Funktionen höherer Ordnung

Standard

Funktionale Programmierung ist ein Programmierparadigma, das Datenverarbeitung als Auswertung mathematischer Funktionen behandelt. Der Gegensatz dazu ist imperative Programmierung, die den Schwerpunkt auf Zustandsänderungen legt und die den derzeit am häufigsten verwendeten Programmiersprachen zugrunde liegt.

In funktionalen Programmiersprachen sind Funktionen ein wichtiges Konzept. Die Strukturierung des Programmcodes erfolgt mit Hilfe von Funktionen. Deshalb werde ich hier eine Reihe von Artikel veröffentlichen, die sich mit Funktionen in funktionalen Programmierspachen beschäftigen.

Funktionen höherer Ordnung

In funktionalen Programmiersprachen können Funktionen als Parameter an andere Funktionen übergeben oder als Rückgabewert verwendet werden. Solche Funktionen nennt man Funktionen höherer Ordnung.

Delegates ermöglichen es, dass man auch in C# Funktionen höherer Ordnung entwickeln kann. In der .NET-Klassenbibliothek finden sich einige Beispiele dafür, z.B. hat die Klasse System.Collections.Generic.List<T> eine Methode Sort, die als einzigen Parameter einen Delegate erwartet, der den Vergleich durchführen soll. Auch in LINQ gibt es einige Extension-Methods, die Delegates als Parameter bekommen.

Map, Filter und Fold

In funktionalen Programmiersprachen werden die drei Funktionen map, filter und fold häufig verwendet, um mit Listen und ähnlichen Datenstrukturen zu arbeiten. Alle drei Funktionen erwarten neben einer Liste eine Funktion als Parameter. Damit handelt es sich um Funktionen höherer Ordnung.

Map

Map wendet die angegebene Funktion auf jedes Element der Liste an und gibt eine Liste der Ergebnisse zurück. LINQ kennt die Extension-Method Select, die IEnumerable<T> erweitert und etwas Ähnliches macht:

    var numbers = new[] { 1, 2, 3, 4, 5 };
    var doubledNumbers = numbers.Select(x => x * x);

In F# sieht das so aus:

    let numbers = [1; 2; 3; 4; 5]
    let doubledNumbers = List.map (fun x -> x * x) numbers

let ist das wichtigste Schlüsselwort für das Programmieren in F#. Es wird verwendet, um Daten, berechnete Werte, Funktionen und Prozeduren zu definieren. Links steht üblicherweise der Bezeichner. Nach dem Gleichheitszeichen folgt ein Ausdruck.

Die Zeile let numbers = [1; 2; 3; 4; 5] weist dem Namen “numbers” die Liste [1; 2; 3; 4; 5] als Wert zu. In F# wird eine Liste in eckigen Klammern eingeschlossen und die einzelnen Listenelemente werden durch einen Strichpunkt (Semikolon) getrennt.

Die zweite Zeile ruft die Funktion map des Moduls List auf. Man sieht, dass es nicht notwendig ist, die Parameter in Klammern anzugeben. Der erste Parameter ist die Funktion, die auf jedes Listenelement angewandt werden soll. In unserem Beispiel ist das die anonyme Methode fun x -> x * x. In F# wird eine anonyme Methode mit dem Schlüsselwort fun deklariert. Danach folgen die Funktionsargumente und nach dem Pfeil folgt der Funktionskörper. Der zweite Parameter ist die Liste “numbers”. Das Ergebnis wird an den Namen “doubledNumbers” gebunden.

Filter

Mit filter lässt sich eine Liste nach einem bestimmten Kriterium filtern. Das Kriterium wird als Funktion angegeben, die true für alle Elemente zurückgeben soll, die in die Ergebnisliste aufgenommen werden sollen. Das Äquivalent in LINQ heißt Where.

    var numbers = new[] { 1, 2, 3, 4, 5 };
    var evenNumbers = numbers.Where (x => (x % 2) == 0);

Hier wieder das Beispiel in F#:

    let numbers = [1; 2; 3; 4; 5]
    let evenNumbers = List.filter (fun x -> (x % 2) = 0) numbers

An diesem Beispiel sieht man, dass Lambda-Ausdrücke und anonyme Methoden nicht immer besser lesbar sind. Um die Lesbarkeit zu erhöhen, können wir die obigen Beispiele umschreiben:

In C#:

    bool IsEven (int x)
    {
        return (x % 2) == 0;
    }
    
    var numbers = new [] { 1, 2, 3, 4, 5 };
    var evenNumbers = numbers.Where (IsEven);

Und in F#:

    let IsEven x = (x % 2) = 0
    let numbers = [1; 2; 3; 4; 5]
    let evenNumbers = List.filter IsEven numbers

Die erste Zeile definiert die Funktion IsEven, die einen Parameter x akzeptiert. Nach dem ersten Gleichheitszeichen folgt der Funktionskörper: (x % 2) = 0. Dieser Ausdruck berechnet den Rest der Division von x durch 2 und vergleicht ihn mit 0. Sowohl beim let`-Binding als auch beim Vergleich wird in F# ein einzelnes Gleichheitszeichen verwendet.

Fold

Fold berechnet einen akkumulierten Wert über alle Elemente einer Liste. Die Funktion gibt an, wie ein neuer akkumulierter Wert aus dem alten Wert und einem Listenelement ermittelt wird. Das LINQ Äquivalent ist Aggregate.

    var numbers = new[] { 1, 2, 3, 4, 5 };
    var sum = numbers.Aggregate (0, (s, x) => s + x);

Dieses Beispiel berechnet die Summe der Zahlen im Array. Um besser zu verstehen, wie Fold funktioniert, hier die Einzelschritte:

Bei Aufruf: s = 0, Liste: 1, 2, 3, 4, 5

  1. s = 0 + 1, Liste: 2, 3, 4, 5
  2. s = (0 + 1) + 2, Liste: 3, 4, 5
  3. s = ((0 + 1) + 2) + 3, Liste: 4, 5
  4. s = (((0 + 1) + 2) + 3) + 4 = 10, Liste: 5
  5. s = ((((0 + 1) + 2) + 3) + 4) + 5 = 15, Liste: –

Die Variable sum im obigen Beispiel hat also den Wert ((((0 + 1) + 2) + 3) + 4) + 5=15.

Hier in F#:

    let numbers = [1; 2; 3; 4; 5]
    let sum = List.fold (fun s x -> s + x) 0 numbers

Es gibt in F# die Möglichkeit, den Operator + als Funktion anzugeben. Statt 4 + 9 kann man also (+) 4 9 schreiben. Damit kann im obigen Beispiel die letzte Zeile so geschrieben werden:

    let sum = List.fold (+) 0 numbers

Es gibt zwei verschiedene Arten von Folds: left Fold und right Fold. In früheren F#-Versionen gab es die zwei Funktionen List.fold_left und List.fold_right. Diese wurden jedoch umbenannt und heißen jetzt fold (left fold) und foldBack (right fold). LINQs Aggregate-Funktion arbeitet wie ein left Fold.

Fazit

Funktionen höherer Ordnung sind ein wichtiges Mittel in der funktionalen Programmierung für die Wiederverwendung von Code. Gemeinsam mit anderen Konzepten ermöglichen sie den deklarativen Stil der funktionalen Programmierung.

518 thoughts on “Funktionen höherer Ordnung

  1. Howdy! Would you mind if I share your blog with my myspace group?

    There’s a lot of people that I think would really enjoy your content.
    Please let me know. Many thanks

  2. I love your blog.. very nice colors & theme. Did you create this website yourself or did you hire someone to do it for you?
    Plz reply as I’m looking to design my own blog and would like to know where
    u got this from. cheers

  3. Autoliker, autoliker, Facebook Liker, Status Liker, Photo Liker, Facebook Autoliker, autolike, Status Auto Liker, Working Auto Liker, Facebook Auto Liker, Autoliker, auto like, facebook auto liker, Auto Like, Autoliker Facebook, Photo Auto Liker, Fb Autoliker, Auto Liker, auto liker, Increase Facebook Likes

  4. ไลค์เพจ, เพิ่มไลค์เพจ, ปั๊มไลค์แฟนเพจ, เพิ่มไลค์เพจ ราคาถูก, ปั๊มไลค์เพจ facebook, ปั๊มไลค์เพจ, ปั้มไลค์แฟนเพจ, ปั้มไลค์เพจ, เพิ่มไลค์แฟนเพจ, ปั๊มไลค์เพจ, ปั้มเพจ

  5. ผู้นำด้านที่ปรึกษาการตลาดออนไลน์ของไทย เพิ่มไลค์ ปั้มไลค์แฟนเพจ รับเพิ่มไลค์แฟนเพจ เพิ่มยอดไลค์ ปั้มไลค์ ปั้มไลค์คนไทย

  6. Wow, awesome weblog structure! How lengthy have you been running
    a blog for? you made blogging look easy. The overall look of your website is
    excellent, let alone the content material!

  7. I don’t even know the way I finished up here, but I believed this submit
    was once good. I don’t recognize who you’re however certainly you are going to a well-known blogger in case you aren’t already.
    Cheers!

  8. I must thank you for the efforts you have put in writing this site.

    I am hoping to see the same high-grade blog posts from you later on as well.
    In fact, your creative writing abilities has motivated me to get
    my own, personal blog now 😉

  9. Hi, i read your blog occasionally and i own a similar one and i was just wondering if
    you get a lot of spam comments? If so how do you stop it, any plugin or anything you can recommend?
    I get so much lately it’s driving me insane so any assistance is very much appreciated.

  10. Hi there! I could have sworn I’ve been to this website before but after checking through some of the post I realized it’s new to me.
    Nonetheless, I’m definitely glad I found it and I’ll
    be bookmarking and checking back frequently!

  11. magnificent post, very informative. I wonder why the
    other experts of this sector do not realize this. You must
    proceed your writing. I am sure, you have a huge readers’ base already!

  12. Hi, I do think this is an excellent site. I stumbledupon it 😉 I may come back once
    again since i have saved as a favorite it. Money and freedom
    is the greatest way to change, may you be rich
    and continue to help others.

  13. Spot on with this write-up, I seriously believe this
    site needs far more attention. I’ll probably be returning to read
    through more, thanks for the advice!

  14. I do consider all of the ideas you’ve presented in your post.

    They are really convincing and will certainly work. Nonetheless, the
    posts are too brief for newbies. May you please prolong them a little
    from next time? Thanks for the post.

  15. wonderful issues altogether, you simply won a brand new reader.
    What might you recommend in regards to your post that you just made some days ago?
    Any positive?

  16. whoah this blog is wonderful i love reading your posts. Keep up the great work! You know, a lot of people are hunting around for this info, you could help them greatly.

  17. I’m still learning from you, but I’m trying to achieve my goals. I absolutely enjoy reading everything that is written on your site.Keep the tips coming. I loved it!

  18. Hi there, You have performed a fantastic job. I’ll definitely digg it and for my part recommend to my friends. I am confident they will be benefited from this website.

  19. hello!,I really like your writing very so much! proportion we communicate extra approximately your post on AOL?

    I need an expert on this area to unravel my problem. May be that’s you!
    Having a look forward to see you.

  20. Hi! Do you know if they make any plugins to assist with Search
    Engine Optimization? I’m trying to get my blog to
    rank for some targeted keywords but I’m not seeing
    very good success. If you know of any please share.
    Thanks!

  21. When I originally commented I clicked the “Notify me when new comments are added” checkbox and now each
    time a comment is added I get three e-mails with
    the same comment. Is there any way you can remove me from that
    service? Thanks a lot!

  22. Hmm it appears like your site ate my first comment (it was extremely long) so I guess I’ll just sum it up
    what I wrote and say, I’m thoroughly enjoying your blog.
    I as well am an aspiring blog blogger but I’m still new to everything.
    Do you have any helpful hints for beginner blog
    writers? I’d really appreciate it.

  23. I do not know if it’s just me or if everybody else experiencing problems with your site.

    It appears like some of the text on your
    content are running off the screen. Can someone else please provide feedback and let me know if this is happening to them too?

    This could be a issue with my internet browser because I’ve
    had this happen previously. Appreciate it

  24. Like Fanpage, รับไลค์ครบวงจรทั่วไทย, ปั้มไลค์เพจ, เพิ่มไลค์เพจ ราคาถูก, รับปั้มไลค์เพจ, รับไลค์แฟนเพจ, กดไลค์แฟนเพจ, บริการปั้มไลค์ฟรี, จ้างปั้มไลค์, รับทำเพจเฟสบุ๊ค, เพิ่มไลค์, ปั้มไลค์ทั่วไป, ไลค์คนไทย 100%, รับเพิ่ม Like Fanpage Facebook ราคาพิเศษ เหมาะสำหรับผู้ที่ต้องการเพิ่ม Like Fanpage ให้ดูเป็นความน่าเชื่อถือของร้าน, ปั้มไลค์ครบวงจร, เพิ่มไลค์แฟนเพจ, ปั้มไลค์ Facebook, การเพิ่ม Like เป็นการเพิ่มโอกาสทางการขายสินค้าของคุณนั่นเอง ด้วยงานบริการเพิ่มไลค์แฟนเพจระดับมืออาชีพ ประสบการณ์การทำงานหลายปี, ปั่นไลค์, จ้างไลค์รูป, โกงไลค์, ปั้มไลค์รูป Facebook, รับจ้างกดไลค์, จ้างกดไลค์, ปั้มไลค์ราคาถูก, รับ Like Fanpage, แฟนเพจพร้อมยอดไลค์, ปั้มไลค์ ในโทรศัพท์, กดไลค์, รับทำไลค์แฟนเพจจำนวนมาก, ปั้มไลค์เพจคนไทย, รับสร้างแฟนเพจพร้อมยอดไลค์, ซื้อไลค์แฟนเพจ, รับจ้างเพิ่มไลค์, บริการปั้มไลค์แฟนเพจฟรี, บริการเพิ่ม Like ให้แฟนเพจของคุณ โดยทีมงานระดับมืออาชีพ ในระยะเวลาอันสั้นและราคาถูก รับประกันไลค์จากคนไทย 100%, กด Like, ปั้มไลค์ฟรี, รับทำเพจสินค้าพร้อมยอดไลค์, Pump Like, เพิ่มไลค์แฟนเพจ ราคาถูก, บริการเพิ่มไลค์แฟนเพจฟรี, กดไลค์รูป, ปั้ม Like ฟรี, ปั้มไลค์รูปเฟส, ไลค์แฟนเพจ, ปั้มไลค์ง่ายๆ, ปั้มยอดไลค์เป็นคนไทย 100%, เพิ่มไลค์ฟรี, ไลค์แฟนเพจราคาถูก, ปั้มเพจเฟสบุ๊ค, Up Like Fanpage, ปั้มรูป, ปั้มเพจ, บริการเพิ่มไลค์เฟสบุ๊คให้แฟนเพจ, ปั้มไลค์เพจ Facebook, ปั้มเพจ เหมาะสำหรับผู้ที่ต้องการยอดไลค์เพจเพจเยอะๆ, รับทำไลค์ครบวงจร, เพิ่มไลค์คนไทย, เพิ่ม Like, เพิ่มไลค์เพจ, จ้างไลค์, ปั้มไลค์เพจฟรี, ไลค์แฟนเพจได้สูงสุดหนึ่งล้านไลค์, ปั้มโพสต์, ปั้มไลค์, Add Like Fanpage, ปั้มไลค์แฟนเพจ, Auto Like, ปั้มไลค์สถานะ, รับจ้างปั้มไลค์, ไลค์แฟนเพจเฟสบุ๊ค, จ้างเพิ่มไลค์, รับปั้มไลค์รูป, ปั้มไลค์เฟสบุ๊ค, รับเพิ่มไลค์, รับเพิ่มไลค์แฟนเพจ เป็นการโปรโมทแฟนเพจ เพื่อเพิ่มยอดขายสินค้าได้, รับเพิ่มไลค์แฟนเพจเฟสบุ๊ค, ปั้มไลค์รูป, ไลค์เพจ, ปั้มไลค์มือถือ

  25. เว็บปั้มไลค์, แฮกไลค์, ออโต้ไลค์, ปั้มไลค์รูปภาพ, Auto Like, Hack Like Facebook, ปั้มไลค์คอมเม้น, ปั้มไลค์, ระบบเพิ่มไลค์, ปั้มไลค์แฟนเพจ

  26. My spouse and i felt really cheerful that Jordan could finish off his investigation out of the precious recommendations he obtained from your web site. It is now and again perplexing to simply happen to be giving out techniques which often many people have been making money from. And we all acknowledge we’ve got the writer to appreciate for this. All the illustrations you’ve made, the straightforward blog navigation, the friendships you can give support to promote – it’s got mostly overwhelming, and it’s really assisting our son in addition to the family believe that that concept is pleasurable, which is rather mandatory. Thanks for the whole thing!

  27. I’m impressed, I have to admit. Genuinely rarely do I encounter a blog that’s both educative and entertaining, and without a doubt, you have hit the nail around the head. Your idea is outstanding; the problem is a thing that too little folks are speaking intelligently about. We are happy that we stumbled across this in my seek out something with this.

  28. I spent four years trying EVERYTHING in Online Dating, and through a huge amount of trial and error, I produced a system that I will share for you. This book will take you, step by step, through everything you need to know to double, triple or even quadruple the number of women you meet online.

  29. I spent four years trying EVERYTHING in Online Dating, and through a huge amount of trial and error, I produced a system that I will share for you. This book will take you, step by step, through everything you need to know to double, triple or even quadruple the number of women you meet online.

  30. I simply want to tell you that I’m all new to blogging and truly enjoyed you’re web-site. Very likely I’m want to bookmark your website . You absolutely have awesome well written articles. Appreciate it for revealing your web page.

  31. A lot of of the things you claim is supprisingly accurate and it makes me ponder the reason why I hadn’t looked at this in this light before. This article truly did turn the light on for me as far as this specific subject goes. Nonetheless at this time there is actually just one issue I am not necessarily too comfy with and whilst I make an effort to reconcile that with the main idea of the issue, permit me observe just what the rest of the visitors have to point out.Very well done.

  32. I wish to show my appreciation to you for rescuing me from this particular instance. As a result of scouting through the search engines and coming across ideas that were not helpful, I thought my entire life was gone. Being alive minus the strategies to the issues you’ve sorted out through your entire blog post is a critical case, and those which might have in a negative way affected my career if I hadn’t encountered your blog post. Your own personal expertise and kindness in dealing with the whole lot was crucial. I don’t know what I would’ve done if I hadn’t discovered such a stuff like this. I can at this moment relish my future. Thanks a lot very much for your professional and result oriented guide. I will not hesitate to propose your web site to anyone who wants and needs care on this issue.

  33. I’m impressed, I have to admit. Seldom do I encounter a blog that’s both equally educative and engaging, and let me tell you, you
    have hit the nail on the head. The issue is something not enough people are speaking intelligently about.

    I am very happy that I stumbled across this in my search for something
    relating to this.

  34. Hi I am so grateful I found your website, I really found you by error, while I was researching on Bing for something else, Nonetheless I am here now and would just like to say thanks for a fantastic post and a all round enjoyable blog (I also love the theme/design), I don’t have time to read it all at the moment but I have book-marked it and also added in your RSS feeds, so when I have time I will be back to read a great deal more, Please do keep up the awesome work.

  35. Simply desire to say your article is as surprising.
    The clarity to your submit is simply excellent and that i could think you’re a professional on this subject.

    Well along with your permission allow me to grasp your feed to keep updated with drawing close post.
    Thank you 1,000,000 and please continue the rewarding work.

  36. I am curious to find out what blog platform you are utilizing? I’m experiencing some small security issues with my latest website and I would like to find something more secure. Do you have any solutions?

  37. Can I just say what a reduction to find someone who actually knows what theyre speaking about on the internet. You positively know learn how to carry a difficulty to light and make it important. Extra people must learn this and perceive this side of the story. I cant imagine youre not more common since you undoubtedly have the gift.

  38. I don’t know whether it’s just me or if everybody else encountering
    issues with your website. It looks like some of the text in your content are running off the screen. Can someone
    else please comment and let me know if this is happening to them
    as well? This may be a problem with my web browser because I’ve had this happen previously.
    Cheers

  39. Can I just say what a reduction to find someone who actually knows what theyre speaking about on the internet. You positively know learn how to carry a difficulty to light and make it important. Extra people must learn this and perceive this side of the story. I cant imagine youre not more common since you undoubtedly have the gift.

  40. You made some decent points there. I regarded on the internet for the difficulty and found most individuals will associate with along with your website.

  41. A formidable share, I simply given this onto a colleague who was doing just a little analysis on this. And he in reality bought me breakfast as a result of I discovered it for him.. smile. So let me reword that: Thnx for the treat! However yeah Thnkx for spending the time to debate this, I feel strongly about it and love studying extra on this topic. If possible, as you develop into expertise, would you mind updating your blog with more particulars? It’s extremely helpful for me. Large thumb up for this blog publish!

  42. You really make it seem so easy with your presentation but I find this matter to be
    actually something which I think I would never understand. It seems too complex
    and very broad for me. I’m looking forward for your next post, I’ll try to get the hang of it!

  43. Quest bars cheap fitnesstipsnew1 quest bars cheap 516999410492780544 quest
    bars cheap
    Hey There. I discovered your weblog using msn. That is an extremely well written article.

    I will make sure to bookmark it and return to read more of your helpful info.
    Thanks for the post. I will definitely return.
    Quest bars cheap fitnesstipsnew1 quest bars cheap 516999410492780544
    quest bars cheap

  44. I think everything posted was actually very reasonable. But, what
    about this? what if you typed a catchier post title? I mean, I don’t want
    to tell you how to run your blog, however suppose you added a title that grabbed a person’s attention? I mean Funktionen höherer Ordnung – Andreas Schlapsi is
    kinda vanilla. You might peek at Yahoo’s front page and watch how they create post titles to grab people
    to open the links. You might try adding a video or a pic or two to
    grab readers excited about what you’ve got to say.
    Just my opinion, it could make your posts a little bit more interesting.

  45. Woah! I’m really loving the template/theme of this
    site. It’s simple, yet effective. A lot of times it’s very difficult to get that “perfect balance” between usability
    and visual appearance. I must say you have done a superb
    job with this. In addition, the blog loads extremely quick for
    me on Opera. Exceptional Blog!

  46. sayah juga anak kost. dan sebagian besar duit sayah abis buat makan. Kadang kepengen makan di A, kadang di B, jadi khusus untuk post ini saya emang ga budget in, tapi hal ini berarti memperketat di post2 lain. seperti hang out, seperti belanja dsb.Makasih udah mampir ke tempat sayah ya.Template dikau sama dengan template blog jie sayah , but it’s ok. Template sayah ajah banyak yang make..xixixi

  47. B) Si la potencia útil nominal a instalar es igual menor que 400 kW y la instalación suministra servicio de calefacción y de agua caliente sanitaria, se podrá emplear un único generador siempre que la potencia demandada por el servicio de agua caliente sanitaria sea igual mayor que la del escalón de potencia mínimo. En las instalaciones todo aire, de caudal de refrigerante variable, el sistema para el control de consumos por usuario será definido por el proyectista el redactor de la memoria técnica en el propio proyecto, en la memoria técnica de la instalación.

  48. Wow that was odd. I just wrote an very long comment but after I clicked submit my comment didn’t appear.
    Grrrr… well I’m not writing all that over again. Anyhow, just wanted to say wonderful blog!

  49. I’ve learn a few good stuff here. Certainly worth bookmarking for revisiting.
    I wonder how much attempt you put to create the sort of excellent informative site.

  50. Son acciones nimias, pero que si no las realizas resultan incómodas en el resultado final, tales como activar el Media Player poner el Nero en español, y lo más importante, asegurarse de que el antivirus AVG tiene la base de datos actualizada y está en funcionamiento. Además de dedicarle todo el tiempo necesario a la reparación y a los consejos de uso, que un reparador conocedor de su profesión puede dar después de tantos a?os de experiencia. Sí es cierto que en el momento de la compra te resultarán un poco más económico los dos aparatos en uno, pero ten en cuenta que es bastante menos eficiente energéticamente hablando.

  51. Un trabajo bien realizado quiere decir un cliente contento por lo que nos esforzamos mucho para ser su Servicio Técnico Bosch Madrid más cercano y económico que nunca. En Reparación y sustitución de piezas de cualquier tipo de frigorífico, nevera congelador. Con lo cual el tecnico me puede elegir el que le parezca para cobrar sin hacer nada.

  52. Así que si necesitas de servicios de trabajado de moldes, estudio personalizado y presupuestos, pásate por nuestra zona de contacto en esta misma web y explicanos tu proyecto. Mecanizados en tornos de precisión y decoletaje con sede en Barcelona. La combinación de una amplia experiencia junto con el uso de las tecnologías más avanzadas nos permite ofrecer un producto final de gran calidad y precisión.

  53. Link exchange is nothing else however it is only placing the other person’s web site link
    on your page at proper place and other person will also do similar
    in favor of you.

  54. My spouse and I absolutely love your blog
    and find many of your post’s to be just what I’m looking for.
    Does one offer guest writers to write content for yourself?
    I wouldn’t mind publishing a post or elaborating on a lot of the subjects you
    write about here. Again, awesome web site!

  55. Finally found a legit way of making some really good money: http://bit.ly/2ODt2Tt – all you have to do is browse through the products you like, then copy your affiliate link and include it as a comment on blogs or forums, or simply recommend it on your Facebook profile. This is one of the best affiliate programs out there, trust me on this one!

  56. Hi my loved one! I want to say that this article is awesome, great written and come with
    approximately all important infos. I’d like to see extra
    posts like this .

  57. Hi, i believe that i noticed you visited my site so i got here to return the desire?.I’m attempting to in finding things to improve my website!I suppose its ok to make use of a few of your ideas!!

  58. Hello there, I found your blog via Google whilst searching for a similar matter, your site came up, it appears to be like good. I’ve bookmarked it in my google bookmarks.

  59. One more thing. It’s my opinion that there are many travel insurance web sites of reputable companies that allow you to enter your journey details and find you the quotations. You can also purchase the actual international travel cover policy on internet by using your own credit card. All you have to do should be to enter your current travel information and you can understand the plans side-by-side. Merely find the program that suits your finances and needs and after that use your credit card to buy the item. Travel insurance on the internet is a good way to do investigation for a reputable company with regard to international holiday insurance. Thanks for giving your ideas.

  60. Hi there, I discovered your web site by means of Google while looking for a similar matter, your site got here up, it seems great. I have bookmarked it in my google bookmarks.

  61. Hello there, I found your website by the use of Google whilst looking for a comparable matter, your site came up, it appears great. I’ve bookmarked it in my google bookmarks.

  62. Hello, i believe that i saw you visited my web site so i came to go back the desire?.I’m trying to in finding issues to enhance my site!I guess its ok to make use of a few of your ideas!!

  63. If you ever did try Phallomax, please post your thoughts below. I’m about to try it out. Heard about those pills some very good reviews. Just wondering on how many of extra centimeters would it add to my little bruh down there hah 😀

  64. This is the suitable blog for anybody who wants to search out out about this topic. You realize so much its virtually hard to argue with you (not that I truly would need…HaHa). You undoubtedly put a brand new spin on a subject thats been written about for years. Nice stuff, simply great!

  65. Hello there! I simply would like to give you a huge thumbs up for your excellent information you’ve got here on this post. I will be coming back to your site for more soon.

  66. Hi there, I discovered your website via Google at the same time as searching for a similar subject, your website came up, it looks good. I have bookmarked it in my google bookmarks.

  67. Youre so cool! I dont suppose Ive read anything like this before. So nice to find any individual with some authentic ideas on this subject. realy thank you for beginning this up. this website is something that is wanted on the internet, someone with a little originality. useful job for bringing one thing new to the internet!

Leave a Reply

Your email address will not be published.