Sunday, May 3, 2015

Modeling garbage collectors with Alloy: part 1

Formal methods for software verification are usually seen as a high-cost tool that you would only use on the most critical systems, and only after extensive informal verification. The Alloy project aims to be something completely different: a lightweight tool you can use at any stage of everyday software development. With just a few lines of code, you can build a simple model to explore design issues and corner cases, even before you've started writing the implementation. You can gradually make the model more detailed as your requirements and implementation get more complex. After a system is deployed, you can keep the model around to evaluate future changes at low cost.

Sounds great, doesn't it? I have only a tiny bit of prior experience with Alloy and I wanted to try it out on something more substantial. In this article we'll build a simple model of a garbage collector, visualize its behavior, and fix some problems. This is a warm-up for exploring more complex GC algorithms, which will be the subject of future articles.

I won't describe the Alloy syntax in full detail, but you should be able to follow along if you have some background in programming and logic. See also the Alloy documentation and especially the book Software Abstractions: Logic, Language, and Analysis by Daniel Jackson, which is a very practical and accessible introduction to Alloy. It's a highly recommended read for any software developer.

You can download Alloy as a self-contained Java executable, which can do analysis and visualization and includes an editor for Alloy code.

The model

We will start like so:

open util/ordering [State]

sig Object { }
one sig Root extends Object { }

sig State {
    pointers: Object -> set Object,
    collected: set Object,
}

The garbage-collected heap consists of Objects, each of which can point to any number of other Objects (including itself). There is a distinguished object Root which represents everything that's accessible without going through the heap, such as global variables and the function call stack. We also track which objects have already been garbage-collected. In a real implementation these would be candidates for re-use; in our model they stick around so that we can detect use-after-free.

The open statement invokes a library module to provide a total ordering on States, which we will interpret as the progression of time. More on this later.

Relations

In the code that follows, it may look like Alloy has lots of different data types, overloading operators with total abandon. In fact, all these behaviors arise from an exceptionally simple data model:

Every value is a relation; that is, a set of tuples of the same non-zero length.

When each tuple has length 1, we can view the relation as a set. When each tuple has length 2, we can view it as a binary relation and possibly as a function. And a singleton set is viewed as a single atom or tuple.

Since everything in Alloy is a relation, each operator has a single definition in terms of relations. For example, the operators . and [] are syntax for a flavor of relational join. If you think of the underlying relations as a database, then Alloy's clever syntax amounts to an object-relational mapping that is at once very simple and very powerful. Depending on context, these joins can look like field access, function calls, or data structure lookups, but they are all described by the same underlying framework.

The elements of the tuples in a relation are atoms, which are indivisible and have no meaning individually. Their meaning comes entirely from the relations and properties we define. Ultimately, atoms all live in the same universe, but Alloy gives "warnings" when the type system implied by the sig declarations can prove that an expression is always the empty relation.

Here are the relations implied by our GC model, as tuple sets along with their types:

Object: {Object} = {O1, O2, ..., Om}
Root:   {Root}   = {Root}
State:  {State}  = {S1, S2, ..., Sn}

pointers:  {(State, Object, Object)}
collected: {(State, Object)}

first: {State} = {S1}
last:  {State} = {Sn}
next:  {(State, State)} = {(S1, S2), (S2, S3), ..., (S(n-1), Sn)}

The last three relations come from the util/ordering library. Note that a sig implicitly creates some atoms.

Dynamics

The live objects are everything reachable from the root:

fun live(s: State): set Object {
    Root.*(s.pointers)
}

*(s.pointers) constructs the reflexive, transitive closure of the binary relation s.pointers; that is, the set of objects reachable from each object.

Of course the GC is only part of a system; there's also the code that actually uses these objects, which in GC terminology is called the mutator. We can describe the action of each part as a predicate relating "before" and "after" states.

pred mutate(s, t: State) {
    t.collected = s.collected
    t.pointers != s.pointers
    all a: Object - t.live |
        t.pointers[a] = s.pointers[a]
}

pred gc(s, t: State) {
    t.pointers = s.pointers
    t.collected = s.collected + (Object - s.live)
    some t.collected - s.collected
}

The mutator cannot collect garbage, but it can change the pointers of any live object. The GC doesn't touch the pointers, but it collects any dead object. In both cases we require that something changes in the heap.

It's time to state the overall facts of our model:

fact {
    no first.collected
    first.pointers = Root -> (Object - Root)
    all s: State - last |
        let t = s.next |
        mutate[s, t] or gc[s, t]
}

This says that in the initial state, no object has been collected, and every object is in the root set except Root itself. This means we don't have to model allocation as well. Each state except the last must be followed by a mutator step or a GC step.

The syntax all x: e | P says that the property P must hold for every tuple x in e. Alloy supports a variety of quantifiers like this.

Interacting with Alloy

The development above looks nice and tidy — I hope — but in reality, it took a fair bit of messing around to get to this point. Alloy provides a highly interactive development experience. At any time, you can visualize your model as a collection of concrete examples. Let's do that now by adding these commands:

pred Show {}
run Show for 5

Now we select this predicate from the "Execute" menu, then click "Show". The visualizer provides many options to customise the display of each atom and relation. The config that I made for this project is "projected over State", which means you see a graph of the heap at one moment in time, with forward/back buttons to reach the other States.

After clicking around a bit, you may notice some oddities:

Diagram of a heap with an object pointing to the root

The root isn't a heap object; it represents all of the pointers that are reachable without accessing the heap. So it's meaningless for an object to point to the root. We can exclude these cases from the model easily enough:

fact {
    all s: State | no s.pointers.Root
}

(This can also be done more concisely as part of the original sig.)

Now we're ready to check the essential safety property of a garbage collector:

assert no_dangling {
    all s: State | no (s.collected & s.live)
}

check no_dangling for 5 Object, 10 State

And Alloy says:

Executing "Check no_dangling for 5 Object, 10 State"
   ...
   8338 vars. 314 primary vars. 17198 clauses. 40ms.
   Counterexample found. Assertion is invalid. 14ms.

Clicking "Counterexample" brings up the visualization:

Diagram of four states. A single heap object is unrooted, then collected, but then the root grows a new pointer to it!

Whoops, we forgot to say that only pointers to live objects can be stored! We can fix this by modifying the mutate predicate:

pred mutate(s, t: State) {
    t.collected = s.collected
    t.pointers != s.pointers
    all a: Object - t.live |
        t.pointers[a] = s.pointers[a]

    // new requirement!
    all a: t.live |
        t.pointers[a] in s.live
}

With the result:

Executing "Check no_dangling for 5 Object, 10 State"
   ...
   8617 vars. 314 primary vars. 18207 clauses. 57ms.
   No counterexample found. Assertion may be valid. 343ms.

SAT solvers and bounded model checking

"May be" valid? Fortunately this has a specific meaning. We asked Alloy to look for counterexamples involving at most 5 objects and 10 time steps. This bounds the search for counterexamples, but it's still vastly more than we could ever check by exhaustive brute force search. (See where it says "8617 vars"? Try raising 2 to that power.) Rather, Alloy turns the bounded model into a Boolean formula, and feeds it to a SAT solver.

This all hinges on one of the weirdest things about computing in the 21st century. In complexity theory, SAT (along with many equivalents) is the prototypical "hardest problem" in NP. Why do we intentionally convert our problem into an instance of this "hardest problem"? I guess for me it illustrates a few things:

  • The huge gulf between worst-case complexity (the subject of classes like NP) and average or "typical" cases that we encounter in the real world. For more on this, check out Impagliazzo's "Five Worlds" paper.

  • The fact that real-world difficulty involves a coordination game. SAT solvers got so powerful because everyone agrees SAT is the problem to solve. Standard input formats and public competitions were a key part of the amazing progress over the past decade or two.

Of course SAT solvers aren't quite omnipotent, and Alloy can quickly get overwhelmed when you scale up the size of your model. Applicability to the real world depends on the small scope hypothesis:

If an assertion is invalid, it probably has a small counterexample.

Or equivalently:

Systems that fail on large instances almost always fail on small instances with similar properties.

This is far from a sure thing, but it already underlies a lot of approaches to software testing. With Alloy we have the certainty of proof within the size bounds, so we don't have to resort to massive scale to find rare bugs. It's difficult (but not impossible!) to imagine a GC algorithm that absolutely cannot fail on fewer than 6 nodes, but is buggy for larger heaps. Implementations will often fall over at some arbitrary resource limit, but algorithms and models are more abstract.

Conclusion

It's not surprising that our correctness property

all s: State | no (s.collected & s.live)

holds, since it's practically a restatement of the garbage collection "algorithm":

t.collected = s.collected + (Object - s.live)

Because reachability is built into Alloy, via transitive closure, the simplest model of a garbage collector does not really describe an implementation. In the next article we'll look at incremental garbage collection, which breaks the reachability search into small units and allows the mutator to run in-between. This is highly desirable for interactive or real-time apps; it also complicates the algorithm quite a bit. We'll use Alloy to uncover some of these complications.

In the meantime, you can play around with the simple GC model and ask Alloy to visualize any scenario you like. For example, we can look at runs where the final state includes at least 5 pointers, and at least one collected object:

pred Show {
    #(last.pointers) >= 5
    some last.collected
}

run Show for 5

Thanks for reading! You can find the code in a GitHub repository which I'll update if/when we get around to modeling more complex GCs.

163 comments:

  1. I really love your article, I also love travel China, in my past 5 years I traveled China a lot, see my favorite site: China vacation packages | China city tours | Beijing Travel Service

    ReplyDelete
  2. I really enjoyed the article. I am a researcher working in formal methods, mostly model based testing and model checking. It is very nice to see someone really trying to take this kind of methodology into actual software development. Did you know that there are some model checkers that would take the source code of the implementation as the model? In particular, there are some that work at LLVM IR level, so you could feed it with the real GC implementation and check for properties or bugs.

    ReplyDelete
  3. Awesome article, I will never comment on other blog, but I will deeply read your article and I am collect many information with your article, thank you so much for share this valuable information with us, I really like to read this type blog, keep sharing like this type useful information am suggest to my all dear friend to visit this blog and get collect this great information, thank you so much for read my comment, if any one searching the website designing and also PPC company in India please come on my website ogeninfo system we are completed all type digital marketing in cheap rate.
    Website Designing Company in India

    ReplyDelete
  4. I feel happy to say this I will deeply learning your blog and it’s really useful for me, keep sharing like this type valuable information regularly, I like to thanks for sharing this superb blog I hope I see you soon again time, thank you so much for read my comment, if any one searching the shipping company in India please visit my website yhcargoindia, we are shift your all type product with care in cheap rate.
    Custom Broker in India

    ReplyDelete
  5. This article is really fantastic and thanks for sharing the valuable post. We are one of the best website development and website image editing company.
    image manipulation service

    ReplyDelete
  6. Wow, amazing blog layout! How long have you been blogging for? you make blogging look easy. The overall look of your website is fantastic, let alone the content!

    Best 3D Animation Service
    Best Chatbot Development Service

    ReplyDelete

  7. شركات نقل عفش بالمدينة المنورة
    لا يقدر المرء بأن يقوم بعملية النقل بنفسه لأنها مهمة صعبة تحتاج إلى الكثير من يد العون، ولكن على العميل أن يحسن اختياراته عندما يقدم على اختيار شركة نقل عفش بالمدينة المنورة، فيجب أن يختار الشركة من خلال خبرتها وأدائها المتميز في العمل بالإضافة إلى الأدوات والمعدات الحديثة التي تقوم باستخدامها والتي تسهل عملية النقل، خاصة الأوناش المستخدمة في رفع وتنزيل العفش من وإلى السيارات المجهزة لنقل العفش إلى أي مكان داخل وخارج المدينة المنورة، فنحن في شركة نقل عفش بالمدينة المنورة نعتمد في عملنا على الخبرة والعمالة المدربى لذلك نضع شروط ومعايير عند اختيارنا للعمال الذين يرغبون في العمل بشركتنا.

    ReplyDelete
  8. Well written article. Did you try iosemus? is it working?

    ReplyDelete
  9. On the off chance that you'd like to turn into an extraordinary author, it is important that you are an astounding peruser. Set aside the effort to truly peruse what you expound on, and appreciate it. When you can peruse it from a guest's perspective, you'll can show signs of improvement comprehension of any adjustments which you have to make for your composition style. opusbeverlyhills

    ReplyDelete
  10. Thanks for sharing this post.It is very informative and helpful djalids

    ReplyDelete
  11. Thusly, to benefit every one of you the perfect information from the strong sources, there are online diaries have related in the market. One such blog is Bcss8, which is unequivocally made with a need to pass on you the most recent and top level information about the various games open in the market. News Credit

    ReplyDelete
  12. LOOKING FOR A SOCIAL MEDIA COMPANIES IN DUBAI? AE CLICKS IS AN AWARD-WINNING SOCIAL MEDIA MARKETING COMPANY IN DUBAI, WHICH IS CONSISTENTLY RANKED AMONG THE TOP 10 DIGITAL MARKETING COMPANIES IN DUBAI SINCE LAST FEW YEARS.

    ReplyDelete
  13. Nice Post, thanks for sharing with us....
    If you have any issue regarding your AOL Email then contact at aol email customer support.

    ReplyDelete
  14. I am a technical writer based at Tampa, USA and I have been writing blogs on many technical products that have impressed me so far. When it comes to streaming, I have explored a lot of devices. But I have never come across a product like Roku.
    My blogs:
    How to use Roku without a Remote?
    How to Reset Roku without Remote?
    What is Roku Express?
    Roku com link features
    Roku.com/link

    ReplyDelete
  15. Get the best Roku customer support by calling us @ +1-844-839-1180 toll-free number. We are experts in Roku com link activation, troubleshooting Roku and also in channel activation on Roku. Navigate to www.roku.com/link to know more

    ReplyDelete
  16. A Tech Gadget lover…! Wanderlust of Nature by heart and a tech-savvy by habit.... I have written and reviewed blogs on many products. As a keen neophyte, I love to discover new Products and their plus points… Get in touch… Or drop in your queries.
    My blogs:
    Roku.com/link create account
    Roku.com/link account
    Roku.com/link activate
    Roku.com/link activation
    Roku.com/link
    Roku com link

    ReplyDelete
  17. If you are someone who loves to watch free movies and series, then you must not miss out Tubi TV. It is one of the streaming services that offers free contents through its website and mobile app. Since it is a free app, you won’t be charged but they do make a revenue out of playing ads in between the videos. To get the channel, download the app from the Channel Store and proceed with the tubitv.com/activate process. Once activated, you can stream across 35+ genres, including action thriller, comedy, documentary and much more.

    ReplyDelete
  18. My Herpes virus that was cured by a great herbal medicine man. Since last 7 months i was having these virus and some time i experience the herpes outbreak. last three weeks I was in a great pain so I told one of my friends about it she told me that there is a great herbal medicine man that can cure Herpes and so many diseases and he also help people in getting pregnant and bringing back EX. I asked her if she had the man contact so i could give it a try, she gave me the contact, I contacted him he talked to me, and he send me the herbal medicine and herbal soap via DHL service to my country, told me how i will be using the herbal soap and drinking the herbs and after two weeks I should go for a test. Which I did, when the doctor told me that am now Herpes negative I couldn't believe myself I went to see another doctor the result was still the same i couldn't keep this to myself when i know that a lot of people are having issues with their health due to ignorant so i decided to let it out on this page that if anyone here need help in curing his/her Herpes virus or trying to conceive should also contact him he also have herbal medicine for HIV, Herpes, Cancer, Hepatitis etc and deal with spiritual problems too once again you can email him on:drafridherbalhome@gmail.com  webs:http://drafridherbalhome.webs.com    

    ReplyDelete
  19. I provide you the details like the subscription costs and program lists of the channels. And along with that also support in the channel activation steps. To get in touch please call +1-877-991-8710.

    My website : tv.youtube.com/start/roku/code

    ReplyDelete
  20. I am a Young fellow who loves to write. I'll quote myself by saying that I am a human by nature, writer by profession and a mighty traveler by passion. I'll always want to write about the things that people are using in their day to day life.

    My Creations : abc.com/activate

    ReplyDelete
  21. Tubi is a video streaming service, not unlike Netflix, Hulu, Amazon Prime Video and others, with an extensive library of TV shows and movies that you can watch free of charge from your phone, smart TV or streaming device.if you need any assistance for activating tubi tv on roku visit tubi.tv/activate

    ReplyDelete
  22. Khodiyar Corporation established by Mr. Vijay Panchal in 1996.Vijay Panchal Group is involved in Manufacturing of Timing Belt Pulley since 17 years.
    Timing pulley exporter | Khodiyar corporation

    ReplyDelete
  23. Amazing! This blog looks exactly like my old one! It's on a completely unique point however it has basically a similar page format and plan. Brilliant selection of hues



    Xfinity Pay Bill, Xfinityn Bill Pay, How to make xfinity pay bill, How to get rid of xfinity pay my bill, How to make xfinity online payment , Xfinity Pay Bill, Xfinity Pay Bill,Xfinity Pay Bill,Xfinity Pay Bill,

    ReplyDelete
  24. After the launching of "Kids & Family" section on Roku channel, Roku is also adding new features to give more control to parents over the channel, what their kids can watch when accessing Roku channels.

    roku.com/link

    ReplyDelete
  25. I rarely share my story with people, not only because it put me at the lowest point ever but because it made me a person of ridicule among family and friends. I put all I had into Binary Options ($690,000) after hearing great testimonies about this new investment

     strategy. I was made to believe my investment would triple, it started good and I got returns (not up to what I had invested). Gathered more and involved a couple family members, but I didn't know I was setting myself up for the kill, in less than no time all we had put ($820,000) was gone. It almost seem I had set them up, they came at me strong and hard. After searching and looking for how to make those scums pay back, I got introduced to maryshea03@gmail.com to WhatsApp her +15623847738.who helped recover about 80% of my lost funds within a month.

    ReplyDelete
  26. I rarely share my story with people, not only because it put me at the lowest point ever but because it made me a person of ridicule among family and friends. I put all I had into Binary Options ($690,000) after hearing great testimonies about this new investment

     strategy. I was made to believe my investment would triple, it started good and I got returns (not up to what I had invested). Gathered more and involved a couple family members, but I didn't know I was setting myself up for the kill, in less than no time all we had put ($820,000) was gone. It almost seem I had set them up, they came at me strong and hard. After searching and looking for how to make those scums pay back, I got introduced to maryshea03@gmail.com to WhatsApp her +15623847738.who helped recover about 80% of my lost funds within a month.

    ReplyDelete
  27. الو اپلیکیشن از سال 1387 فعالیت خود را در حوزه IT شروع نمود و تا به امروز با تلاش و کار حرفه ای در طراحی اپلیکیشن موبایل و انجام نوآوری در پروژه های مختلف به یکی از شرکت های معتبر طراحی و ساخت اپ موبایل تبدیل شده است.
    طراحی اپ اندروید

    ReplyDelete
  28. با بکار گیری حرفه ای ترین تیم برنامه نویسی اندروید و iOS، همچنین تحلیلگران و برنامه نویسان سمت سرور به طراحی اپلیکیشن iOS و اندروید می پردازیم و همواره دانش و توانایی خود را برای ساخت، طراحی و توسعه برترین اپلیکیشن های موبایل بروزرسانی می کنیم.

    ReplyDelete
  29. Finally, got what I was looking for!! I’ve really enjoying every small bit of this. Ecstatic I stumbled into this post! and also I’ve bookmarked to look at unique information for your blog post. read this article

    ReplyDelete
  30. I know the value of Garmin Support Number and keep reading good content about the same. I found this blog very informative and it increased my understanding about garmin update to a great extent. For right guidance from efficient Garmin experts, keep +1-888-295-9190 handy all the time.

    ReplyDelete
  31. Roku.com/link - Steps to interface your Player to your TV. www.roku.com/link | Roku.com/link | Roku streaming device support Roku activate device is the easiest method to stream stimulation to your TV. visit for roku .

    ReplyDelete
  32. Find effective solutions for all kinds of technical snags from QuickBooks Customer Service Number 1-833-780-0086. QuickBooks is one of the reliable accounting applications that has given a lot to business. For More : https://g.page/quickbooks-support-california

    ReplyDelete
  33. Want to know the activation process of Roku via Roku.com/link? Then make sure to read our blogs to get to know the detailed steps. This is a simple and effortless process if you visit our website. You can get the activation code by reaching your registered account. After that, navigate to the Players section and get the Roku link code. Then open a web browser and reach Roku.com/link activate account
     to enter the code. live tv on roku

    ReplyDelete
  34. KUBET được cộng đồng cá cược đánh giá là nhà cái số 1 Châu Á trong năm 2019 hiện tại. Với nhiều trò chơi hấp dẫn, tỷ lệ cược cực cao, trải nghiệm mượt mà mang tới cơ hội kiếm tiền cho anh em. KUBET.IO là trang web cung cấp link đăng ký, đăng nhập KU BET - KU CASINO chính thức, hướng dẫn hội viên tham gia các trò cá cược trên nhà cái, cũng như cách nạp tiền, rút tiền.



    Từ khóa: #ku, #kubet, #kucasino, #kubetio, #ku777, #ku888, #ku999, #casino, #thienhabet, #kubetcasino



    Mạng xã hội KUBET chính thức:


    https://infogram.com/dang-ky-kubet-cach-tao-lap-tai-khoan-ku-bet-don-gian-1h8j4xglr0od6mv

    https://trello.com/kubet

    https://block-x.co/dang-ky-kubet/

    https://www.youtube.com/channel/UCyPQbqZIZKV60Q7njSmKe3A


    https://www.surveymonkey.com/r/S5X7VBD


    ReplyDelete
  35. Taxitaithanhhung.vn - công ty cung cấp giải pháp chuyển nhà trọn gói tại Hà Nội. Với mong muốn mang đến cho quý khách hàng dịch vụ vận chuyển nhà tại Hà Nội tốt nhất. Đội ngũ nhân viên chuyển nhà trọn gói Thành Hưng chuyên nghiệp, hệ thống xe tải với số lượng lớn, chúng tôi tự tin cam kết mang đến cho quý khách hàng 1 dịch vụ tốt nhất!

    Từ khóa chuyển nhà Hà Nội - công ty cung cấp dịch vụ chuyển nhà Thành Hưng:

    #chuyennhahanoi #chuyennhataihanoi #dichvuchuyennhahanoi #dichvuchuyennhataihanoi #dichvuchuyennhathanhhung #chuyennhatrongoithanhhung #chuyennhatrongoihanoi #chuyennhatrongoitaihanoi #donnhathanhhung #donnhatrongoihanoi #chuyennhagiarehanoi #dichvuchuyennhagiarehanoi

    https://tuoitre.vn/chuyen-nha-thanh-hung-20-nam-dong-hanh-va-phat-trien-thuong-hieu-20200422112222106.htm

    https://vnexpress.net/20-nam-taxi-tai-thanh-hung-phuc-vu-khach-hang-4075831.html

    https://dantri.com.vn/kinh-doanh/dich-vu-chuyen-nha-tron-goi-thanh-hung-20200319160451993.htm

    https://filmfreeway.com/chuyennhatrongoithanhhung

    https://medium.com/@vantaitthanhhung/dich-vu-chuyen-nha-thanh-hung-tai-ha-noi-9ddbff5cda4

    ReplyDelete
  36. I seriously love your website.. Very nice colors & theme. Did you make this site yourself? Please reply back as I’m attempting to create my own personal website KBC Winner and want to learn where you got this from or what the theme is named. Kudos!

    ReplyDelete
  37. Hi, I read your post and found it quite interesting. The post you shared is very unique and informative. Thanks for sharing such a useful post. Click Here: Change Roadrunner Email Password

    ReplyDelete
  38. Thanks for provide great informatic and looking beautiful blog, really nice required information & the things i never imagined and i would request, wright more blog and blog post like that for us. Thanks you once agian
    we offer services birth certificate in delhi
    which inculde name add in birth certificate and
    birth certificate correction complete process is online and we offer
    birth certificate apply online and we offer this birth certificate online same service offers at yourdoorstep at birth certificate in ghaziabad
    our dream to provide birth certificate in india and other staes like

    birth certificate in bengaluru and
    birth certificate in gurgaon book service with us birth certificate in noida also, service at yoursdoorstep only birth certificate in india or

    ReplyDelete

  39. شركة مكافحة الحمام بالمدينة المنورة

    يواجه الكثيرون مشكلة استقرار اعشاش الحمام على حواف الشبابيك أو أسفل أجهزة التكيف فشركة تركيب شبك طارد للحمام بالمدينة المنورة تساعدك على حل هذه المشكلة لأنها توفر لك جميع أنواع شباك طوارد الحمام بأسعار مناسبة.
    ويركب شباك طارد الحمام بواسطة فريق عمل خبير عقب معاينة المكان لتحديد أنسب طارد ومساحته.

    ReplyDelete

  40. شركة مكافحة الحمام بالمدينة المنورة

    يواجه الكثيرون مشكلة استقرار اعشاش الحمام على حواف الشبابيك أو أسفل أجهزة التكيف فشركة تركيب شبك طارد للحمام بالمدينة المنورة تساعدك على حل هذه المشكلة لأنها توفر لك جميع أنواع شباك طوارد الحمام بأسعار مناسبة.
    ويركب شباك طارد الحمام بواسطة فريق عمل خبير عقب معاينة المكان لتحديد أنسب طارد ومساحته.

    ReplyDelete
  41. Read your article with the title “how to activate xfinity internet activation”. It’s excellent. The activation steps are clear. Do not miss the guidelines, if you are ready to activate the channel. I have no words to express. The article is good and informative. Stay entertained watching the channel programs

    ReplyDelete
  42. Here are the tips to keep the Spine Healthy. Position your spine correctly, practicing ergonomics while you are sitting or sleeping. A good massage can offer therapeutic benefits. Mild to moderate exercise can help to loosen the tight muscles and increase the Blood flow. Contact best orthopedic doctor in chennai through +918101555555

    ReplyDelete
  43. Are suffering from back pain and spine surgeries? Looking for an best spine surgeon in chennai? Then dont worry, Dr. vijay balaji orthopedic surgeon efficiently treats sports injures all types of spine problems and gets you recover fastly. for more info consult through +918101 555 555

    ReplyDelete
  44. I appreciate your work you have given very interesting and useful information through this blog. Thanks a lot. Keep posting.
    If you have any query related to hp printer please follow these given links-
    Connect HP 2630 printer to Wi-Fi
    connect iPad to HP Printer without Air Print
    HP printer assistant not opening error in Windows
    Install HP Wireless Printer on MacOS
    reinstall HP Printer Drivers

    ReplyDelete
  45. Enjoy with many games that are prepared for you to play for real money will make you have fun. Apply for membership today. Get up to 2000 baht 928bet ทางเข้า Welcome everyone to the world of online gambling.

    ReplyDelete
  46. It is a valid link to activate www.amazon.com/mytv or primevideo.com/mytv in your device. You can watch Amazon prime video on amazon mytv, just you need to enter a 6 digit amazon registration code on your device.

    ReplyDelete
  47. Forgetting some or other things at this point in time is quite normal. But, if you have forgotten the PayPal password, you don't need to worry. Gladly, you can change PayPal password with ease of mind. All the PayPal password resetting steps are quite simple and straightforward that you can perform either on your phone or PayPal site. Also, even if you have not forgotten the PayPal password, still you must change PayPal password at some regular intervals for security reasons.

    Visit Here:- Cancel a Paypal Payment

    ReplyDelete
  48. Amazing post, I do not read anything like that before! AOL Mail Supports Team here is a well-researched guide to Recover AOL Password online. And you might end up losing your account password in an effort to protect the account. or this problem, Dial AOL Email Supports Toll-Free Number and get instant help.

    ReplyDelete
  49. Web tasarım ve SEO hizmetleri ile web sitenizi Google arama motorunda ilk sayfaya getirin.

    ReplyDelete
  50. AHSEC (Assam Higher Secondary Educational Council) is going to conduct the class 12th standard exams for all AHSEC Assamese Medium and English Medium students for the academic year of 2021, the students who have wish to continue their study in Assam state class 11th and 12th standard of Higher Secondary Science, Arts and Commerce course those boys and girl students AHSEC 12th Question Paper 2021 can download the AHSEC Question Paper 2021 Pdf with subject wise answer solutions through Assam Board HS Model question papers 2021 and AHSEC important question papers for Science, Arts and Commerce group annual final public examination tests for the academic year of 2021.

    ReplyDelete
  51. Techie crews is one best digital marketing agency that can help your business to meet it's next phase using tools like content creation and development, Search Engine Optimization, Social Media Marketing, Website Development, Digital marketing, Google Ad, Graphic design, Email Marketing and Web Hosting. The unerring method to get the core audience and enlarge the brand recognition is by working with the best digital marketing company in Chennai.
    Best Digital Marketing Company in Chennai

    ReplyDelete
  52. SEO Services Delhi includes strategic consulting, on-site and off-site technical interventions. PPC Services Delhi

    ReplyDelete
  53. SEO Services Delhi includes strategic consulting, on-site and off-site technical interventions. PPC Services Delhi

    ReplyDelete
  54. India's Best CBSE, ICSE, State Boards School Syllabus mapped E Learning App for K-12 Students. This Learning App covers learning courses from Kindergarten to Class 12th which makes Concept Learning Effective and Easy Learning Experience. Download The APP Now.

    ReplyDelete
  55. Excellent post! Your post is very useful and I felt quite interesting reading it. Expecting more post like this. Thanks for posting such a good post. laptop service in home. To service your laptop with offer prices, Please visit : Laptop service center in Navalur

    ReplyDelete
  56. Goappx is a web and mobile app development company that builds on-demand apps, clone scripts for popular on-demand services and delivers custom IT solutions.
    Web app development

    ReplyDelete
  57. Goappx is a web and mobile app development company that builds on-demand apps, clone scripts for popular on-demand services and delivers custom IT solutions.
    Web app development

    ReplyDelete
  58. Our TikTok clone application is a world class readymade selfie video recording application, which is completely customizable based on the requirement.

    ReplyDelete
  59. Goappx is a web and mobile app development company that builds on-demand apps, clone scripts for popular on-demand services and delivers custom IT solutions.
    Web app development

    ReplyDelete
  60. Our TikTok clone application is a world class readymade selfie video recording application, which is completely customizable based on the requirement.

    ReplyDelete
  61. http://blogger.com/comment.g?blogID=8613771832678558370&postID=7136447079775013075&page=3&token=1611316294709

    ReplyDelete
  62. Nice to be visiting your blog again, it has been months for me. Well, this article that I've been waited for so long. I need this article to complete my assignment in college, and it has the same topic as your article. Thanks, great share. Know the cost of paytm like app development.

    ReplyDelete
  63. Deep penetration is not all the time the type Family Porn of intercourse you're in the mood for Porn Best Website especially if you're at a degree in your cycle the place your vagina and cervix really feel sensitive. Whether you’re dealing with sexual operate points

    ReplyDelete
  64. Deep penetration is not all the time the type Family Porn of intercourse you're in the mood for
    https://www.pornpag.com especially if you're at a degree in your cycle the place your vagina and cervix really feel sensitive. Whether you’re dealing with sexual operate points

    ReplyDelete
  65. Governmentyojanas website is a blogging site from where you can read information about the government's upcoming schemes in Hindi. samagra samajik suraksha mission


    ReplyDelete
  66. Jaipur Escort Service:- In case you are thinking same request to You than let us help you with picking best escort in Jaipur. As we said above there are various escorts office available in Jaipur which offer help at reasonable and moderate rate yet all of them are not. By far most of them Only acquires money and offers no kinds of help. They could manage without the necessities of their customers.

    Read More:- http://www.diaroy.com/

    ReplyDelete
  67. Thanks for sharing your ideas Gail. You have added my list of ideas on how to make my resources be of use after the initial usage.
    Your video is very informative also. I hope more online marketers read your post. Thanks.
    dragon-city-mod-apk

    ReplyDelete
  68. First of all, I want to thank you. Because for this great post you really deserve a big thumbs up. this blog helped me so much.
    Read more

    ReplyDelete
  69. Unity Keto Fulfillment, weight loss surgery is surely the only lengthy-term weight loss and healthful life-style answer for significantly obese patients. Studies display that maximum patients that go through weightloss surgical procedure will lose among 50-70% in their extra body weight inside the first three years following their method. Those that go through gastric pass surgical operation will lose extra body weight greater rapidly within the first twelve months than people who select LAP-BAND surgical treatment. However, gastric skip patients usually revel in a greater wide variety of headaches and aspect effects than LAP-BAND patients, because the LAP-BAND procedure permits for extra gradual and herbal long-term weight reduction. From a clinical attitude, a weight-loss surgical procedure is taken into consideration a hit when the patient loses at least 50% of their extra frame weight and continues the weight off for as a minimum five years. While important lifestyle adjustments want to be made to ensure that the weight loss is maintained in the long term, research have shown that most weight reduction surgical treatment sufferers are capable of hold a 50-60% lack of extra frame weight 10 years after the surgical procedure. However, it is crucial to notice that a weight loss of simply 10% of overall frame weight can start to have high quality fitness outcomes in decision of obesity-related situation like asthma, gastric reflux (GERD), and diabetes. As weightloss surgical operation is generally completed on patients that are at the least 75-100 pounds obese or have a Body Mass Index (BMI) of at least 35 with a fitness condition, universal weight loss can range everywhere from forty pounds to over a hundred kilos. But the affected person is surely the chief at the back of achieving those results. While patients will without a doubt appearance and feel better after weightloss surgical operation, there also are numerous health benefits related to successful weight loss. In maximum cases, health situations that increase due to immoderate frame weight or are worsened with the aid of obesity may be stepped forward upon or, in a few instances, remedied through weight reduction surgery. But there are different ways to measuring success with weight loss surgical procedure, like the LAP-BAND System. For instance, https://www.healthpubmed.com/unity-keto/

    ReplyDelete
  70. We source Escorts Service in Ahmedabad, And also just what various other terrific ways can one enjoy aside from picking a high-quality Independent Call Girls in Ahmedabad? Enjoy Hot Escorts Service in Ahmedabad for excellent amusement, High-class Escorts Service in Ahmedabad just call us on our number we will provide you, we are the main expert office with an extraordinary assortment of prominent Escorts Service in Ahmedabad.

    ReplyDelete
  71. Dr Vijay Balaj is one of the best Orthopedic Surgeons and carries over vast years of broad and rich experience in his field of specialization. Call the best orthopedic doctor in Chennai, at 8101 555 555 for any ortho queries

    ReplyDelete
  72. I found so many exciting matters in this particular content, I would like to request please keep posting such informative content. Check out free eyeglasses free shipping

    ReplyDelete
  73. Dr Vijay Balaj is one of the most trusted orthopaedic surgeons in Chennai. Dr Vijay Balaj has experience in performing minimally invasive spine procedures and injection therapies. Dr Vijay Balaj provides you specialized care to patients afflicted by arthritis, pelvic fractures and complicated trauma. Dr Vijay Balaj also offers honest and best advice and treats his patients to the fullest of their satisfaction. Call the best orthopedic doctor in Chennai, at 8101 555 555 for any ortho queries

    ReplyDelete
  74. ใช้งานง่าย เล่นง่าย บริการดี ตลอด24ชั่วโมง

    แทงบอล168


    ReplyDelete
  75. Thanks for sharing.Very Informative one.Our Tiktok Clone /Dubsmash/Musically Clone application is one of the best entertainment application available on market with innovative features and functionality.

    ReplyDelete
  76. mens pajamas Lounge Around in Comfort with the Best Men's Pyjamas. Having a perfect pair of Pyjamas And Lounge Pants can be the best answer for your casual comfort.

    ReplyDelete
  77. Your Article is so good and readble thanx for sahring this content. The sooner you will seek the help of a Sexologist in Delhi the faster you will start seeing the results. sexologist in Delhi is something that you certainly need. He has registered himself in the list of the top reputed sexologist. You have got it here! He is an honorable name in the industry of sexologist treatment and best sexologist in Delhi or top sexologist in Faridabad.

    ReplyDelete
  78. FuboTv streaming platform uses your location to include local channels with your monthly subscription and gives you access to more than 150 live channels. FuboTv also allows you to enhance your streaming experience with a series of channel add-ons, which can be added to your plan for an extra fee each month. Specifically, FuboTv currently offers six premium network add-on options. you'll also get 90 hours of cloud-based DVR storage to record and watch anything you want. fubotv/Connect

    ReplyDelete
  79. This comment has been removed by the author.

    ReplyDelete
  80. You can track the information you need here.สล็อตแตกง่าย

    ReplyDelete
  81. If the fubotv connect code, or different options are no longer working, you may also think about uninstalling and reinstalling the utility again. Download the software from the favored App save and deploy it again. In different cases, you can additionally attempt updating your application. fubo.tv/activate

    ReplyDelete
  82. Brown Rice Flour or Bhura Chawal Ka Atta- Gluten Free Flour | 500gms · 15% OFF WITH BANK & CARD PAYMENTS · Customer Reviews · Organic Rice Flour (Chawal Atta) ... Earthon's Organic Rice Flour is Best quality, made from organically grown rice, no preservative, Buy Rice Flour (Chawal Atta) & other Special Flours online at best discounted price in Noida on Grocio.in.

    ReplyDelete
  83. Buy Rice Flour (Chawal Ka Atta Benefits) from AYNSH IMPEX Find Company contact details & address in Jaipur, Rajasthan Rice flour is gluten-free, making it safe for people with gluten allergies or celiac disease. Rice flour enhances liver health, as it contains choline,

    ReplyDelete
  84. Your content is nothing short of bright in many forms. I think this is friendly and eye-opening material. I have gotten so many ideas from your blog. Thank you so much.สล็อต แตกง่าย

    ReplyDelete
  85. Hi, I am John Smith I am Web Developer, It is an amazing blog thanks for the sharing the blog. Frantic infotech provide the android app development such as an information about software development for costumer service. Frantic infotech also provide the tablet app development company. The development of advanced web applications is Orient Software’s specialty and we will successfully fulfill all your web application development requirements, from small-sized to wider-ranged projects. We Also do work multiple platforms like:
    mobile app development services
    android app development on mobile
    ios app development services
    react native app development
    Hardware Mobile App Development
    flutter app development company
    angularjs web development

    ReplyDelete
  86. Nice content, keep sharing with us.

    ReplyDelete
  87. Alhamdulillah, this Online Quran Academy has been magnificently laying out its services for the last 10 years. It was founded by our very well-reputed Mr. Mazhar Shafiq
    Our Online Quran Academy in Pakistan has always ensured that our students have the maximum possible interactive one-on-one Skype sessions with our tutors to provide a better understanding of the Holy Quran. Learn Online Quran e pak ,Online Quran Academy In Pakistan
    Learn Madani Qaida With Tajweed
    Learn Noorani Qaida With Tajweed

    ReplyDelete
  88. If you’re looking for Online Quran Classes, then you’re in the right place. Rising Quran is an online school, mainly for students from all over the world. We welcome people from all over the world to learn about the Quran and the commandments of Islam regardless of race, color or cast.
    Contact us
    Learn Online Quran Courses
    Learn Online Courses

    ReplyDelete
  89. I admire this article for the well-researched content and excellent wording. I got so involved in this material that I couldn't stop reading. I am impressed with your work and skill. Thank you so much. Feel free to visit my website; 바카라사이트

    ReplyDelete
  90. I have read your article; it is very informative and helpful for me. I admire the valuable information you offer in your articles. Thanks for posting it. Feel free to visit my website;
    바카라사이트

    ReplyDelete
  91. The pandemic has been quite a disaster for many industries out there. With tons of people losing their jobs and national economies declining, this is perhaps one of the roughest patches hit by us. In this environment of uncertainty, having a safe and steady income is key for sustainability which is why everyone is looking for the world best business opportunity in India in low investment.

    Studynlearn

    ReplyDelete
  92. pandemic has been quite a disaster for many industries out there. With tons of people losing their jobs and national economies declining, this is perhaps one of the roughest patches hit by us. In this environment of uncertainty, having a safe and steady income is key for sustainability which is why everyone is looking for the world best business opportunity in India in low investment.

    Studynlearn

    ReplyDelete
  93. Great article, thanks for sharing with us!

    ReplyDelete
  94. Have you ever tasted the Jackfruit Chips from Nagercoil?.. Sweetkadai.com delivers the Best Jackfruit Chips at your doorstep.. Order now!!

    ReplyDelete
  95. Euphoria Spa also known as “Euphoria Wellness Spa or Euphoria Spa & Salon”.Established in April 2016 in SDA Market. Luxury should not always be high-priced. We aim to strike a balance in cost and quality in Best spa delhi.

    ReplyDelete
  96. We appreciate you sharing this content with us! It's great to see how Tesla is helping make our roads safer. Thanks for helping us spread the word!

    Thailand Embassy Attestation Services is a leading Thai government approved Thailand embassy attestation service provider who specializes in providing first-class fully completed and accepted Thailand embassies, foreign legalisation of documents.246 charactersThailand Embassy Attestation

    ReplyDelete
  97. We often offer special discounts and coupons for Modelones.Com Coupon Code. Check back often to see what's available!

    ReplyDelete
  98. Thank you for posting a lot of interesting posts.

    ReplyDelete

  99. I wanted to thank you for this excellent read.

    ReplyDelete

  100. I definitely loved every little bit of it.

    ReplyDelete
  101. thank you for sharing such a great bog it is very helpful.

    ReplyDelete

  102. I have a presentation subsequent week, and I’m at the search for such info."

    ReplyDelete
  103. I’m very pleased to discover this site. I want to to thank you for ones time for this particularly wonderful read!

    ReplyDelete
  104. IPL Win App is a cutting-edge mobile application designed to enhance the experience of cricket enthusiasts during the Indian Premier League (IPL) season. This innovative app, known as iplwin, offers users a seamless platform to engage with their favorite cricket teams and players while providing opportunities to win exciting prizes.

    With its user-friendly interface, iplwin allows cricket fans to stay updated on match schedules, scores, player statistics, and team standings throughout the IPL tournament. Whether you're a seasoned cricket aficionado or a casual fan, this app caters to your needs by delivering real-time updates and comprehensive coverage of all IPL matches.

    One of the key features of the iplwin app is its interactive prediction game, which adds an element of excitement and competitiveness to the IPL experience. Users can participate in various prediction contests, such as match outcomes, player performances, and milestone achievements, to earn points and rewards.

    To access the full range of features and participate in prediction contests, users are required to create an account and log in to the iplwin platform. The iplwin login process is simple and secure, ensuring that users can enjoy a personalized and immersive experience tailored to their preferences.

    Whether you're cheering for your favorite team or competing against friends in prediction contests, iplwin offers a dynamic and engaging platform for cricket enthusiasts to celebrate the thrill of the IPL season. So, download the IPL Win App now, log in to iplwin, and elevate your IPL experience to new heights at 24KBET!

    Check our latest article below:
    ipl win app
    iplwin
    iplwin login
    ipl win
    ipl win login

    ReplyDelete
  105. Flights from Singapore to Krabi Airport provide a convenient and efficient way to travel between these two destinations. The flight duration typically ranges from 2 to 2.5 hours, offering a relatively short journey. Krabi Airport (KBV) serves as the gateway to the beautiful province of Krabi in southern Thailand, known for its stunning beaches, limestone cliffs, and vibrant culture. Upon arrival, travelers can easily access popular destinations such as Ao Nang, Railay Beach, and Phi Phi Islands, where they can indulge in various activities such as snorkeling, rock climbing, or simply unwinding by the turquoise waters.

    ReplyDelete
  106. Thank you for this wonderful post! It's so important to take a step back and appreciate the little things in life, and your blog always reminds me to do just that. rappahannock traffic lawyer

    ReplyDelete
  107. I really enjoy reading your blog. It is very informative and I can always find new information that I can use. Your writing is very clear and easy to follow, which makes it a pleasure to read.
    Unabridged Birth Certificates
    Unabridged Death certificate
    Retention of South African Citizenship
    Apostilles
    Police Clearances
    Ancestrial Visas for the UK
    UK Citizenship ARD

    ReplyDelete
  108. This comment has been removed by the author.

    ReplyDelete
  109. I am really happy to say it’s an interesting post to read. I learn new information from your blog.
    Visit Us - Ecommerce Website Development

    ReplyDelete