I've just started learning J, which is very interesting, but I was wondering what kind of language it is exactly, in relation to common paradigms and classifications. For example, you could say that F# is a strongly typed, mainly functional (it supports OO and procedural programming, but it's considered to be "functional") language which belongs to the ML family. For J, however, I couldn't find much on how to classify it "conventionally", or find anything on Stackoverflow confirming that it's a functional programming language. Wikipedia says that it "is a very terse array programming language", "supports function-level programming", and "is not a Von Neumann programming language", none of which are more helpful.
I have a couple of questions:
What main paradigm (procedural, OO, functional, logical) do J/K/APL fall under? If their paradigm is only "array programming", what paradigm does that fall under or is most similar to?
What well-known programming languages are J/K/APL most similar to? For example, I'd guess that they're like Lisp, since they operate on arrays (lists) and have minimal, no comma syntax.
I'm just trying to categorize these languages in my head according to what I already know. Thank you.
J is related to the kind of functional programming (sometimes known as function-level programming, as opposed to value-level) advocated by John Backus, who is probably better known as the inventor of Fortran but spent the latter part of his career trying to move programming away from the style used by Fortran.
In his Turing Award Lecture entitled "Can Programming be Liberated from the von Neumann Style?" Backus presented an overview of his ideas, which he experimented with in his FP and FL languages. Those were inspired largely by Ken Iverson's APL, and Iverson in turn borrowed from Backus' languages when he developed J.
The key idea behind these, which was expanded and developed as a paradigm as the language family grew, was the formation of an algebra of programming. Using these algebraic tools, a programmer could derive or calculate a correct program to solve a problem by combining standard higher-order functions according to well-known mathematical rules. From the abstract of the lecture above:
Associated with the functional style of programming is an algebra of
programs whose variables range over programs and whose operations are
combining forms. This algebra can be used to transform programs and to
solve equations whose "unknowns" are programs in much the same way one
transforms equations in high school algebra. These transformations are
given by algebraic laws and are carried out in the same language in
which programs are written. Combining forms are chosen not only for
their programming power but also for the power of their associated
algebraic laws. General theorems of the algebra give the detailed
behavior and termination conditions for large classes of programs.
Although there doesn't seem to be a lot of recent research that uses the notation of this family of languages, the key ideas have seen somewhat recent development in other functional languages. Richard Bird and Lambert Meertens worked on a related formalism for algebraic manipulation and derivation of programs and the data they operate on; this is known as the Bird-Meertens Formalism or, informally, Squiggol.
Bird and Philip Wadler later wrote a text, "Introduction to Functional Programming", which introduced students to the more well-known "value-level" functional programming based on the lambda calculus. It originally used the Miranda programming language, a forerunner to Haskell, but in its 2nd edition was translated to use Haskell. I mention this because Erik Meijer, Maarten Fokkinga, and Ross Paterson used the example functions in the text as the motivating examples in their well-known paper "Functional Programming with Bananas, Lenses, Envelopes, and Barbed Wire", where they extend the Bird-Meertens Formalism, give it a basis in Category Theory, and show how the solution to each of the examples can be calculated based on the laws of the formalism and the recursion schemes captured by its higher-order functions.
These ideas took root in Haskell, and there you can find a style of programming known as "point-free" that bears a strong resemblance to FP programming. It eschews named variables and creates a new function purely by composition of other functions. Most of the language is not optimized for this use, so many functions are awkward to create in point-free style using only the standard libraries, but alternate libraries that provide more Squiggol-style combinator functions are available.
The algebraic style of constructing programs, thanks to its mathematical nature, is amenable to high-level analysis and transformation by sophisticated compilers. This has led to developments in "Fusion" or "Deforestation" optimizations in functional language compilers that allow algorithms expressed in this style to be reduced to highly efficient machine code loops without all the garbage data and redundant loops that a more naive translation would require. Earlier this year, a framework for generalized stream fusion was presented that showed very practical results from this style of programming.
Hopefully this background gives you a better idea of what the Wikipedia article was talking about and how the underlying paradigm works.
While other tags could also apply (as with other languages), J is certainly a functional language. It has most major attributes attributed to functional languages, such as functions being 'first class citizens,' currying, higher order functions, etc. Furthermore, if it means anything to you, I have read articles where the language creators themselves described the language as 'functional.'
You could also say that it is an array programming language, as all functions operate on arrays vs. single elements.
I think the short answer you are looking for is that J is a functional array programming language. You could also throw other descriptors out there, such as non-statically typed, etc.
As to your numbered questions:
Functional and array programming.
As far as array programming goes, they are not similar to any other well-known language; rather they are in their own category of 'array programming languages.' As far as functional aspects go, they'd be in the functional category.
Related
There are programming languages and theorem prover based on higher order logic (HOL). Examples include Twelf, lambda prolog, Isabelle. For example Twelf is is both a programming language and a theorem prover, while Isabelle is mainly a theorem prover, but for Isabelle code extraction is available.
I am looking for a HOL programming language based on haskell. The reason is that I like, for instance, lambda prolog very much, but it is not meant as a practical programming language. Lambda prolog lacks a standard library and interfacing with external libraries doesn't seem trivial. The problem is if you need some functionality, like writing a parser for a text file, you can't interface, say, with the many available existing libraries for haskell, and further, there is no standard library so you start from scratch.
Today I came across the Caledon programming language that was implemented as a master thesis, it seems. From the github page:
Caledon is a dependently typed, polymorphic, higher order logic
programming language.
This is interesting, since it is written in haskell so it should be easy to extend and interface with existing haskell libraries. But it seems that the project is in a bit early stage, I am not sure if input-output (IO) is implemented. Since I learned only today about Caledon, I think I might have missed some further projects. (BTW, I am not interested in standard logic programming languages like prolog).
Are there programming languages based on higher order logic besides Caledon that are implemented in haskell?
(I am asking for "implemented in haskell", as it is rather easy to connect programming languages that can be extracted to or are implemented in haskell. For example the Agda programming language can compile to haskell code and haskell libraries can be used conveniently and is extremly easy to use haskell libraries if you know how. Many other programming languages (e.g., ATS) I belive only provide the smallest common denominator which is a C based foreign function interface (FFI). In my eyes it is quite cumbersome to connect two higher programming languages via their respective C-based FFI interface. Thus the seemly abitrary part that "it should be implemented in haskell". Further, as a side note some users have downvoted in the past for my description of Agda as a programming language, but of course this is not true, i.e., consider Curry-Howard )
"Haskabelle is a converter from Haskell source files to Isabelle/HOL theories implemented in Haskell itself."
Haskabelle
Strange Statement: Haskell' is a higher order logic programming language based on Haskell. Type inference in Haskell with multiparameter type classes, type families, undecidable inference and whatnot actually forms a higher order logic programming language. This probably doesn't help you very much because:
The spec is literally constantly changing (I've had a few packages loose compatibility as they were based on hacks that got "fixed")
The type system itself doesn't have IO (yet?)
It can't really call other Haskell libraries from type inference
Its not very fast.
The logic programming semantics aren't exactly clear or stable.
It doesn't permit you to unify with lambdas or other type classes, although it does permit unification with functions.
Sadly, I know of extraordinarily few full HOL languages let alone ones implemented in Haskell - it turns out higher order unification is a huge pain to implement.
short answer: i don't know. long answer: you have small chances you will find purely academic language with thousands of libraries and tools for it. if you for some reason need that specific language for some specific problem then use it ONLY for that problem. not for parsing files, calculating taxes or launching rockets. create library and link it with other programs. or even better: create a microservice or connect the programs in other way (e.g. standard input/output) that doesn't require much effort. always use best tool for the job
Can anyone name a language with all the following properties:
Has algebraic data types
Has good support for linear algebra
Is fast(-er than python, at least)
Has at least some functional programming ability (I don't need monads)
Has been heard of, is not dead, and can interface on a C calling level
Scala
According to Wikipedia it has algebraic datatypes. And it is fast. Scala is both functional and object oriented. And it's a young language with a growing userbase but still to some extent compatible with Java.
There is a Scala library Scalala for linear algebra:
A high performance numeric linear algebra library for Scala, with rich Matlab-like operators on vectors and matrices; a library of numerical routines
I have my own favorite pet languages, and this isn't one of them, but it sounds to me like R is probably what you are looking for. It seems to be the hot new language these days for people doing heavy math.
As for the "faster than Python" part, that's tough to say. In general, languages don't really have a speed; language implementations do. So the only way to tell really is to compare your time-constraining algorithm on each implementation you can get.
I'd say C and C++. And they work well with:
Matlab
Maple
I have had previous exposure to imperative languages (C, some Java) however I would say I had no experience in programming. Therefore: treating me as a non-programmer, would Haskell be suitable as a first language?
My interests in Pure Mathematics and CS seem to align to the intention of most Haskell tutorials, and although i can inherently recognise the current and future industry value of imperative programming, I find the potential of functional programming (in as much as it seems such a paradigm shift) fascinating.
I guess my question can be distilled as follows - would a non-programmer have to understand imperative programming to appreciate and fully utilise functional programming?
Some references:
Are there any studies on whether functional/declarative or imperative programming is easier to learn as a first language?
Which programming languages have helped you to understand programming better?
Well, the existence of SICP suggests that functional languages can be used as introductory material. Scheme is perhaps more approachable than Haskell, however.
Haskell seems to have a reputation for being "difficult" to learn, but people tend to forget that classic imperative programming is difficult to learn as well. Many people struggle at first with the concept of assigning a value to a variable, and a surprising number of programmers never actually do become comfortable with pointers and indirect references.
The connections between Haskell and abstract mathematics don't really matter as much as people sometimes assume, but for someone interested in the math anyway, looking at the analogies might provide an interesting bonus.
There has been at least one study on the effects of teaching Haskell to beginner programmers:
The Risks and Benefits of Teaching Purely Functional Programming in First Year. Manuel M. T. Chakravarty and Gabriele Keller. Journal of Functional Programming 14(1), pp 113-123, 2004.
With the following abstract:
We argue that teaching purely
functional programming as such in
freshman courses is detrimental to
both the curriculum as well as to
promoting the paradigm. Instead, we
need to focus on the more general aims
of teaching elementary techniques of
programming and essential concepts of
computing. We support this viewpoint
with experience gained during several
semesters of teaching large first-year
classes (up to 600 students) in
Haskell. These classes consisted of
computer science students as well as
students from other disciplines. We
have systematically gathered student
feedback by conducting surveys after
each semester. This article
contributes an approach to the use of
modern functional languages in first
year courses and, based on this,
advocates the use of functional
languages in this setting.
So, yes, you can use Haskell, but you should focus on elementary, general techniques and essential concepts, rather than functional programming per se.
There are a number of popular books for beginner programmers that also make it an attractive target for teaching these elementary concepts, including:
"Programming in Haskell"
"The Craft of Functional Programming"
Additionally, Haskell is already widely taught as a first language. -- but remember, the key is to focus on the core concepts as illustrated in Haskell, not to teach the large, rich language that is Haskell itself.
I'll go against the popular opinion and say that Haskell is NOT a good first programming language for the typical first-time programmer. I don't think it is as approachable for a raw beginner as imperative languages like Ruby.
The reason for this, is that people do not think about the world in a functional manner. When they see a car driving down the street, they see the same car, with ever-changing mutable state. They don't see a series of slightly different immutable cars.
If you check out other SO questions, you'll see that Haskell is pretty much never mentioned as a good choice for a beginner.
However, if you are a mathematician, or already know enough about programming to understand the value of functional programming, I think Haskell is a fine choice.
So to summarize, I think Haskell is a perfect fit for you, but not a good fit for the typical beginner.
EDIT: Thanks for the insightful comments. Owen's point that people think in a multi-paradigm manner is very true. This strengthens my belief that a multi-paradigm language like Ruby would be easier to pick up, and has the added benefit of exposing the student to both imperative and functional thinking. Haskell is decidedly not multi-paradigm.
Chuck mentioned Haskell's sophisticated type system which is another great point. While I personally prefer statically typed languages, using a dynamic language allows a beginner to ignore that piece of the puzzle until they are curious enough to find out what is going on behind the scenes. Haskell's type system, while elegant, is in your face from day 1.
Eleven reasons to use Haskell as a mathematician
I cannot write it better than that. But to summarize:
Haskell is declarative and mathematics is the ultimate declarative language, which means that code written in Haskell is remarkably similar to what you would write as a mathematical statement.
Haskell is high-level, no need to know details about caches, memory management and all the other hardware stuff. Also that means short programs which is always good.
Haskell is great for symbolic computation, algebra, logic ...
Haskell is pretty :)
To answer your question: you'll have no problem to start with a functional language as a mathematician with no programming experience. Actually it's the better choice, you won't have to repair the brain damage you would get from C/Java/whatever.
You should also check Mathematica. Some people tend to dislike it since it is a commercial closed-source product, but I think it's a pretty good environment for doing mathematics.
If you haven't had any experience at all, it will in fact be easier for you to be productive in functional programming, especially PURE functional programming. I'm an immigrant from imperative to function, I had to deal with having to forget about 80% of what I learned to be productive in Haskell.
In contrast, it's easier to switch from functional to imperative later on.
On one hand, I think Haskell is nice as a first language, but I suppose, for anyone seriously interested in programming, it should be learned in parallel with C or after C (or an assembly). C is necessary to learn what's happening under the hood, what are the costs of doing this and that, and finally appreciate the usefulness of higher level of abstraction and automatic resource management. I think when being exposed to both C (as a low-level imperative language) and Haskell (as a high-level functional language), most students will find Haskell both practical and expressive.
On the other hand, I think that programming is a craft. It is a practical activity, and it is important to learn the joy of creating something new, useful or interesting. So you need to get things done. And the easiest way for this is using a language which has tools for your problems, i.e. libraries for your data formats, algorithms for your kind of problems. And at this point, Python (or Ruby) may be a better choice, because Hackage still lags behind PyPI in many areas (and say, how many days you need to teach a novice to manipulate an image, or to plot charts in Haskell?).
So, my opinion is that some exposure to low-level imperative programming is necessary (to OOP, probably, not). Then you can understand the value of Haskell. But to get things done, and to quickly become productive, Python is a better choice for beginners. Haskell requires a few weeks before it becomes your tool.
I would say that it is suitable as a first language, and that having learned an imperative language first would probably only interfere with the learning process (since it requires lots of unlearning first).
As a caveat, I would add that a functional language principles would probably be best understood by someone with a mathematical background, as the concepts are abstract mathematical ones.
I know that many schools do teach it as a first functional language, but not as a first language.
Yes it is. Real World Haskell is a great way to get into it http://book.realworldhaskell.org/
I would hesitantly say "yes" except for the fact that in learning, finding someone as a mentor or tutor would be a much less daunting task if you chose a more imperative language to start programming. Might I suggest R or Python (with NumPy and SciPy) instead?
No.
It's very easy for a haskell98 program to be clearly understood. LYAH is a great tutorial for people with no experience but trying to prevent a learner from stumbling on extensions x, y z is gona be tricky. Soon they start to explore and become overwhelmed with advanced programming/mathematical concepts which are much harder to understand but need to be understood to read other's code.
If every piece of haskell was written in just haskell'98/'10 I would probably say yes though.
Without necessarily addressing the question as such, I would add: if you find haskell's persnicketiness too hard, do not be discouraged.
There are other programming languages, even functional ones, which are late bound.
In formal specifications based on abstract algebraic types and equational theory you use formulas of equational theory to specify theory. System which will satisfy those constraints is called in formal logic a model.
Modeling is process of creating a model, which abstracts of some aspects, which are unnecessary details for a specific case. So concrete system has to adhere to created model in observed aspects.
Programming is a process of creating a program which will have specific behaviour - will perform specific algorithms - and programming languages through different paradigms enable us to think in a certain specific way, which abstracts of some details, usually machine specific ones.
So could we be doing all those things at the same time, because they are principially the same? Is declarative programming the nearest attempt to do that? Could we use some sort f programming languages which will be good for programming as well as for modeling and specification?
The scientist who has done the most to advance this point of view is Tony Hoare. Tony, along with his colleague Edsger Dijkstra, advocated nondeterministic programming languages so that there would be a smoother path from specification to implementation. Tony definitely wanted a single language for both specification and implementation. For more on this view, read his book on the Alegbra of Programming. Tony also did the seminal work on proving correctness of abstractions. All of this work was done in the context of simple, imperative languages with structured control flow and classic, side-effecting procedures. So there is not any connection with declarative programming of necessity. And historically, work on functional programming (the main branch of declarative programming) has followed more from Backus's Turing lecture on "liberating programming from the von Neumann bottleneck"; functional programming has been about programming productivity as much as anything else.
What we discovered since Hoare is that formal specifications and formal modelsl are very expensive. The expense hasn't been shown to be justified except in very special circumstances, like "if the software doesn't work, the patient will die" or "if the software doesn't work, the plane will crash." Informal models and specifications are quite useful, and much cheaper to produce and work with. There is still interesting research going on around the fringes on modelling, model checking, and so on. One of my personal favorites is the Alloy language done by Daniel Jackson's group at MIT. There's also great stuff done at Microsoft Research and plenty of good stuff elsewhere. There's some work in declarative programming as well, but it too is of the "cheap and cheerful" variety rather than a comprehensive, programmatic approach like Hoare's. One of my favorites there is Claessen's and Hughes's QuickCheck, which provides a way to state formal properties and explore them by random testing. No proofs or theorems, but still jolly useful.
In summary, you describe an agenda of doing formal models, specifications, and programs, all within a single framework. There is still plenty of good work going on piecemeal, but the unified agenda has been abandoned.
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What kind of problems is better solved in Prolog than in Haskell? What are the main differences between these two languages?
Edit
Is there a Haskell library (kind of a logical solver) that can mimic Prolog functionality?
Regarding the logic library question: If it doesn't exist, it should be possible to build one a variety of ways. The Reasoned Schemer builds logical reasoning capabilities into Scheme. Chapters 33-34 of PLAI discuss Prolog and implementing Prolog. These authors are building bridges between Scheme and Prolog. The creators of PLT Scheme have built as one of their languages a Lazy Scheme after the lazy evaluation feature of Haskell. Oleg Kiselyov's LogicT paper is brilliant as usual--he pushes the boundary for what is possible in many languages. There is also a logic programming example on the Haskell Wiki.
The Reasoned Schemer by Daniel P. Friedman, William E. Byrd, and Oleg Kiselyov
Programming Languages: Application and Interpretation by Shriram Krishnamurthi
LogicT - backtracking monad transformer with fair operations and pruning
Logic programming on Haskell Wiki
Prolog is mainly a language targeted at logical problems, especially from the AI and linguistic fields. Haskell is more of a general-purpose language.
Prolog is declarative (logical) language, what makes it easier to state logical problems in it. Haskell is a functional language and hence much better suited to computational problems.
Wikipedia on declarative programming:
In computer science, declarative
programming is a programming paradigm
that expresses the logic of a
computation without describing its
control flow. It attempts to minimize
or eliminate side effects by
describing what the program should
accomplish, rather than describing how
to go about accomplishing it. This is
in contrast from imperative
programming, which requires a detailed
description of the algorithm to be
run.
Declarative programming consider
programs as theories of a formal
logic, and computations as deductions
in that logic space. Declarative
programming has become of particular
interest recently, as it may greatly
simplify writing parallel programs.
Wikipedia on functional programming:
In computer science, functional
programming is a programming paradigm
that treats computation as the
evaluation of mathematical functions
and avoids state and mutable data. It
emphasizes the application of
functions, in contrast to the
imperative programming style, which
emphasizes changes in state.
Functional programming has its roots
in the lambda calculus, a formal
system developed in the 1930s to
investigate function definition,
function application, and recursion.
Many functional programming languages
can be viewed as embellishments to the
lambda calculus.
In short a declarative language declares a set of rules about what outputs should result from which inputs and uses those rules to deduce an output from an input, while a functional language declares a set of mathematical or logical functions which define how input is translated to output.
As for the ADDED question : none that I know of but you can either translate Haskell to Prolog, or implement Prolog in Haskell :)
Prolog is a logic programming language, whereas Haskell is a functional language. Functional languages are based on the concept of a function which takes a number of arguments and computes a value.
Prolog, on the other hand, does not have functions. Instead, predicates are used to prove a "theorem". Prolog predicates do not compute a value, they can answer "yes" or "no" and optionally bind input variables to values:
The usefulness of functional and logic programming often overlap. Functional programming has gained quite a bit of traction lately, while Prolog is still much a niche language, much due to the fact that it is much more different from the common concepts of functions and methods of mainstream OOP than functional programming is, and often considered (very) difficult to learn.
Certain problems become almost trivial to implement in Prolog, especially in combination with constraint solvers.
You can read more about logic programming on Wikipedia.
You might find the paper Escape from Zurg: An Exercise in Logic Programming an interesting read. It shows a side-by-side comparison of the implementation of a simple search problem in Prolog and Haskell, along with a little typeclass framework for representing search problems more generally. The conclusion that the authors come to is that expressing at least some of these types of problems in Haskell is easier than in Prolog, primarily because the Haskell type system makes it easier to come up with nice representations of search states and moves from state to state.
In reality there are only 2 languages:
Machine language
Human language.
All other languages in between are merely translators and nothing more. When we use the machine language we must think like the machine and when using human languages we think like humans.
The true job of a programmer is to think both ways. Some programming tools like the assembler force the programmer to spend a lot more time thinking like the machine. Other tools like Prolog allows us to spend more time thinking like a human.
There is a penalty to be paid at each extreme either in performance or in cost.
If the business logic of your application can be reduced to a set of rules and its output to a set of goals (for example writing a game of Chess) then Prolog is ideal. On the other hand if you need to take the input and tell the computer how to compute the output then a functional language would be more appropriate.