I've been tasked with the portion of the code that reads through two lists and finds a path between the two lists.
My problem is however with reading and returning a TRUE case if I find the required node in the first list. I've been writing my code as below.
%declare the list
circle_line([cc1,cc2,cc3,cc4,cc5,cc6,cc7,cc8,cc9,cc10,cc11,cc12,cc13,cc14,cc15,cc16]).
%the predicate that finds the station i need
check_for_station(A) :- circle_line(X),
member(A,X),
write(A),nl.
Then in the cosole I type: check_for_station(cc9).
But the answer I get is "no."
I have a feeling that I'm declaring the list wrong, because in the debugger the value of X comes out to be "H135" or something and it clearly does not loop through every element to find the one that I need.
As whythehack found, in Amzi! Prolog the classic (and nondeterministic) member/2 predicate is not a "built-in" but is provided (along with other useful list manipulation predicates like length/2) in the list library. See here for some context about the built-in versus library predicates for lists.
If check_for_station/1 is only to be called with its argument A bound (as the example suggests), then Amzi!'s built-in (and deterministic) predicate is_member/2 will do the job (and a bit more quickly).
The thinking seems to be that nondeterministic member/2 is a two-line user-definition, and providing a faster deterministic version (not permitting backtracking over members of a list) is something the user could not easily provide for themselves.
Related
In System.Random.Shuffle,
shuffle' :: RandomGen gen => [a] -> Int -> gen -> [a]
The hackage page mentions this Int argument as
..., its length,...
However, it seems that a simple wrapper function like
shuffle'' x = shuffle' x (length x)
should've sufficed.
shuffle operates by building a tree form of its input list, including the tree size. The buildTree function performs this task using Data.Function.fix in a manner I haven't quite wrapped my head around. Somehow (I think due to the recursion of inner, not the fix magic), it produces a balanced tree, which then has logarithmic lookup. Then it consumes this tree, rebuilding it for every extracted item. The advantage of the data structure would be that it only holds remaining items in an immutable form; lazy updates work for it. But the size of the tree is required data during the indexing, so there's no need to pass it separately to generate the indices used to build the permutation. System.Random.Shuffle.shuffle indeed has no random element - it is only a permutation function. shuffle' exists to feed it a random sequence, using its internal helper rseq. So the reason shuffle' takes a length argument appears to be because they didn't want it to touch the list argument at all; it's only passed into shuffle.
The task doesn't seem terribly suitable for singly linked lists in the first place. I'd probably consider using VectorShuffling instead. And I'm baffled as to why rseq isn't among the exported functions, being the one that uses a random number generator to build a permutation... which in turn might have been better handled using Data.Permute. Probably the reasons have to with history, such as Data.Permute being written later and System.Random.Shuffle being based on a paper on immutable random access queues.
Data.Random.Extras seems to have a more straight forward Seq-based shuffle function.
It might be a case when length of the given list is already known, and doesn't need to be calculated again. Thus, it might be considered as an optimisation.
Besides, in general, the resulting list doesn't need to have the same size as the original one. Thus, this argument could be used for setting this length.
This is true for the original idea of Oleg (source - http://okmij.org/ftp/Haskell/perfect-shuffle.txt):
-- examples
t1 = shuffle1 ['a','b','c','d','e'] [0,0,0,0]
-- "abcde"
-- Note, that rseq of all zeros leaves the sequence unperturbed.
t2 = shuffle1 ['a','b','c','d','e'] [4,3,2,1]
-- "edcba"
-- The rseq of (n-i | i<-[1..n-1]) reverses the original sequence of elements
However, it's not the same for the 'random-shuffle' package implementation:
> shuffle [0..10] [0,0,0,0]
[0,1,2,3random-shuffle.hs: [shuffle] called with lists of different lengths
I think it worth to follow-up with the packages maintainers in order to understand the contract of this function.
I am doing OCaml 99, and can't quite understand some terms in this problem.
A string representation of binary trees. (medium)
Somebody represents binary trees as strings of the following type (see example): "a(b(d,e),c(,f(g,)))".
Write an OCaml function which generates this string representation, if the tree is given as usual (as Empty or Node(x,l,r) term).
Then write a function which does this inverse; i.e. given the string
representation, construct the tree in the usual form.
Finally, combine the two predicates in a single function
tree_string which can be used in both directions.
Write the same predicate tree_string using difference lists and a
single predicate tree_dlist which does the conversion between a tree
and a difference list in both directions.
For simplicity, suppose the information in the nodes is a single letter and there are no spaces in the string.
Here are my questions:
What does predicate mean in this problem?
For the 3rd point, it asks to make a function which can be used in both directions, i.e., can accept a tree and output a string or accept a string and output a tree. Should I use functor or something like that?
I totally can't understand the 4th point. What is difference lists?
These problems were originally intended to be solved in Prolog, which explains the terminology I think.
In Prolog a predicate can represent an equality (or maybe isomorphism is a better word?) between two sorts of values, such that if you have a value of one sort it can actually calculate the value of the other sort. I.e., it works as a two-way function. It's not at all clear how to code this in OCaml. Maybe you should peek at the answers?
A difference list is a Prolog data structure. Here's a SO page that seems to explain them (I googled very quickly): Understanding difference lists (Prolog)
Is there any particular reason for the inconsistent return types of the functions in Dart's ListBase class?
Some of the functions do what (as a functional programmer) I would expect, that is: List -> (apply function) -> List. These include: take, skip, reversed.
Others do not: thus l.removeLast() returns just the final element of the list; to get the List without the final element, you have to use a cascade: l..removeLast().
Others return a lazy Iterable, which requires further work to retrieve the list: newl = l.map(f).toList().
Some functions operate more like properties l.last, as opposed to functions l.removeLast()
Is there some subtle reason for these choices?
mbmcavoy is right. Dart is an imperative language and many List members modify the list in-place. The most prominent is the operator []=, but sort, shuffle, add, removeLast, etc. fall into the same category.
In addition to these imperative members, List inherits some functional-style members from Iterable: skip, take, where, map, etc. These are lazy and do not modify the List in place. They are backed by the original list. Modifying the backing list, will change the result of iterating over the iterable. List furthermore adds a few lazy members, like reversed.
To avoid confusion, lazy members always return an Iterable and not an object implementing the List interface. Some of the iterables guarantee fast length and index-operators (like take, skip and reversed) and could easily implement the List interface. However, this would inevitably lead to bugs, since they are lazy and backed by the original list.
(Disclaimer: I have not yet used Dart specifically, but hope to soon.)
Dart is not a functional programming language, which may the the source of your confusion.
Methods, such as .removeLast() are intended to change the state of the object they are called upon. The operation performed by l.removeLast() is to modify l so that it no longer contains the last item. You can access the resulting list by simply using l in your next statement.
(Note they are called "methods" rather than "functions", as they are not truly functions in the mathematical sense.)
The choice to return the removed item rather than the remaining list is a convenience. most frequently, the program will need to do something with the removed item (like move it to a different list).
For other methods, the returned data will relate to a common usage scenario, but it isn't always necessary to capture it.
In C, you can have a pointer to the first and last element of a singly-linked list, providing constant time access to the end of a list. Thus, appending one list to another can be done in constant time.
As far as I am aware, scheme does not provide this functionality (namely constant access to the end of a list) by default. To be clear, I am not looking for "pointer" functionality. I understand that is non-idiomatic in scheme and (as I suppose) unnecessary.
Could someone either 1) demonstrate the ability to provide a way to append two lists in constant time or 2) assure me that this is already available by default in scheme or racket (e.g., tell me that append is in fact a constant operation if I am wrong to think otherwise)?
EDIT:
I should make myself clearer. I am trying to create an inspectable queue. I want to have a list that I can 1) push onto the front in constant time, 2) pop off the back in constant time, and 3) iterate over using Racket's foldr or something similar (a Lisp right fold).
Standard Lisp lists cannot be appended to in constant time.
However, if you make your own list type, you can do it. Basically, you can use a record type (or just a cons cell)---let's call this the "header"---that holds pointers to the head and tail of the list, and update it each time someone adds to the list.
However, be aware that if you do that, lists are no longer structurally inductive. i.e., a longer list isn't simply an extension of a shorter list, because of the extra "header" involved. Thus, you lose a great part of the simplicity of Lisp algorithms which involve recursing into the cdr of a list at each iteration.
In other words, the lack of easy appending is a tradeoff to enable recursive algorithms to be written much more easily. Most functional programmers will agree that this is the right tradeoff, since appending in a pure-functional sense means that you have to copy every cell in all but the last list---so it's no longer O(1), anyway.
ETA to reflect OP's edit
You can create a queue, but with the opposite behaviour: you add elements to the back, and retrieve elements in the front. If you are willing to work with that, such a data structure is easy to implement in Scheme. (And yes, it's easy to append two such queues in constant time.)
Racket also has a similar queue data structure, but it uses a record type instead of cons cells, because Racket cons cells are immutable. You can convert your queue to a list using queue->list (at O(n) complexity) for times when you need to fold.
You want a FIFO queue. user448810 mentions the standard implementation for a purely-functional FIFO queue.
Your concern about losing the "key advantage of Lisp lists" needs to be unpacked a bit:
You can write combinators for custom data structures in Lisp. If you implement a queue type, you can easily write fold, map, filter and so on for it.
Scheme, however, does lack in the area of providing polymorphic sequence functions that can work on multiple sequence types. You do often end up either (a) converting your data structures back to lists in order to use the rich library of list functions, or (b) implementing your own versions of various of these functions for your custom types.
This is very much a shame, because singly-linked lists, while they are hugely useful for tons of computations, are not a do-all data structure.
But what is worse is that there's a lot of Lisp folk who like to pretend that lists are a "universal datatype" that can and should be used to represent any kind of data. I've programmed Lisp for a living, and oh my god I hate the code that these people produce; I call it "Lisp programmer's disease," and have much too often had to go in and fix a lot of n^2 that uses lists to represent sets or dictionaries to use hash tables or search trees instead. Don't fall into that trap. Use proper data structures for the task at hand. You can always build your own opaque data types using record types and modules in Racket; you make them opaque by exporting the type but not the field accessors for the record type (you export your type's user-facing operations instead).
It sounds like you are looking for a deque, not a list. The standard idiom for a deque is to keep two lists, the front half of the list in normal order and the back half of the list in reverse order, thus giving access to both ends of the deque. If the half of the list that you want to access is empty, reverse the other half and swap the meaning of the two halves. Look here for a fuller explanation and sample code.
I've noticed that in functional languages such as Haskell and OCaml you can do 2 actions with lists. First you can do x:xs where x is an element ans xs is a list and the resulting action is we get a new list where x is appended to the beginning of xs in constant time. Second is x++y where both x and y are lists and the resulting action is we get a new list where y gets appended to the end of x in linear time with respect to the number of elements in x.
Now I'm no expert in how languages are designed and compilers are built, but this seems to me a lot like a simple implementation of a linked list with one pointer to the first item. If I were to implement this data structure in a language like C++ I would find it to be generally trivial to add a pointer to the last element. In this case if these languages were implemented this way (assuming they do use linked lists as described) adding a "pointer" to the last item would make it much more efficient to add items to the end of a list and would allow pattern matching with the last element.
My question is are these data structures really implemented as linked lists, and if so why do they not add a reference to the last element?
Yes, they really are linked lists. But they are immutable. The advantage of immutability is that you don't have to worry about who else has a pointer to the same list. You might choose to write x++y, but somewhere else in the program might be relying on x remaining unchanged.
People who work on compilers for such languages (of whom I am one) don't worry about this cost because there are plenty of other data structures that provide efficient access:
A functional queue represented as two lists provides constant-time access to both ends and amortized constant time for put and get operations.
A more sophisticated data structure like a finger tree can provide several kinds of list access at very low cost.
If you just want constant-time append, John Hughes developed an excellent, simple representation of lists as functions, which provides exactly that. (In the Haskell library they are called DList.)
If you're interested in these sorts of questions you can get good info from Chris Okasaki's book Purely Functional Data Structures and from some of Ralf Hinze's less intimidating papers.
You said:
Second is x++y where both x and y are
lists and the resulting action is y
gets appended to the end of x in
linear time with respect to the number
of elements in x.
This is not really true in a functional language like Haskell; y gets appended to a copy of x, since anything holding onto x is depending on it not changing.
If you're going to copy all of x anyway, holding onto its last node doesn't really gain you anything.
Yes, they are linked lists. In languages like Haskell and OCaml, you don't add items to the end of a list, period. Lists are immutable. There is one operation to create new lists — cons, the : operator you refer to earlier. It takes an element and a list, and creates a new list with the element as the head and the list as the tail. The reason x++y takes linear time is because it must cons the last element of x with y, and then cons the second-to-last element of x with that list, and so on with each element of x. None of the cons cells in x can be reused, because that would cause the original list to change as well. A pointer to the last element of x would not be very helpful here — we still have to walk the whole list.
++ is just one of dozens of "things you can do with lists". The reality is that lists are so versatile that one rarely uses other collections. Also, we functional programmers almost never feel the need to look at the last element of a list - if we need to, there is a function last.
However, just because lists are convenient this does not mean that we do not have other data structures. If you're really interested, have a look at this book http://www.cs.cmu.edu/~rwh/theses/okasaki.pdf (Purely Functional Data Structures). You'll find trees, queues, lists with O(1) append of an element at the tail, and so forth.
Here's a bit of an explanation on how things are done in Clojure:
The easiest way to avoid mutating state is to use immutable data structures. Clojure provides a set of immutable lists, vectors, sets and maps. Since they can't be changed, 'adding' or 'removing' something from an immutable collection means creating a new collection just like the old one but with the needed change. Persistence is a term used to describe the property wherein the old version of the collection is still available after the 'change', and that the collection maintains its performance guarantees for most operations. Specifically, this means that the new version can't be created using a full copy, since that would require linear time. Inevitably, persistent collections are implemented using linked data structures, so that the new versions can share structure with the prior version. Singly-linked lists and trees are the basic functional data structures, to which Clojure adds a hash map, set and vector both based upon array mapped hash tries.
(emphasis mine)
So basically it looks you're mostly correct, at least as far as Clojure is concerned.