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  • What is the advantage of currying?

    - by Mad Scientist
    I just learned about currying, and while I think I understand the concept, I'm not seeing any big advantage in using it. As a trivial example I use a function that adds two values (written in ML). The version without currying would be fun add(x, y) = x + y and would be called as add(3, 5) while the curried version is fun add x y = x + y (* short for val add = fn x => fn y=> x + y *) and would be called as add 3 5 It seems to me to be just syntactic sugar that removes one set of parentheses from defining and calling the function. I've seen currying listed as one of the important features of a functional languages, and I'm a bit underwhelmed by it at the moment. The concept of creating a chain of functions that consume each a single parameter, instead of a function that takes a tuple seems rather complicated to use for a simple change of syntax. Is the slightly simpler syntax the only motivation for currying, or am I missing some other advantages that are not obvious in my very simple example? Is currying just syntactic sugar?

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  • What's special about currying or partial application?

    - by Vigneshwaran
    I've been reading articles on Functional programming everyday and been trying to apply some practices as much as possible. But I don't understand what is unique in currying or partial application. Take this Groovy code as an example: def mul = { a, b -> a * b } def tripler1 = mul.curry(3) def tripler2 = { mul(3, it) } I do not understand what is the difference between tripler1 and tripler2. Aren't they both the same? The 'currying' is supported in pure or partial functional languages like Groovy, Scala, Haskell etc. But I can do the same thing (left-curry, right-curry, n-curry or partial application) by simply creating another named or anonymous function or closure that will forward the parameters to the original function (like tripler2) in most languages (even C.) Am I missing something here? There are places where I can use currying and partial application in my Grails application but I am hesitating to do so because I'm asking myself "How's that different?" Please enlighten me.

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  • Is currying just a way to avoid inheritance?

    - by Alex Mcp
    So my understanding of currying (based on SO questions) is that it lets you partially set parameters of a function and return a "truncated" function as a result. If you have a big hairy function takes 10 parameters and looks like function (location, type, gender, jumpShot%, SSN, vegetarian, salary) { //weird stuff } and you want a "subset" function that will let you deal with presets for all but the jumpShot%, shouldn't you just break out a class that inherits from the original function? I suppose what I'm looking for is a use case for this pattern. Thanks!

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  • Extending Currying: Partial Functions in Javascript

    - by kerry
    Last week I posted about function currying in javascript.  This week I am taking it a step further by adding the ability to call partial functions. Suppose we have a graphing application that will pull data via Ajax and perform some calculation to update a graph.  Using a method with the signature ‘updateGraph(id,value)’. To do this, we have do something like this: 1: for(var i=0;i<objects.length;i++) { 2: Ajax.request('/some/data',{id:objects[i].id},function(json) { 3: updateGraph(json.id, json.value); 4: } 5: } This works fine.  But, using this method we need to return the id in the json response from the server.  This works fine, but is not that elegant and increase network traffic. Using partial function currying we can bind the id parameter and add the second parameter later (when returning from the asynchronous call).  To do this, we will need the updated curry method.  I have added support for sending additional parameters at runtime for curried methods. 1: Function.prototype.curry = function(scope) { 2: scope = scope || window 3: var args = []; 4: for (var i=1, len = arguments.length; i < len; ++i) { 5: args.push(arguments[i]); 6: } 7: var m = this; 8: return function() { 9: for (var i=0, len = arguments.length; i < len; ++i) { 10: args.push(arguments[i]); 11: } 12: return m.apply(scope, args); 13: }; 14: } To partially curry this method we will call the curry method with the id parameter, then the request will callback on it with just the value.  Any additional parameters are appended to the method call. 1: for(var i=0;i<objects.length;i++) { 2: var id=objects[i].id; 3: Ajax.request('/some/data',{id: id}, updateGraph.curry(id)); 4: } As you can see, partial currying gives is a very useful tool and this simple method should be a part of every developer’s toolbox.

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  • F# currying efficiency?

    - by Eamon Nerbonne
    I have a function that looks as follows: let isInSet setElems normalize p = normalize p |> (Set.ofList setElems).Contains This function can be used to quickly check whether an element is semantically part of some set; for example, to check if a file path belongs to an html file: let getLowerExtension p = (Path.GetExtension p).ToLowerInvariant() let isHtmlPath = isInSet [".htm"; ".html"; ".xhtml"] getLowerExtension However, when I use a function such as the above, performance is poor since evaluation of the function body as written in "isInSet" seems to be delayed until all parameters are known - in particular, invariant bits such as (Set.ofList setElems).Contains are reevaluated each execution of isHtmlPath. How can best I maintain F#'s succint, readable nature while still getting the more efficient behavior in which the set construction is preevaluated. The above is just an example; I'm looking for a general pattern that avoids bogging me down in implementation details - where possible I'd like to avoid being distracted by details such as the implementation's execution order since that's usually not important to me and kind of undermines a major selling point of functional programming.

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  • Challenge: Neater way of currying or partially applying C#4's string.Join

    - by Damian Powell
    Background I recently read that .NET 4's System.String class has a new overload of the Join method. This new overload takes a separator, and an IEnumerable<T> which allows arbitrary collections to be joined into a single string without the need to convert to an intermediate string array. Cool! That means I can now do this: var evenNums = Enumerable.Range(1, 100) .Where(i => i%2 == 0); var list = string.Join(",",evenNums); ...instead of this: var evenNums = Enumerable.Range(1, 100) .Where(i => i%2 == 0) .Select(i => i.ToString()) .ToArray(); var list = string.Join(",", evenNums); ...thus saving on a conversion of every item to a string, and then the allocation of an array. The Problem However, being a fan of the functional style of programming in general, and method chaining in C# in particular, I would prefer to be able to write something like this: var list = Enumerable.Range(1, 100) .Where(i => i%2 == 0) .string.Join(","); This is not legal C# though. The closest I've managed to get is this: var list = Enumerable.Range(1, 100) .Where(i => i%2 == 0) .ApplyTo( Functional.Curry<string, IEnumerable<object>, string> (string.Join)(",") ); ...using the following extension methods: public static class Functional { public static TRslt ApplyTo<TArg, TRslt>(this TArg arg, Func<TArg, TRslt> func) { return func(arg); } public static Func<T1, Func<T2, TResult>> Curry<T1, T2, TResult>(this Func<T1, T2, TResult> func) { Func<Func<T1, T2, TResult>, Func<T1, Func<T2, TResult>>> curried = f => x => y => f(x, y); return curried(func); } } This is quite verbose, requires explicit definition of the parameters and return type of the string.Join overload I want to use, and relies upon C#4's variance features because we are defining one of the arguments as IEnumerable rather than IEnumerable. The Challenge Can you find a neater way of achieving this using the method-chaining style of programming?

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  • OCaml: Currying without defined values

    - by nicotine
    I have two functions f and g and I am trying to return f(g(x)) but I do not know the value of x and I am not really sure how to go about this. A more concrete example: if I have functions f = x + 1 and g = x * 2 and I am trying to return f(g(x)) I should get a function equal to (x*2) + 1

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  • Currying a function n times in Scheme

    - by user1724421
    I'm having trouble figuring out a way to curry a function a specified number of times. That is, I give the function a natural number n and a function fun, and it curries the function n times. For example: (curry n fun) Is the function and a possible application would be: (((((curry 4 +) 1) 2) 3) 4) Which would produce 10. I'm really not sure how to implement it properly. Could someone please give me a hand? Thanks :)

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  • Function currying in Javascript

    - by kerry
    Do you catch yourself doing something like this often? 1: Ajax.request('/my/url', {'myParam': paramVal}, function() { myCallback(paramVal); }); Creating a function which calls another function asynchronously is a bad idea because the value of paramVal may change before it is called.  Enter the curry function: 1: Function.prototype.curry = function(scope) { 2: var args = []; 3: for (var i=1, len = arguments.length; i < len; ++i) { 4: args.push(arguments[i]); 5: } 6: var m = this; 7: return function() { 8: m.apply(scope, args); 9: }; 10: } This function creates a wrapper around the function and ‘locks in’ the method parameters.  The first parameter is the scope of the function call (usually this or window).  Any remaining parameters will be passed to the method call.  Using the curry method the above call changes to: 1: Ajax.request('/my/url', {'myParam': paramVal}, myCallback.curry(window,paramVal)); Remember when passing objects to the curry method that the objects members may still change.

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  • Is there a programming language that performs currying when named parameters are omitted?

    - by Adam Gent
    Many functional programming languages have support for curried parameters. To support currying functions the parameters to the function are essentially a tuple where the last parameter can be omitted making a new function requiring a smaller tuple. I'm thinking of designing a language that always uses records (aka named parameters) for function parameters. Thus simple math functions in my make believe language would be: add { left : num, right : num } = ... minus { left : num, right : num } = .. You can pass in any record to those functions so long as they have those two named parameters (they can have more just "left" and "right"). If they have only one of the named parameter it creates a new function: minus5 :: { left : num } -> num minus5 = minus { right : 5 } I borrow some of haskell's notation for above. Has any one seen a language that does this?

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  • scala currying by nested functions or by multiple parameter lists

    - by Morgan Creighton
    In Scala, I can define a function with two parameter lists. def myAdd(x :Int)(y :Int) = x + y This makes it easy to define a partially applied function. val plusFive = myAdd(5) _ But, I can accomplish something similar by defining and returning a nested function. def myOtherAdd(x :Int) = { def f(y :Int) = x + y f _ } Cosmetically, I've moved the underscore, but this still feels like currying. val otherPlusFive = myOtherAdd(5) What criteria should I use to prefer one approach over the other?

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  • Haskell Monad bind currying

    - by Chime
    I am currently in need of a bit of brain training and I found this article on Haskell and Monads I'm having trouble with exercise 7 re. Randomised function bind. To make the problem even simpler to experiment, I replaced the StdGen type with an unspecified type. So instead of... bind :: (a -> StdGen -> (b,StdGen)) -> (StdGen -> (a,StdGen)) -> (StdGen -> (b,StdGen)) I used... bind :: (a -> c -> (b,c)) -> (c -> (a,c)) -> (c -> (b,c)) and for the actual function impelemtation (just straight from the exercise) bind f x seed = let (x',seed') = x seed in f x' seed' and also 2 randomised functions to trial with: rndf1 :: (Num a, Num b) => a -> b -> (a,b) rndf1 a s = (a+1,s+1) rndf2 :: (Num a, Num b) => a -> b -> (a,b) rndf2 a s = (a+8,s+2) So with this in a Haskell compiler (ghci), I get... :t bind rndf2 bind rndf2 :: (Num a, Num c) => (c -> (a, c)) -> c -> (a, c) This matches the bind curried with rndf2 as the first parameter. But the thing I don't understand is how... :t bind rndf2 . rndf1 Suddenly gives bind rndf2 . rndf1 :: (Num a, Num c) => a -> c -> (a, c) This is the correct type of the composition that we are trying to produce because bind rndf2 . rndf1 Is a function that: takes the same parameter type(s) as rndf1 AND takes the return from rndf1 and pipes it as an input of rndf2 to return the same type as rndf2 rndf1 can take 2 parameters a -> c and rndf2 returns (a, c) so it matches that a composition of these function should have type: bind rndf2 . rndf1 :: (Num a, Num c) => a -> c -> (a, c) This does not match the naive type that I initially came up with for bind bind f :: (a -> b -> (c, d)) -> (c, d) -> (e, f) Here bind mythically takes a function that takes two parameters and produces a function that takes a tuple in order that the output from rndf1 can be fed into rndf2 why the bind function needs to be coded as it is Why the bind function does not have the naive type

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  • Why doesn't functools.partial return a real function (and how to create one that does)?

    - by epsilon
    So I was playing around with currying functions in Python and one of the things that I noticed was that functools.partial returns a partial object rather than an actual function. One of the things that annoyed me about this was that if I did something along the lines of: five = partial(len, 'hello') five('something') then we get TypeError: len() takes exactly 1 argument (2 given) but what I want to happen is TypeError: five() takes no arguments (1 given) Is there a clean way to make it work like this? I wrote a workaround, but it's too hacky for my taste (doesn't work yet for functions with varargs): def mypartial(f, *args): argcount = f.func_code.co_argcount - len(args) params = ''.join('a' + str(i) + ',' for i in xrange(argcount)) code = ''' def func(f, args): def %s(%s): return f(*(args+(%s))) return %s ''' % (f.func_name, params, params, f.func_name) exec code in locals() return func(f, args)

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  • How do I create a partial function with generics in scala?

    - by Matteo Caprari
    Hello. I'm trying to write a performance measurements library for Scala. My idea is to transparently 'mark' sections so that the execution time can be collected. Unfortunately I wasn't able to bend the compiler to my will. An admittedly contrived example of what I have in mind: // generate a timing function val myTimer = mkTimer('myTimer) // see how the timing function returns the right type depending on the // type of the function it is passed to it val act = actor { loop { receive { case 'Int => val calc = myTimer { (1 to 100000).sum } val result = calc + 10 // calc must be Int self reply (result) case 'String => val calc = myTimer { (1 to 100000).mkString } val result = calc + " String" // calc must be String self reply (result) } Now, this is the farthest I got: trait Timing { def time[T <: Any](name: Symbol)(op: => T) :T = { val start = System.nanoTime val result = op val elapsed = System.nanoTime - start println(name + ": " + elapsed) result } def mkTimer[T <: Any](name: Symbol) : (() => T) => () => T = { type c = () => T time(name)(_ : c) } } Using the time function directly works and the compiler correctly uses the return type of the anonymous function to type the 'time' function: val bigString = time('timerBigString) { (1 to 100000).mkString("-") } println (bigString) Great as it seems, this pattern has a number of shortcomings: forces the user to reuse the same symbol at each invocation makes it more difficult to do more advanced stuff like predefined project-level timers does not allow the library to initialize once a data structure for 'timerBigString So here it comes mkTimer, that would allow me to partially apply the time function and reuse it. I use mkTimer like this: val myTimer = mkTimer('aTimer) val myString= myTimer { (1 to 100000).mkString("-") } println (myString) But I get a compiler error: error: type mismatch; found : String required: () => Nothing (1 to 100000).mkString("-") I get the same error if I inline the currying: val timerBigString = time('timerBigString) _ val bigString = timerBigString { (1 to 100000).mkString("-") } println (bigString) This works if I do val timerBigString = time('timerBigString) (_: String), but this is not what I want. I'd like to defer typing of the partially applied function until application. I conclude that the compiler is deciding the return type of the partial function when I first create it, chosing "Nothing" because it can't make a better informed choice. So I guess what I'm looking for is a sort of late-binding of the partially applied function. Is there any way to do this? Or maybe is there a completely different path I could follow? Well, thanks for reading this far -teo

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  • Functional Adaptation

    - by Charles Courchaine
    In real life and OO programming we’re often faced with using adapters, DVI to VGA, 1/4” to 1/8” audio connections, 110V to 220V, wrapping an incompatible interface with a new one, and so on.  Where the adapter pattern is generally considered for interfaces and classes a similar technique can be applied to method signatures.  To be fair, this adaptation is generally used to reduce the number of parameters but I’m sure there are other clever possibilities to be had.  As Jan questioned in the last post, how can we use a common method to execute an action if the action has a differing number of parameters, going back to the greeting example it was suggested having an AddName method that takes a first and last name as parameters.  This is exactly what we’ll address in this post. Let’s set the stage with some review and some code changes.  First, our method that handles the setup/tear-down infrastructure for our WCF service: 1: private static TResult ExecuteGreetingFunc<TResult>(Func<IGreeting, TResult> theGreetingFunc) 2: { 3: IGreeting aGreetingService = null; 4: try 5: { 6: aGreetingService = GetGreetingChannel(); 7: return theGreetingFunc(aGreetingService); 8: } 9: finally 10: { 11: CloseWCFChannel((IChannel)aGreetingService); 12: } 13: } Our original AddName method: 1: private static string AddName(string theName) 2: { 3: return ExecuteGreetingFunc<string>(theGreetingService => theGreetingService.AddName(theName)); 4: } Our new AddName method: 1: private static int AddName(string firstName, string lastName) 2: { 3: return ExecuteGreetingFunc<int>(theGreetingService => theGreetingService.AddName(firstName, lastName)); 4: } Let’s change the AddName method, just a little bit more for this example and have it take the greeting service as a parameter. 1: private static int AddName(IGreeting greetingService, string firstName, string lastName) 2: { 3: return greetingService.AddName(firstName, lastName); 4: } The new signature of AddName using the Func delegate is now Func<IGreeting, string, string, int>, which can’t be used with ExecuteGreetingFunc as is because it expects Func<IGreeting, TResult>.  Somehow we have to eliminate the two string parameters before we can use this with our existing method.  This is where we need to adapt AddName to match what ExecuteGreetingFunc expects, and we’ll do so in the following progression. 1: Func<IGreeting, string, string, int> -> Func<IGreeting, string, int> 2: Func<IGreeting, string, int> -> Func<IGreeting, int>   For the first step, we’ll create a method using the lambda syntax that will “eliminate” the last name parameter: 1: string lastNameToAdd = "Smith"; 2: //Func<IGreeting, string, string, int> -> Func<IGreeting, string, int> 3: Func<IGreeting, string, int> addName = (greetingService, firstName) => AddName(greetingService, firstName, lastNameToAdd); The new addName method gets us one step close to the signature we need.  Let’s say we’re going to call this in a loop to add several names, we’ll take the final step from Func<IGreeting, string, int> -> Func<IGreeting, int> in line as a lambda passed to ExecuteGreetingFunc like so: 1: List<string> firstNames = new List<string>() { "Bob", "John" }; 2: int aID; 3: foreach (string firstName in firstNames) 4: { 5: //Func<IGreeting, string, int> -> Func<IGreeting, int> 6: aID = ExecuteGreetingFunc<int>(greetingService => addName(greetingService, firstName)); 7: Console.WriteLine(GetGreeting(aID)); 8: } If for some reason you needed to break out the lambda on line 6 you could replace it with 1: aID = ExecuteGreetingFunc<int>(ApplyAddName(addName, firstName)); and use this method: 1: private static Func<IGreeting, int> ApplyAddName(Func<IGreeting, string, int> addName, string lastName) 2: { 3: return greetingService => addName(greetingService, lastName); 4: } Splitting out a lambda into its own method is useful both in this style of coding as well as LINQ queries to improve the debugging experience.  It is not strictly necessary to break apart the steps & functions as was shown above; the lambda in line 6 (of the foreach example) could include both the last name and first name instead of being composed of two functions.  The process demonstrated above is one of partially applying functions, this could have also been done with Currying (also see Dustin Campbell’s excellent post on Currying for the canonical curried add example).  Matthew Podwysocki also has some good posts explaining both Currying and partial application and a follow up post that further clarifies the difference between Currying and partial application.  In either technique the ultimate goal is to reduce the number of parameters passed to a function.  Currying makes it a single parameter passed at each step, where partial application allows one to use multiple parameters at a time as we’ve done here.  This technique isn’t for everyone or every problem, but can be extremely handy when you need to adapt a call to something you don’t control.

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  • Partial Function Application

    - by AngelEyes
    This is long overdo... Just a short and simple example of Partial Function Application.   For some good explanations, which also include the difference between Currying and Partial Function Application, check out: http://msmvps.com/blogs/jon_skeet/archive/2012/01/30/currying-vs-partial-function-application.aspx and also this answer on stackoverflow: http://stackoverflow.com/a/8826698/532517   And here is the example, taken from real code:           internal void Addfile(string parentDirName, string fileName, long size)         {             AddElement(parentDirName, fileName, (name, parent) => new File(name, size, parent));         }           public void AddDir(string parentDirName, string dirName)         {             AddElement(parentDirName, dirName, (name, parent) => new Directory(dirName, parent));         }           private void AddElement(string parentDirName, string name,                                 Func<string, FileSystemElement, FileSystemElement> elementCreator)         {             ValidateFileNames(parentDirName, name);             var parent = (Directory)_index[parentDirName];             FileSystemElement element = elementCreator(name, parent);             parent._elements.Add(element);             _index.Add(name, element);         }

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  • What is a 'Closure'?

    - by Ben
    I asked a question about Currying and closures where mentioned. What is a closure? How does it relate to currying? Additional: Kyle's answer is great but to my poor procedural/OO mind Ben Childs answer is really useful.

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  • What Functional features are worth a little OOP confusion for the benefits they bring?

    - by bonomo
    After learning functional programming in Haskell and F#, the OOP paradigm seems ass-backwards with classes, interfaces, objects. Which aspects of FP can I bring to work that my co-workers can understand? Are any FP styles worth talking to my boss about retraining my team so that we can use them? Possible aspects of FP: Immutability Partial Application and Currying First Class Functions (function pointers / Functional Objects / Strategy Pattern) Lazy Evaluation (and Monads) Pure Functions (no side effects) Expressions (vs. Statements - each line of code produces a value instead of, or in addition to causing side effects) Recursion Pattern Matching Is it a free-for-all where we can do whatever the programming language supports to the limit that language supports it? Or is there a better guideline?

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  • What are the factors affecting a new programming language?

    - by Saurav Sengupta
    I am developing a new general-purpose programming language of my own design. It's currently my own personal project. I have read of some experts saying that new languages do not usually survive (unfortunately I can't find a reference to that right now). What are the most substantial problems that a new language faces? The language syntax is similar to C/Python families, it does not use S-expressions, and it is an imperative language, but I'm doing first-class functions in it to provide the facilities of currying. In particular, I am concentrating on translating the source language to an intermediate language for execution by an interpreter, but I'm not in a position to translate to native code yet. What would be the issues with that? I've not personally used many non-native code languages, so I'm not well aware of the performance issues on today's machines. I also can't decide upon a lexer and parser generator. What would be the pros and cons of Flex and Yacc vs. hand-made? And what benefits will LLVM provide? I need to get the interpreter ready as quickly as possible. Finally, what factors will affect the language's use post release? I am planning a small library of essentials and full documentation for the first phase.

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  • Composing programs from small simple pieces: OOP vs Functional Programming

    - by Jay Godse
    I started programming when imperative programming languages such as C were virtually the only game in town for paid gigs. I'm not a computer scientist by training so I was only exposed to Assembler and Pascal in school, and not Lisp or Prolog. Over the 1990s, Object-Oriented Programming (OOP) became more popular because one of the marketing memes for OOP was that complex programs could be composed of loosely coupled but well-defined, well-tested, cohesive, and reusable classes and objects. And in many cases that is quite true. Once I learned object-oriented programming my C programs became better because I structured them more like classes and objects. In the last few years (2008-2014) I have programmed in Ruby, an OOP language. However, Ruby has many functional programming (FP) features such as lambdas and procs, which enable a different style of programming using recursion, currying, lazy evaluation and the like. (Through ignorance I am at a loss to explain why these techniques are so great). Very recently, I have written code to use methods from the Ruby Enumerable library, such as map(), reduce(), and select(). Apparently this is a functional style of programming. I have found that using these methods significantly reduce code volume, and make my code easier to debug. Upon reading more about FP, one of the marketing claims made by advocates is that FP enables developers to compose programs out of small well-defined, well-tested, and reusable functions, which leads to less buggy code, and low code volume. QUESTIONS: Is the composition of complex program by using FP techniques contradictory to or complementary to composition of a complex program by using OOP techniques? In which situations is OOP more effective, and when is FP more effective? Is it possible to use both techniques in the same complex program? Do the techniques overlap or contradict each other?

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  • Hidden Features of C#?

    - by Serhat Özgel
    This came to my mind after I learned the following from this question: where T : struct We, C# developers, all know the basics of C#. I mean declarations, conditionals, loops, operators, etc. Some of us even mastered the stuff like Generics, anonymous types, lambdas, linq, ... But what are the most hidden features or tricks of C# that even C# fans, addicts, experts barely know? Here are the revealed features so far: Keywords yield by Michael Stum var by Michael Stum using() statement by kokos readonly by kokos as by Mike Stone as / is by Ed Swangren as / is (improved) by Rocketpants default by deathofrats global:: by pzycoman using() blocks by AlexCuse volatile by Jakub Šturc extern alias by Jakub Šturc Attributes DefaultValueAttribute by Michael Stum ObsoleteAttribute by DannySmurf DebuggerDisplayAttribute by Stu DebuggerBrowsable and DebuggerStepThrough by bdukes ThreadStaticAttribute by marxidad FlagsAttribute by Martin Clarke ConditionalAttribute by AndrewBurns Syntax ?? operator by kokos number flaggings by Nick Berardi where T:new by Lars Mæhlum implicit generics by Keith one-parameter lambdas by Keith auto properties by Keith namespace aliases by Keith verbatim string literals with @ by Patrick enum values by lfoust @variablenames by marxidad event operators by marxidad format string brackets by Portman property accessor accessibility modifiers by xanadont ternary operator (?:) by JasonS checked and unchecked operators by Binoj Antony implicit and explicit operators by Flory Language Features Nullable types by Brad Barker Currying by Brian Leahy anonymous types by Keith __makeref __reftype __refvalue by Judah Himango object initializers by lomaxx format strings by David in Dakota Extension Methods by marxidad partial methods by Jon Erickson preprocessor directives by John Asbeck DEBUG pre-processor directive by Robert Durgin operator overloading by SefBkn type inferrence by chakrit boolean operators taken to next level by Rob Gough pass value-type variable as interface without boxing by Roman Boiko programmatically determine declared variable type by Roman Boiko Static Constructors by Chris Easier-on-the-eyes / condensed ORM-mapping using LINQ by roosteronacid Visual Studio Features select block of text in editor by Himadri snippets by DannySmurf Framework TransactionScope by KiwiBastard DependantTransaction by KiwiBastard Nullable<T> by IainMH Mutex by Diago System.IO.Path by ageektrapped WeakReference by Juan Manuel Methods and Properties String.IsNullOrEmpty() method by KiwiBastard List.ForEach() method by KiwiBastard BeginInvoke(), EndInvoke() methods by Will Dean Nullable<T>.HasValue and Nullable<T>.Value properties by Rismo GetValueOrDefault method by John Sheehan Tips & Tricks nice method for event handlers by Andreas H.R. Nilsson uppercase comparisons by John access anonymous types without reflection by dp a quick way to lazily instantiate collection properties by Will JavaScript-like anonymous inline-functions by roosteronacid Other netmodules by kokos LINQBridge by Duncan Smart Parallel Extensions by Joel Coehoorn

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  • What are the most interesting equivalences arising from the Curry-Howard Isomorphism?

    - by Tom
    I came upon the Curry-Howard Isomorphism relatively late in my programming life, and perhaps this contributes to my being utterly fascinated by it. It implies that for every programming concept there exists a precise analogue in formal logic, and vice versa. Here's an "obvious" list of such analogies, off the top of my head: program/definition | proof type/declaration | proposition inhabited type | theorem function | implication function argument | hypothesis/antecedent function result | conclusion/consequent function application | modus ponens recursion | induction identity function | tautology non-terminating function | absurdity tuple | conjunction (and) disjoint union | exclusive disjunction (xor) parametric polymorphism | universal quantification So, to my question: what are some of the more interesting/obscure implications of this isomorphism? I'm no logician so I'm sure I've only scratched the surface with this list. For example, here are some programming notions for which I'm unaware of pithy names in logic: currying | "((a & b) => c) iff (a => (b => c))" scope | "known theory + hypotheses" And here are some logical concepts which I haven't quite pinned down in programming terms: primitive type? | axiom set of valid programs? | theory ? | disjunction (or)

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