Pack{2,2} (case t x 7 6 of
<1> -> 1;
<2> -> 2) Pack{1,0} ;
main = f 3
== transformed into ==>
t a b = Pack{2,1} ;
f x = Pack{2,2} ($Case1 (t x 7 6)) Pack{1,0} ;
$Case1 x = case x of
<1> -> 1;
<2> -> 2 ;
main = f 3
I implemented this solution and it works like charm, that is, the output is Pack{2,2} 2 Pack{1,0}.
However, what I don't understand is - why all that trouble? I hope it's not just me, but the first thought I had of solving the problem was to just implement compilation of ECase expressions in C scheme. And I did it by mimicking the rule for compilation in E scheme (page 134 in 1 but I present that rule here for completeness): so I used
E[[case e of alts]] p = E[[e]] p ++ [Casejump D[[alts]] p]
and wrote
C[[case e of alts]] p = C[[e]] p ++ [Eval] ++ [Casejump D[[alts]] p]
I added [Eval] because Casejump needs an argument on top of the stack in weak head normal form (WHNF) and C scheme doesn't guarantee that, as opposed to E scheme.
But then the output changes to enigmatic: Pack{2,2} 2 6.
The same applies when I use the same rule as for E scheme, i.e.
C[[case e of alts]] p = E[[e]] p ++ [Casejump D[[alts]] p]
So I guess that my "obvious" solution is inherently wrong - and I can see that from outputs. But I'm having trouble stating formal arguments as to why that approach was bound to fail.
Can someone provide me with such argument/proof or some intuition as to why the naive approach doesn't work?
The purpose of the C scheme is to not perform any computation, but just delay everything until an EVAL happens (which it might or might not). What are you doing in your proposed code generation for case? You're calling EVAL! And the whole purpose of C is to not call EVAL on anything, so you've now evaluated something prematurely.
The only way you could generate code directly for case in the C scheme would be to add some new instruction to perform the case analysis once it's evaluated.
But we (Thomas Johnsson and I) decided it was simpler to just lift out such expressions. The exact historical details are lost in time though. :)

Translate list comprehension to Prolog

I have a list comprehension in Haskell that I want to translate to Prolog.
The point of the list comprehension is rotating a 4 by 4 grid:
rotate :: [Int] -> [Int]
rotate grid = [ grid !! (a + 4 * b) | a <- [0..3], b <- [0..3] ]
Now in Prolog, I translated it like this:
rotateGrid([T0,T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,T15],
[T0,T4,T8,T12,T1,T5,T9,T13,T2,T6,T10,T14,T3,T7,T11,T15]).
Can we do better?
We can use findall/3 for list comprehensions (Cf. the SWI-Prolog Documentation). E.g.,
?- findall(X, between(1,10,X), Xs).
Xs = [1,2,3,4,5,6,7,8,9,10]
Xs is a list holding all values that can unify with X when X is a number between 1 and 10. This is roughly equivalent to the Haskell expression let Xs = [x | x <- [1..10]](1). You can read a findall/3 statement thus: "find all values of [First Argument] such that [Conditions in Second Argument] hold, and put those values in the list, [Third Argument]".
I've used findall/3 to write a predicate rotate_grid(+Grid, ?RotatedGrid). Here is a list of the approximate Haskell-Prolog equivalences I used in the predicate; each line shows the relation between the value that the Haskell expression will evaluate to and the Prolog variable with the same value:
a <- [0..3] = A in between(0, 3, A)
b <- [0..3] = B in between(0, 3, B)
(a + 4 * d) = X in X is A + 4 * D
<Grid> !! <Index> = Element in nth0(Index, Grid, Element)
Then we simply need to find all the values of Element:
rotate_grid(Grid, RotatedGrid) :-
findall( Element,
( between(0,3,A),
between(0,3,B),
Index is A + 4 * B,
nth0(Index, Grid, Element) ),
RotatedGrid
).
To verify that this produces the right transformation, I down-cased the Prolog code from the question and posed the following query:
?- rotate_grid([t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15],
[t0,t4,t8,t12,t1,t5,t9,t13,t2,t6,t10,t14,t3,t7,t11,t15]).
| true.
Footnotes:
(1): between/3 isn't actually the analogue of [m..n], since the latter returns a list of values from m to n where between(M,N,X) will instantiate X with each value between M and N (inclusive) on backtracking. To get a list of numbers in SWI-Prolog, we can use numlist(M,N,Ns). So a stricter analogue for x <- [1.10] would be the conjunction member(X, Ns), numlist(1, 10, Ns).
You want a permutation of a list. The concrete elements are not considered. Therefore, you can generalize your Haskell signature to
rotate :: [x] -> [x]
This is already a very valuable hint for Prolog: the list's elements will not be considered - elements will not even be compared. So a Prolog solution should be able to handle variables directly, like so:
?- rotateGrid(L,R).
L = [_A,_B,_C,_D,_E,_F,_G,_H,_I,_J,_K,_L,_M,_N,_O,_P],
R = [_A,_E,_I,_M,_B,_F,_J,_N,_C,_G,_K,_O,_D,_H,_L,_P].
And your original definition handles this perfectly.
Your version using list comprehensions suggests itself to be realized via backtracking, certain precautions have to be taken. Using findall/3, as suggested by #aBathologist will rename variables:
?- length(L,16),rotate_grid(L,R).
L = [_A,_B,_C,_D,_E,_F,_G,_H,_I,_J,_K,_L,_M,_N,_O,_P],
R = [_Q,_R,_S,_T,_U,_V,_W,_X,_Y,_Z,_A1,_B1,_C1,_D1,_E1,_F1].
The built-in predicate bagof/3 addresses this problem. Note that we have to declare all local, existential variables explicitly:
rotate_grid2(Grid, RotatedGrid) :-
bagof(
Element,
A^B^Index^ % declaration of existential variables
( between(0,3,A),
between(0,3,B),
Index is A + 4 * B,
nth0(Index, Grid, Element)
),
RotatedGrid).
For lists that are shorter than 16 elements, the Haskell version produces a clean error, but here we get pretty random results:
?- L=[1,2,3,4],rotate_grid(L,R).
L = [1,2,3,4], R = [1,2,3,4].
?- L=[1,2,3,4,5],rotate_grid(L,R).
L = [1,2,3,4,5], R = [1,5,2,3,4].
This is due to the unclear separation between the part that enumerates and "generates" a concrete element. The cleanest way is to add length(Grid, 16) prior to the goal bagof/3.
List comprehensions in Prolog
Currently, only B-Prolog offers a form of list comprehensions:
R#=[E: A in 0..3,B in 0..3,[E,I],(I is A+4*B,nth0(I,L,E))].
However, it does not address the second problem:
| ?- L = [1,2,3], R#=[E: A in 0..3,B in 0..3,[E,I],(I is A+4*B,nth0(I,L,E))].
L = [1,2,3]
R = [1,2,3]
yes
Use a loop predicate foreach/4
If the comprehension should retain variables, which is for example important in constraint programming, a Prolog system could offer a predicate foreach/4. This predicate is the DCG buddy of foreach/2.
Here is how variables are not retained via findall/3, the
result R contains fresh variables according to the ISO
core semantics of findall/3:
Welcome to SWI-Prolog (threaded, 64 bits, version 7.7.1)
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software.
?- functor(L,foo,5), findall(X,
(between(1,5,N), M is 6-N, arg(M,L,X)), R).
L = foo(_5140, _5142, _5144, _5146, _5148),
R = [_5210, _5204, _5198, _5192, _5186].
And here is how variables can be retained via foreach/4,
the resulting list has the same variables as the compound
we started with:
Jekejeke Prolog 3, Runtime Library 1.3.0
(c) 1985-2018, XLOG Technologies GmbH, Switzerland
?- [user].
helper(N,L) --> [X], {M is 6-N, arg(M,L,X)}.
Yes
?- functor(L,foo,5), foreach(between(1,5,N),helper(N,L),R,[]).
L = foo(_A,_G,_M,_S,_Y),
R = [_Y,_S,_M,_G,_A]
Using foreach/4 instead of bagof/3 might seem a little bit over the top. foreach/4 will probably only show its full potential when implementing Picat loops, since it can build up constraints, what bagof/3 cannot do.
foreach/4 is an implementation without the full materialization of all solution that are then backtracked. It shares with bagof/3 the reconstruct of variables, but still allows backtracking in the conjunction of the closures.

What does the "#" symbol mean in reference to lists in Haskell?

I've come across a piece of Haskell code that looks like this:
ps#(p:pt)
What does the # symbol mean in this context? I can't seem to find any info on Google (it's unfortunately hard to search for symbols on Google), and I can't find the function in the Prelude documentation, so I imagine it must be some sort of syntactic sugar instead.
Yes, it's just syntactic sugar, with # read aloud as "as". ps#(p:pt) gives you names for
the list: ps
the list's head : p
the list's tail: pt
Without the #, you'd have to choose between (1) or (2):(3).
This syntax actually works for any constructor; if you have data Tree a = Tree a [Tree a], then t#(Tree _ kids) gives you access to both the tree and its children.
The # Symbol is used to both give a name to a parameter and match that parameter against a pattern that follows the #. It's not specific to lists and can also be used with other data structures.
This is useful if you want to "decompose" a parameter into it's parts while still needing the parameter as a whole somewhere in your function. One example where this is the case is the tails function from the standard library:
tails :: [a] -> [[a]]
tails [] = [[]]
tails xxs#(_:xs) = xxs : tails xs
I want to add that # works at all levels, meaning you can do this:
let a#(b#(Just c), Just d) = (Just 1, Just 2) in (a, b, c, d)
Which will then produce this: ((Just 1, Just 2), Just 1, 1, 2)
So basically it's a way for you to bind a pattern to a value. This also means that it works with any kind of pattern, not just lists, as demonstrated above. This is a very useful thing to know, as it means you can use it in many more cases.
In this case, a is the entire Maybe Tuple, b is just the first Just in the tuple, and c and d are the values contained in the first and second Just in the tuple respectively
To add to what the other people have said, they are called as-patterns (in ML the syntax uses the keyword "as"), and are described in the section of the Haskell Report on patterns.

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