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I'm wondering if there's a way to emulate Haskell's typeclasses in Common Lisp.
Generic functions allow overloading, and it's possible to define types using deftype(which could be defined by membership to some list of instances, for example).
But I can't dispatch on a type. Is there a way to make a class a subclass(and a subtype) of some other class after its definition(e.g. making the cons class a subclass of a sequence class, without redefining cons)?
Thanks.
Type classes in Haskell are a means to statically look up implementations for "interfaces" in the form of dictionaries (similarly to how vtables in e.g. C++ are used but (almost) fully statically, unlike C++ which does dynamic dispatch at runtime). Common Lisp however is a dynamically typed language so such lookup would make no sense. However you can implement your own look up of "type class" implementations (instances) at runtime — a design not too hard to imagine in a language as expressive as Common Lisp.
P.S. Python's Zope has an adaption mechanism with very similar charactetistics, if you feel like referring to an existing solution in a dynamic setting.
You cannot modify the class hierarchy in the way you envision, but you can achieve pretty much the same effect.
Suppose that your definition of a sequence is that it has a method for the function sequence-length.
(defclass sequence ...)
(defmethod sequence-length ((s sequence)) ...)
Then you can easily extend your sequence-length method to conses:
(defmethod sequence-length ((s cons))
(length s))
Did that create a new class that includes cons? Not really. You can express the type of things that have a sequence-length method by saying (or sequence cons), but that's not really useful.
I'm in the process of learning Haskell, and type classes seem like a powerful way to make type-safe polymorphic functions. But a lot of the Haskell Prelude functions don't use them. More specifically:
Most of the list functions don't work with other data structures (for instance, foldr and length are only implemented for lists and can't be used on arrays).
Modules like Data.ByteString are unusable unless you use import qualified since they include functions that have the same names as Prelude functions.
It seems like both of these problems would go away if the standard library used generic functions with type classes (please let me know if I'm totally off base with this).
I have two questions:
Are there technical or design
reasons that the Prelude is like this, or is it just for
historical reasons?
Looking around, it looks like there are a
couple of libraries (like
Data.Foldable and, if I'm not
mistaken, Scrap Your Boilerplate)
that replace the standard Prelude functions
with generic alternatives. Are
there any plans to incorporate these ideas into future versions of Haskell?
There is a very good pragmatic reason that "standard" Haskell (Prelude + base + maybe some more) doesn't use more polymorphism:
Designing general-use type classes is hard. Good designs for classes that abstract over container types like lists, arrays and "bytestrings" (personally I don't really consider Bytestring a container) aren't floating round waiting to be included in Haskell 2012. There are some designs e.g Listlike and the Edison classes, and a number of people have chipped away at the problem but excepting Foldable and Traversable no-one has produced any compelling designs.
The Haskell base library used to be more polymorphic - list comprehensions used to work for any monad, map and ++ weren't limited to List, and perhaps other things.
But folks at the time thought that it led to confusing error messages for beginners and that folks who aren't beginners can use the specifically polymorphic versions.
While there are many things in base, and specifically Prelude, that are historic I think any generalization would see plenty of technical push-back. The main issue is speed - if you're function has a type class constraint then you're going to be passing around a dictionary for the type class functions and maybe eating more space for specialization.
Some of the libraries, such as SYB, use extensions that aren't part of Haskell. The first task would be to formalize and build support for these features. Look at the Haskell' documents to see where Haskell is going and how you might be able to influence that path.
Real World Haskell has some insights about this in the Monad Transformers chapter:
In an ideal world, would we make a break from the past, and switch over Prelude to use Traversable and Foldable types? Probably not. Learning Haskell is already a stimulating enough adventure for newcomers. The Foldable and Traversable abstractions are easy to pick up when we already understand functors and monads, but they would put early learners on too pure a diet of abstraction. For teaching the language, it's good that map operates on lists, not on functors.
One of the main characteristics of functional programming is the use of side-effectless functions. However, this can be done in an imperative language also. The same is true for recursion and lambda functions (for example C++0x). Therefore I wonder whether imperative programming languages are a superset of functional ones.
I can't really say whether they are subset of one another. What I can tell, though, that (except for really esoteric languages) they are all Turing-complete, which means that in the end they're all equally powerful, but not neccesarily equally expressive.
Generally speaking, no; functional programming is a subset of declarative programming (which includes logic programming languages, like Prolog). Many imperative languages borrow elements from functional programming languages, but simply having lambdas or referentially-transparent functions does not make an imperative language functional; functional programming is about more than just these elements.
It is possible to implement a certain programming paradigm in a language which doesn't support the programming paradigm natively. For example its possible to write Object Oriented Code in C while it is not designed for this purpose.
Functional programming is a well developed programming paradigm of its own and is best learnt through languages like Haskell, LISP etc. And after you have learnt them well, even though you don't use these languages regularly, you may start using those principles in the day to day language you use on regular basis.
Some people may like to Google for Object oriented programming in C
A paradigm is a way of doing things, and there are two main programming paradigms: imperative and declarative. The fact that some languages allow to mix both paradigms doesn't mean that one is included in the other, but that the languages are multi-paradigm.
To clarify it a little bit more, let me continue with your analogy: if Lisp and OCaml (for example) are considered functional languages, and both of them allow imperative style... then should imperative be considered a subset of functional?
Most imperative languages don't have functions as first-order types, whereas most functionald o. (As does C++, via boost::function.)
By first-order type, this meas a value/variable can be of any type, an int, a bool, a function from int->bool. It usually also includes closures or bound values as well, where you have the same function, but some arguments are already filled in.
Those two are what functional programming is mostly about, IMHO.
I think it might be helpful to draw a distinction between paradigm and language.
To me, paradigms represent "ways of thinking" (concepts and abstractions such as functions, objects, recursion), whereas languages offer "ways of doing" (syntax, variables, evaluations).
All true programming languages are equivalent in the sense that they are Turing-complete and able, in theory, to compute any Turing-computable function as well as simulate or be simulated by a universal Turing machine.
The interesting thing is how difficult it is to accomplish certain tasks in certain languages or paradigms, how appropriate the tool is to the task. Even Conway's Game of Life is Turing-complete, but that does not make me want to program with it.
Many languages support a number of paradigms. C++ was designed as an object-oriented extension for C, but it is possible to write purely procedural code in it.
Some languages borrow/acquire features from other languages or paradigms over time (just look at the evolution of Java).
A few languages, like Common Lisp, are impressively multi-paradigm languages. It is possible to write code that is functional, object oriented or procedural in Lisp. Arguably, aspect-orientation is already part of the common lisp object system, and therefore "nothing special". In Lisp, it is easy to extend the language itself to do whatever you need it to do, thus it is sometimes called the "programmable programming language". (I'll point out here that Lisp describes a family of languages of which Common Lisp is only one dialect).
I think it doesn't matter which of the terms, declarative, imperative, functional or procedural, is a subset of which. What matters more is to understand the tools languages you're working with, and how those are different from other tools. Even more important is to understand the different ways of thinking that the paradigms represent, since those are your thought-tools. As with most other things in life, the more you understand, the more effective you become.
One way to look at it (not saying it's the right way 'cos I'm not a lang designer or theorist by any means) is that if the language is essentially converted to something else then that 'something else' must be the superset of the source. So bytecode is necessarily a superset of Java. .NET IL is a superset of C# and of F#. The functional constructs in C# (i.e. LINQ) are thus a subset of the imperative constructs of IL.
Since machine language is imperative, you could take the position that, therefore, all languages are imperative, because they are just abstractions useful for humans that are then boiled away by the compiler to procedural, imperative machine code.
Pattern mapping like
f:: [int] -> int
f [] = 0
f (x:xs) = 1 + f(xs)
is something that is for instance one thing that is not available in imperative languages.
Also constructs like curried functions:
add2 :: int -> int
add2 = (2 +)
is not available in most imperative languages
Yes, functional programming is a subset of imperative programming, but...
Yes, because there is nothing in functional programming that you can't do in imperative programming (syntax differences notwithstanding). You can "do" functional programming in an imperative language.
But...
The things you can't do are the key features of functional programming.
By limiting what you can do,
you make certain mistakes impossible,
you enable features (such as program analysis, simpler concurrency, simpler testing, etc).
Other benefits of functional programming are more subjective.
You often hear these arguments.
State allows side effects. Side effects are bad. Functional programming has no state. You can't have side effects without state.
This is a dubious benefit.
First, only unintended side effects are bad. Proper programming practices, such as limiting modification of state to privileged code, alleviate side effect issues.
Second, functional programming only has no internal state. If the program has IO (accessing files, network, hardware) you have external state, thus the potential of side effects.
Functional programs are easier to debug.
In some ways yes, like knowing the explicit path to an exception.
But having state to examine is a debugging benefit that functional programming does not have.
Functional programs are easier to understand.
This is only true if you are fluent in functional programming and not fluent in imperative programming.
I for one, being more fluent in imperative programming, find this argument to be false.
UML is a standard aimed at the modeling of software which will be written in OO languages, and goes hand in hand with Java. Still, could it possibly be used to model software meant to be written in the functional programming paradigm? Which diagrams would be rendered useful given the embedded visual elements?
Is there a modeling language aimed at functional programming, more specifically Haskell? What tools for putting together diagrams would you recommend?
Edited by OP Sept 02, 2009:
What I'm looking for is the most visual, lightest representation of what goes on in the code. Easy to follow diagrams, visual models not necessarily aimed at other programmers. I'll be developing a game in Haskell very soon but because this project is for my graduation conclusion work I need to introduce some sort of formalization of the proposed solution. I was wondering if there is an equivalent to the UML+Java standard, but for Haskell.
Should I just stick to storyboards, written descriptions, non-formalized diagrams (some shallow flow-chart-like images), non-formalized use case descriptions?
Edited by jcolebrand June 21, 2012:
Note that the asker originally wanted a visual metphor, and now that we've had three years, we're looking for more/better tools. None of the original answers really addressed the concept of "visual metaphor design tool" so ... that's what the new bounty is looking to provide for.
I believe the modeling language for Haskell is called "math". It's often taught in schools.
Yes, there are widely used modeling/specification languages/techniques for Haskell.
They're not visual.
In Haskell, types give a partial specification.
Sometimes, this specification fully determines the meaning/outcome while leaving various implementation choices.
Going beyond Haskell to languages with dependent types, as in Agda & Coq (among others), types are much more often useful as a complete specification.
Where types aren't enough, add formal specifications, which often take a simple functional form.
(Hence, I believe, the answers that the modeling language of choice for Haskell is Haskell itself or "math".)
In such a form, you give a functional definition that is optimized for clarity and simplicity and not all for efficiency.
The definition might even involve uncomputable operations such as function equality over infinite domains.
Then, step by step, you transform the specification into the form of an efficiently computable functional program.
Every step preserves the semantics (denotation), and so the final form ("implementation") is guaranteed to be semantically equivalent to the original form ("specification").
You'll see this process referred to by various names, including "program transformation", "program derivation", and "program calculation".
The steps in a typical derivation are mostly applications of "equational reasoning", augmented with a few applications of mathematical induction (and co-induction).
Being able to perform such simple and useful reasoning was a primary motivation for functional programming languages in the first place, and they owe their validity to the "denotative" nature of "genuinely functional programming".
(The terms "denotative" and "genuinely functional" are from Peter Landin's seminal paper The Next 700 Programming languages.)
Thus the rallying cry for pure functional programming used to be "good for equational reasoning", though I don't hear that description nearly as often these days.
In Haskell, denotative corresponds to types other than IO and types that rely on IO (such as STM).
While the denotative/non-IO types are good for correct equational reasoning, the IO/non-denotative types are designed to be bad for incorrect equational reasoning.
A specific version of derivation-from-specification that I use as often as possible in my Haskell work is what I call "semantic type class morphisms" (TCMs).
The idea there is to give a semantics/interpretation for a data type, and then use the TCM principle to determine (often uniquely) the meaning of most or all of the type's functionality via type class instances.
For instance, I say that the meaning of an Image type is as a function from 2D space.
The TCM principle then tells me the meaning of the Monoid, Functor, Applicative, Monad, Contrafunctor, and Comonad instances, as corresponding to those instances for functions.
That's a lot of useful functionality on images with very succinct and compelling specifications!
(The specification is the semantic function plus a list of standard type classes for which the semantic TCM principle must hold.)
And yet I have tremendous freedom of how to represent images, and the semantic TCM principle eliminates abstraction leaks.
If you're curious to see some examples of this principle in action, check out the paper Denotational design with type class morphisms.
We use theorem provers to do formal modelling (with verification), such as Isabelle or Coq. Sometimes we use domain specific languages (e.g. Cryptol) to do the high level design, before deriving the "low level" Haskell implementation.
Often we just use Haskell as the modelling language, and derive the actual implementation via rewriting.
QuickCheck properties also play a part in the design document, along with type and module decompositions.
Yes, Haskell.
I get the impression that programmers using functional languages don't feel the need to simplify their language of choice away when thinking about their design, which is one (rather glib) way of viewing what UML does for you.
I have watched a few video interviews, and read some interviews, with the likes of erik meijer and simon peyton-jones. It seems as when it comes to modelling and understanding ones problem domain, they use type signatures, especially function signatures.
Sequence diagrams (UML) could be related to the composition of functions.
A static class diagram (UML) could be related to type signatures.
In Haskell, you model by types.
Just begin with writing your function-, class- and data signatures without any implementation and try to make the types fit. Next step is QuickCheck.
E.g. to model a sort:
class Ord a where
compare :: a -> a -> Ordering
sort :: Ord a => [a] -> [a]
sort = undefined
then tests
prop_preservesLength l = (length l) == (length $ sort l)
...
and finally the implementation ...
Although not a recommendation to use (as it appears to be not available for download), but the HOPS system visualizes term graphs, which are often a convenient representation of functional programs.
It may be also considered a design tool as it supports documenting the programs as well as constructing them; I believe it can also step through the rewriting of the terms if you want it to so you can see them unfold.
Unfortunately, I believe it is no longer actively developed though.
I realize I'm late to the party, but I'll still give my answer in case someone would find it useful.
I think I'd go for systemic methodologies of the likes of SADT/IDEF0.
https://en.wikipedia.org/wiki/Function_model
https://en.wikipedia.org/wiki/Structured_Analysis_and_Design_Technique
Such diagrams can be made with the Dia program that is available on both Linux, Windows and MacOS.
You can a data flow process network model as described in Realtime Signal Processing: Dataflow, Visual, and Functional Programming by Hideki John Reekie
For example for code like (Haskell):
fact n | n == 0 = 1
| otherwise = n * fact (n - 1)
The visual representation would be:
What would be the point in modelling Haskell with Maths? I thought the whole point of Haskell was that it related so closely to Maths that Mathematicians could pick it up and run with it. Why would you translate a language into itself?
When working with another functional programming language (f#) I used diagrams on a white board describing the large blocks and then modelled the system in an OO way using UML, using classes. There was a slight miss match in the building blocks in f# (split the classes up into data structures and functions that acted upon them). But for the understanding from a business perspective it worked a treat. I would add mind that the problem was business/Web oriented and don't know how well the technique would work for something a bit more financial. I think I would probably capture the functions as objects without state and they should fit in nicely.
It all depends on the domain your working in.
I use USL - Universal Systems Language. I'm learning Erlang and I think it's a perfect fit.
Too bad the documentation is very limited and nobody uses it.
More information here.
This question is of course inspired by Monads in Haskell.
wrapping my head around continuation passing style has helped my javascript coding a lot
I would say First-class functions.
In computer science, a programming
language is said to support
first-class functions (or function
literals) if it treats functions as
first-class objects. Specifically,
this means that the language supports
constructing new functions during the
execution of a program, storing them
in data structures, passing them as
arguments to other functions, and
returning them as the values of other
functions. This concept doesn't cover
any means external to the language and
program (metaprogramming), such as
invoking a compiler or an eval
function to create a new function.
Do you want to measure the usefulness in connection with functional-programming itself or programming in general?
In general, the positive experience of functional programming doesn't result from particular techniques but from the way it changes your thinking -
Holding immutable data
Formulating declaratively (recursion, pattern-matching)
Treating functions as data
So I'd say that functional programming is the answer to your question itself.
But to give a more specific answer too, I'd vote for functional abstraction mechanisms like
monads
arrows
continuation-passing-style
zippers
higher-order-functions
generics + typeclasses.
As already said, they are very abstract things on the first view, but once you have understood them, they are extremely cool and valueable techniques to write concise, error-safe and last but not least highly reusable code.
Compare the following (Pseudocode):
// Concrete
def sumList(Data : List[Int]) = ...
// Generic
def sumGeneric[C : Collection[T], T : Num](Data : C) = ...
The latter might be somewhat unintuitive compared with the first definition, but it allows you to work with any collection and numeric type in general!
All in all, many modern (mainstream) languages have discovered such benefits and introduced very functional features like lambda functios or Linq. Having understood these techniques will also improve writing code in this languages.
One from the "advanced" department: Programming with phantom types (sometimes also called indexed types). It's admittedly not a "standard" technique in functional programming but not entirely esoteric either, and it's something to keep your brain busy for awhile (you asked for something difficult, right? ;)).
In a nutshell, it is about parameterizing types to encode and statically enforce certain properties at compile time. One of the standard examples is the vector addition function that statically ensures that given two vectors of length N and M will return a vector of length N+M or otherwise you get a compile-time error. Yes, there are more interesting applications.
These techniques are not quite as useful in C++ as they are in a proper functional programming language, but so far I've managed to sneak some of this stuff in all of my recent projects at work to a varying degree, most recently in a C++ EDSL context where it worked out really well. You don't necessarily have to encode fancy stuff, learning this helped me catching the situations where a few type tags can reduce the verbosity of an EDSL or allowed a cleaner syntax, for example.
Admittedly, the usefulness is somewhat restricted by language support and what you're trying to achieve.
Some starters:
Generic and Indexed Type (slides with some brief applications overview)
Fun with Phantom Types
The Kennedy and Russo paper mentioned in the slides is Generalized Algebraic Data Types
and Object Oriented Programming and puts some of this stuff into the context of C#/Java.
Chapter 3 in Dave Abraham's book C++ Template Metaprogramming is available online as sample chapter and uses these techniques in C++ for dimensional analysis.
A practical FP project using phantom types is HaskellDB.
I would say that Structural typing in OCaml is particularly rewarding.
recursion. Difficult to wrap your head around it at times
The concept of higher-order functions, lambda functions and the power of generic algorithms that are easy to combine were very beneficial for me. I'm always excited when I see what I can do with a fold in haskell.
Likewise my programming in C# has changed a lot (to the better, I hope) since I got into functional programming (haskell specifically).