What is inside Erlang's digraph? - erlang

Disclaimer: The author is a newbie in Erlang.
I would like to implement some kind of shortest-path algorithm in Erlang.
There is a standard implementation of graph data structure in Erlang: http://www.erlang.org/doc/man/digraph.html
However, I have not found any information on the actual data structure it uses.
Mostly I would like to know:
what is the worst case performance of getting all 'neighbours' for a vertex action?
what is the worst case performance of fetching a vertex from the graph?

A digraph uses 3 ets tables (vertices, edges and neighbour vertices).
So both of that operations are O(1).
Take a look at OTP code, it's clean and in most cases idiomatic Erlang. stdlib's gen.erl + gen_server.erl, proc_lib.erl and sys.erl are must read :)

Related

Parse batch of SequenceExample

There is function to parse SequenceExample --> tf.parse_single_sequence_example().
But it parses only single SequenceExample, which is not effective.
Is there any possibility to parse a batch of SequenceExamples?
tf.parse_example can parse many Examples.
Documentation for tf.parse_example contain a little info about SequenceExample:
Each FixedLenSequenceFeature df maps to a Tensor of the specified type (or tf.float32 if not specified) and shape (serialized.size(), None) + df.shape. All examples in serialized will be padded with default_value along the second dimension.
But it is not clear, how to do that. Have not found any examples in google.
Is it possible to parse many SequenceExamples using parse_example() or may be other function exists?
Edit:
Where can I ask question to tensorflow developers: does they plan to implement parse function for multiple SequenceExample -s?
Any help ll be appreciated.
If you have many small sequences where batching at this stage is important, I would recommend VarLenFeatures or FixedLenSequenceFeatures with regular Example protos (which, as you note, can be parsed in batches with parse_example). For examples of this, see the unit tests associated with example parsing (testSerializedContainingSparse parses Examples with FixedLenSequenceFeatures).
SequenceExamples are more geared toward cases where there is significant amounts of preprocessing work to be done for each SequenceExample (which can be done in parallel with queues). parse_example does does not support SequenceExamples.

F# tail recursion and why not write a while loop?

I'm learning F# (new to functional programming in general though used functional aspects of C# for years but let's face it, that's pretty different) and one of the things that I've read is that the F# compiler identifies tail recursion and compiles it into a while loop (see http://thevalerios.net/matt/2009/01/recursion-in-f-and-the-tail-recursion-police/).
What I don't understand is why you would write a recursive function instead of a while loop if that's what it's going to turn into anyway. Especially considering that you need to do some extra work to make your function recursive.
I have a feeling someone might say that the while loop is not particularly functional and you want to act all functional and whatnot so you use recursion but then why is it sufficient for the compiler to turn it into a while loop?
Can someone explain this to me?
You could use the same argument for any transformation that the compiler performs. For instance, when you're using C#, do you ever use lambda expressions or anonymous delegates? If the compiler is just going to turn those into classes and (non-anonymous) delegates, then why not just use those constructions yourself? Likewise, do you ever use iterator blocks? If the compiler is just going to turn those into state machines which explicitly implement IEnumerable<T>, then why not just write that code yourself? Or if the C# compiler is just going to emit IL anyway, why bother writing C# instead of IL in the first place? And so on.
One obvious answer to all of these questions is that we want to write code which allows us to express ourselves clearly. Likewise, there are many algorithms which are naturally recursive, and so writing recursive functions will often lead to a clear expression of those algorithms. In particular, it is arguably easier to reason about the termination of a recursive algorithm than a while loop in many cases (e.g. is there a clear base case, and does each recursive call make the problem "smaller"?).
However, since we're writing code and not mathematics papers, it's also nice to have software which meets certain real-world performance criteria (such as the ability to handle large inputs without overflowing the stack). Therefore, the fact that tail recursion is converted into the equivalent of while loops is critical for being able to use recursive formulations of algorithms.
A recursive function is often the most natural way to work with certain data structures (such as trees and F# lists). If the compiler wants to transform my natural, intuitive code into an awkward while loop for performance reasons that's fine, but why would I want to write that myself?
Also, Brian's answer to a related question is relevant here. Higher-order functions can often replace both loops and recursive functions in your code.
The fact that F# performs tail optimization is just an implementation detail that allows you to use tail recursion with the same efficiency (and no fear of a stack overflow) as a while loop. But it is just that - an implementation detail - on the surface your algorithm is still recursive and is structured that way, which for many algorithms is the most logical, functional way to represent it.
The same applies to some of the list handling internals as well in F# - internally mutation is used for a more efficient implementation of list manipulation, but this fact is hidden from the programmer.
What it comes down to is how the language allows you to describe and implement your algorithm, not what mechanics are used under the hood to make it happen.
A while loop is imperative by its nature. Most of the time, when using while loops, you will find yourself writing code like this:
let mutable x = ...
...
while someCond do
...
x <- ...
This pattern is common in imperative languages like C, C++ or C#, but not so common in functional languages.
As the other posters have said some data structures, more exactly recursive data structures, lend themselves to recursive processing. Since the most common data structure in functional languages is by far the singly linked list, solving problems by using lists and recursive functions is a common practice.
Another argument in favor of recursive solutions is the tight relation between recursion and induction. Using a recursive solution allows the programmer to think about the problem inductively, which arguably helps in solving it.
Again, as other posters said, the fact that the compiler optimizes tail-recursive functions (obviously, not all functions can benefit from tail-call optimization) is an implementation detail which lets your recursive algorithm run in constant space.

What are advantages and disadvantages of "point free" style in functional programming?

I know that in some languages (Haskell?) the striving is to achieve point-free style, or to never explicitly refer to function arguments by name. This is a very difficult concept for me to master, but it might help me to understand what the advantages (or maybe even disadvantages) of that style are. Can anyone explain?
The point-free style is considered by some author as the ultimate functional programming style. To put things simply, a function of type t1 -> t2 describes a transformation from one element of type t1 into another element of type t2. The idea is that "pointful" functions (written using variables) emphasize elements (when you write \x -> ... x ..., you're describing what's happening to the element x), while "point-free" functions (expressed without using variables) emphasize the transformation itself, as a composition of simpler transforms. Advocates of the point-free style argue that transformations should indeed be the central concept, and that the pointful notation, while easy to use, distracts us from this noble ideal.
Point-free functional programming has been available for a very long time. It was already known by logicians which have studied combinatory logic since the seminal work by Moses Schönfinkel in 1924, and has been the basis for the first study on what would become ML type inference by Robert Feys and Haskell Curry in the 1950s.
The idea to build functions from an expressive set of basic combinators is very appealing and has been applied in various domains, such as the array-manipulation languages derived from APL, or the parser combinator libraries such as Haskell's Parsec. A notable advocate of point-free programming is John Backus. In his 1978 speech "Can Programming Be Liberated From the Von Neumann Style ?", he wrote:
The lambda expression (with its substitution rules) is capable of
defining all possible computable functions of all possible types
and of any number of arguments. This freedom and power has its
disadvantages as well as its obvious advantages. It is analogous
to the power of unrestricted control statements in conventional
languages: with unrestricted freedom comes chaos. If one
constantly invents new combining forms to suit the occasion, as
one can in the lambda calculus, one will not become familiar with
the style or useful properties of the few combining forms that
are adequate for all purposes. Just as structured programming
eschews many control statements to obtain programs with simpler
structure, better properties, and uniform methods for
understanding their behavior, so functional programming eschews
the lambda expression, substitution, and multiple function
types. It thereby achieves programs built with familiar
functional forms with known useful properties. These programs are
so structured that their behavior can often be understood and
proven by mechanical use of algebraic techniques similar to those
used in solving high school algebra problems.
So here they are. The main advantage of point-free programming are that they force a structured combinator style which makes equational reasoning natural. Equational reasoning has been particularly advertised by the proponents of the "Squiggol" movement (see [1] [2]), and indeed use a fair share of point-free combinators and computation/rewriting/reasoning rules.
[1] "An introduction to the Bird-Merteens Formalism", Jeremy Gibbons, 1994
[2] "Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire", Erik Meijer, Maarten Fokkinga and Ross Paterson, 1991
Finally, one cause for the popularity of point-free programming among Haskellites is its relation to category theory. In category theory, morphisms (which could be seen as "transformations between objects") are the basic object of study and computation. While partial results allow reasoning in specific categories to be performed in a pointful style, the common way to build, examine and manipulate arrows is still the point-free style, and other syntaxes such as string diagrams also exhibit this "pointfreeness". There are rather tight links between the people advocating "algebra of programming" methods and users of categories in programming (for example the authors of the banana paper [2] are/were hardcore categorists).
You may be interested in the Pointfree page of the Haskell wiki.
The downside of pointfree style is rather obvious: it can be a real pain to read. The reason why we still love to use variables, despite the numerous horrors of shadowing, alpha-equivalence etc., is that it's a notation that's just so natural to read and think about. The general idea is that a complex function (in a referentially transparent language) is like a complex plumbing system: the inputs are the parameters, they get into some pipes, are applied to inner functions, duplicated (\x -> (x,x)) or forgotten (\x -> (), pipe leading nowhere), etc. And the variable notation is nicely implicit about all that machinery: you give a name to the input, and names on the outputs (or auxiliary computations), but you don't have to describe all the plumbing plan, where the small pipes will go not to be a hindrance for the bigger ones, etc. The amount of plumbing inside something as short as \(f,x,y) -> ((x,y), f x y) is amazing. You may follow each variable individually, or read each intermediate plumbing node, but you never have to see the whole machinery together. When you use a point-free style, all the plumbing is explicit, you have to write everything down, and look at it afterwards, and sometimes it's just plain ugly.
PS: this plumbing vision is closely related to the stack programming languages, which are probably the least pointful programming languages (barely) in use. I would recommend trying to do some programming in them just to get of feeling of it (as I would recommend logic programming). See Factor, Cat or the venerable Forth.
I believe the purpose is to be succinct and to express pipelined computations as a composition of functions rather than thinking of threading arguments through. Simple example (in F#) - given:
let sum = List.sum
let sqr = List.map (fun x -> x * x)
Used like:
> sum [3;4;5]
12
> sqr [3;4;5]
[9;16;25]
We could express a "sum of squares" function as:
let sumsqr x = sum (sqr x)
And use like:
> sumsqr [3;4;5]
50
Or we could define it by piping x through:
let sumsqr x = x |> sqr |> sum
Written this way, it's obvious that x is being passed in only to be "threaded" through a sequence of functions. Direct composition looks much nicer:
let sumsqr = sqr >> sum
This is more concise and it's a different way of thinking of what we're doing; composing functions rather than imagining the process of arguments flowing through. We're not describing how sumsqr works. We're describing what it is.
PS: An interesting way to get your head around composition is to try programming in a concatenative language such as Forth, Joy, Factor, etc. These can be thought of as being nothing but composition (Forth : sumsqr sqr sum ;) in which the space between words is the composition operator.
PPS: Perhaps others could comment on the performance differences. It seems to me that composition may reduce GC pressure by making it more obvious to the compiler that there is no need to produce intermediate values as in pipelining; helping make the so-called "deforestation" problem more tractable.
While I'm attracted to the point-free concept and used it for some things, and agree with all the positives said before, I found these things with it as negative (some are detailed above):
The shorter notation reduces redundancy; in a heavily structured composition (ramda.js style, or point-free in Haskell, or whatever concatenative language) the code reading is more complex than linearly scanning through a bunch of const bindings and using a symbol highlighter to see which binding goes into what other downstream calculation. Besides the tree vs linear structure, the loss of descriptive symbol names makes the function hard to intuitively grasp. Of course both the tree structure and the loss of named bindings also have a lot of positives as well, for example, functions will feel more general - not bound to some application domain via the chosen symbol names - and the tree structure is semantically present even if bindings are laid out, and can be comprehended sequentially (lisp let/let* style).
Point-free is simplest when just piping through or composing a series of functions, as this also results in a linear structure that we humans find easy to follow. However, threading some interim calculation through multiple recipients is tedious. There are all kinds of wrapping into tuples, lensing and other painstaking mechanisms go into just making some calculation accessible, that would otherwise be just the multiple use of some value binding. Of course the repeated part can be extracted out as a separate function and maybe it's a good idea anyway, but there are also arguments for some non-short functions and even if it's extracted, its arguments will have to be somehow threaded through both applications, and then there may be a need for memoizing the function to not actually repeat the calculation. One will use a lot of converge, lens, memoize, useWidth etc.
JavaScript specific: harder to casually debug. With a linear flow of let bindings, it's easy to add a breakpoint wherever. With the point-free style, even if a breakpoint is somehow added, the value flow is hard to read, eg. you can't just query or hover over some variable in the dev console. Also, as point-free is not native in JS, library functions of ramda.js or similar will obscure the stack quite a bit, especially with the obligate currying.
Code brittleness, especially on nontrivial size systems and in production. If a new piece of requirement comes in, then the above disadvantages get into play (eg. harder to read the code for the next maintainer who may be yourself a few weeks down the line, and also harder to trace the dataflow for inspection). But most importantly, even something seemingly small and innocent new requirement can necessitate a whole different structuring of the code. It may be argued that it's a good thing in that it'll be a crystal clear representation of the new thing, but rewriting large swaths of point-free code is very time consuming and then we haven't mentioned testing. So it feels that the looser, less structured, lexical assignment based coding can be more quickly repurposed. Especially if the coding is exploratory, and in the domain of human data with weird conventions (time etc.) that can rarely be captured 100% accurately and there may always be an upcoming request for handling something more accurately or more to the needs of the customer, whichever method leads to faster pivoting matters a lot.
To the pointfree variant, the concatenative programming language, i have to write:
I had a little experience with Joy. Joy is a very simple and beautiful concept with lists. When converting a problem into a Joy function, you have to split your brain into a part for the stack plumbing work and a part for the solution in the Joy syntax. The stack is always handled from the back. Since the composition is contained in Joy, there is no computing time for a composition combiner.

Probabilistic Generation of Semantic Networks

I've studied some simple semantic network implementations and basic techniques for parsing natural language. However, I haven't seen many projects that try and bridge the gap between the two.
For example, consider the dialog:
"the man has a hat"
"he has a coat"
"what does he have?" => "a hat and coat"
A simple semantic network, based on the grammar tree parsing of the above sentences, might look like:
the_man = Entity('the man')
has = Entity('has')
a_hat = Entity('a hat')
a_coat = Entity('a coat')
Relation(the_man, has, a_hat)
Relation(the_man, has, a_coat)
print the_man.relations(has) => ['a hat', 'a coat']
However, this implementation assumes the prior knowledge that the text segments "the man" and "he" refer to the same network entity.
How would you design a system that "learns" these relationships between segments of a semantic network? I'm used to thinking about ML/NL problems based on creating a simple training set of attribute/value pairs, and feeding it to a classification or regression algorithm, but I'm having trouble formulating this problem that way.
Ultimately, it seems I would need to overlay probabilities on top of the semantic network, but that would drastically complicate an implementation. Is there any prior art along these lines? I've looked at a few libaries, like NLTK and OpenNLP, and while they have decent tools to handle symbolic logic and parse natural language, neither seems to have any kind of proabablilstic framework for converting one to the other.
There is quite a lot of history behind this kind of task. Your best start is probably by looking at Question Answering.
The general advice I always give is that if you have some highly restricted domain where you know about all the things that might be mentioned and all the ways they interact then you can probably be quite successful. If this is more of an 'open-world' problem then it will be extremely difficult to come up with something that works acceptably.
The task of extracting relationship from natural language is called 'relationship extraction' (funnily enough) and sometimes fact extraction. This is a pretty large field of research, this guy did a PhD thesis on it, as have many others. There are a large number of challenges here, as you've noticed, like entity detection, anaphora resolution, etc. This means that there will probably be a lot of 'noise' in the entities and relationships you extract.
As for representing facts that have been extracted in a knowledge base, most people tend not to use a probabilistic framework. At the simplest level, entities and relationships are stored as triples in a flat table. Another approach is to use an ontology to add structure and allow reasoning over the facts. This makes the knowledge base vastly more useful, but adds a lot of scalability issues. As for adding probabilities, I know of the Prowl project that is aimed at creating a probabilistic ontology, but it doesn't look very mature to me.
There is some research into probabilistic relational modelling, mostly into Markov Logic Networks at the University of Washington and Probabilstic Relational Models at Stanford and other places. I'm a little out of touch with the field, but this is is a difficult problem and it's all early-stage research as far as I know. There are a lot of issues, mostly around efficient and scalable inference.
All in all, it's a good idea and a very sensible thing to want to do. However, it's also very difficult to achieve. If you want to look at a slick example of the state of the art, (i.e. what is possible with a bunch of people and money) maybe check out PowerSet.
Interesting question, I've been doing some work on a strongly-typed NLP engine in C#: http://blog.abodit.com/2010/02/a-strongly-typed-natural-language-engine-c-nlp/ and have recently begun to connect it to an ontology store.
To me it looks like the issue here is really: How do you parse the natural language input to figure out that 'He' is the same thing as "the man"? By the time it's in the Semantic Network it's too late: you've lost the fact that statement 2 followed statement 1 and the ambiguity in statement 2 can be resolved using statement 1. Adding a third relation after the fact to say that "He" and "the man" are the same is another option but you still need to understand the sequence of those assertions.
Most NLP parsers seem to focus on parsing single sentences or large blocks of text but less frequently on handling conversations. In my own NLP engine there's a conversation history which allows one sentence to be understood in the context of all the sentences that came before it (and also the parsed, strongly-typed objects that they referred to). So the way I would handle this is to realize that "He" is ambiguous in the current sentence and then look back to try to figure out who the last male person was that was mentioned.
In the case of my home for example, it might tell you that you missed a call from a number that's not in its database. You can type "It was John Smith" and it can figure out that "It" means the call that was just mentioned to you. But if you typed "Tag it as Party Music" right after the call it would still resolve to the song that's currently playing because the house is looking back for something that is ITaggable.
I'm not exactly sure if this is what you want, but take a look at natural language generation wikipedia, the "reverse" of parsing, constructing derivations that conform to the given semantical constraints.

Do concepts like Map and Reduce apply to all Functional Programming Languages?

I have just started delving into the world of functional programming.
A lot of OOP (Object Oriented Programming) concepts such as inheritance and polymorphism apply to most modern OO languages like C#, Java and VB.NET.
But how about concepts such as Map, Reduce, Tuples and Sets, do they apply to all FP (Functional Programming) languages?
I have just started with F#. But do aforementioned concepts apply to other FP like Haskell, Nemerle, Lisp, etc.?
You bet. The desirable thing about function programming is that the mathematical concepts you describe are more naturally expressed in an FP.
It's a bit of tough going, but John Backus' Turing Award paper in which he described functional (or "applicative") programming is a good read. The Wikipedia article is good too.
Yes; higher-order functions, algebraic data types, folds/catamorphisms, etc are common to almost all functional languages (though they sometimes go by slightly different names in each language).
Functional tools apply to all programming, not just languages that handle that explicitly. For example, python has map and reduce builtin functions that do exactly what you expect, besides out of order evaluation. you'll need something like the multiprocessing module to get really clever.
Even if the language doesn't provide the exact primitives, most modern languages still make it possible to get the desired effect with a bit more work. This is similar to the way a class-like concept can be coded in pure C.
I would interpret what you're asking as, "Are higher-order functions (map, reduce, filter, ...) and immutable data structures (tuples, cons lists, records, maps, sets, ...) common across FP languages?" and I would say, absolutely yes.
Like you say, OOP has well known pillars (encapsulation, inheritance, polymorphism). The "pillars" of functional programming I'd say are 1) Using functions as first-class values and 2) Expressing yourself without side effects.
You'll likely find common tools to apply these ideas across various FP languages (F# is an excellent choice BTW!) and you'll see them finding their way into more mainstream languages; maybe in a less recognizable form (e.g. LINQ's Select = map, Aggregate = reduce/fold, Where = filter, C# has light weight lambda syntax, System.Tuple, etc.).
As an aside, the thing that seems to be generally missing from non-explicitly-FP languages is good immutable data structures and syntax support for them (not merely a library) which makes it hard to stick to pillar #2 in those languages. F# lists, records, tuples, etc. all are good examples of great language and library combined support for this.
If you really want to jump into the deep end and understand why these concepts are not just conventional but, ahem, foundational, check out the paper "Functional programming with bananas, lenses, envelopes and barbed wire".
They apply to all languages that contain data types that can be "mapped" and "reduced", i.e maps, arrays/vectors, or lists.
In a "pure lambda calculus" language, where every data structure is defined via function application, you can of course apply functions in parallel (i.e., in a call fn(expr1, expr2), you can evaluate expr1 and expr2 in parallel), but that isn't really what map/reduce is about.

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