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|Title Translation of
The Smurf Who Would Be King
|Le Schtroumpf qui devient roi
|El pitufo que debería ser rey
|Der Schlumpf, der König sein wollte
|Il puffo che divenne re
|De Smurf die koning wilde zijn
"The Smurf Who Would Be King" is a Season 3 episode from the Smurfs cartoon show.
After reading a story about a king who ruled with fairness and kindness, Dreamy begins to fantasize about being a king, even to the point of walking around wearing Handy's machine cog for a crown and Tailor's purple cloth for a cape while carrying Farmer's hoe for a scepter, calling himself "King Dreamy the Smurf-Hearted". But Dreamy's fantasizing is cut short when Handy, Tailor, and Farmer retrieve their things from him. Undaunted, he goes out to where the S.S. Smurf II is docked wearing his captain's hat, continuing to pontificate there with only a few bear cubs listening to him nearby, when the wind causes part of the mast to knock Dreamy off the ship. Grabbing a rope, Dreamy accidentally releases the S.S. Smurf II from its dock and it starts to set sail downstream, with Dreamy still clinging to the rope crying for help. Soon both Dreamy and the ship go over the waterfall and then down into a whirlpool, Dreamy still crying out for help, when he ends up shipwrecked in a cavernous region that he has no idea where it is and no idea how to escape.
Soon he hears some chanting: pooka pooka pooka, oh wee oh. Fearfully, Dreamy goes to investigate when he falls into a hole and lands on a throne, greeted by a group of bear-like beings who are excited to see their "king" return. This leaves Dreamy confused, because he had no idea that these beings were waiting for him at all. They show him the statue they made of him which he broke in his fall and they restored, proving that they were waiting for him to return.
|Dreamy meets the Pookies.
The bear-like beings, who call themselves Pookies, then search the wrecked S.S. Smurf II for the "secret weapon" that the custodian of the Pookies was asking about, the one their king promised to return with to defeat the Norf Nags. As Dreamy asks them whether they had the right king, the ground shakes and rocks fall from the ceiling. The custodian Gabby then tells him that was the Norf Nags who want more jewels. He is then taken to the mines where the Pookies work, saying that since Dreamy left, the Norf Nags have been demanding for more jewels or else they will destroy the Pookies. Back in the throne room, Dreamy tries to convince his unexpected subjects that he's not their king, nor does he have a "secret weapon" to defeat their enemies, when some loyal Pookies bring in his royal crown, cape, and scepter to adorn their king with. Dreamy decides to accept them and soon his subjects join in with his saying they make him look "absosmurfly smurfy", though one of them does wonder what "smurfy" means.
Soon, with Dreamy deciding to act like a king, he sees a big kettle dropping from a hole in the ceiling. Gabby the Pookie custodian tells Dreamy that they fill his every day with the jewels they mine for the Norf Nags, whom they have never seen but describe as being fearsome. Dreamy decides to ride up in the kettle to take a look at them, and so with Gabby along for the ride, Dreamy goes up and gets carried into the vast jewel repository by a machine that dumps them there. They find a fortress where the Norf Nags' quake-making machine is located, but soon they see a giant shadow speaking with a fearsome loud voice, telling them to thank the Pookies for another day's job well done. Another giant shadow appears, calling the Pookies fools. "And the more we shake them up, the harder they work," the first shadow bellows with such laughter. Dreamy realizes that that must be the Norf Nags, and as he and Gabby return to the cauldron, now empty, a message is sent with them: to deliver twice as many jewels or the quakes will never cease. This message makes the other Pookies scared, fearing that their realm will be destroyed by the quake-making machines. Gabby tells his fellow Pookies not to fear because their king is here to deliver them, but Dreamy, who was rather intimidated by the appearance of the Norf Nags, tells his subjects he needs time alone to think.
Out by the waterfall in the cavern, Dreamy dons his captain's hat again and wonders what he's going to do when a vision of Smurfette tells him that he must help the Pookies because they need him. Dreamy says he wants to help them, but he just doesn't have the courage. The vision of Smurfette reminds Dreamy that he does have courage and proves it by stating three situations where he showed courage: sailing aboard the S.S. Smurf II across a stormy sea, going through the tests of the Swoofs while visiting their planet, and even sailing away on Handy's kite. Dreamy realizes that she is right and decides that he will help the Pookies.
|The Norf Nags as they appeared...
|...and the Norf Nags as they really are
Back among the Pookies, Dreamy dons his royal attire once again and tells them that he has come with his "secret weapon" to help defeat the Norf Nags once and for all, and that their days of slavery are over. Riding up the kettle to where the Norf Nags were, Dreamy challenges them to show themselves, to which they respond by activating the quake-maker, taking it to its full height in order to destroy the Pookies. But Dreamy quickly enters their fortress and, instead of giant beings, he sees that the Norf Nags were just two rather weak beings no bigger than he is, using shadow casting and megaphones to make themselves sound big and fearsome. The Norf Nags, realizing that they have been exposed by the Pookies' king, give themselves up.
Soon, with the Norf Nags tied up, Dreamy is crowned with praises by the Pookies, saying, "All hail King Dreamy the Smurf-Hearted". Dreamy tells them that the only "secret weapon" he had was the one they all carried inside, which was courage. Gabby agrees, but then he accidentally activates the quake-making machine, causing a loud and powerful enough thump in the ground that it makes Dreamy hit his head against a shelf, knocking him out cold. But soon Dreamy finds himself awakened to the sound of Papa Smurf calling out to him, and finds himself back near the Smurf Village on board the S.S. Smurf II, all safe and sound. Dreamy tells Papa Smurf about his adventure about being a king, but Papa Smurf tells him that what he experienced was just a dream caused when the mast hit him in the back of the head.
Some of his fellow Smurfs call out to Dreamy to follow them back to the village. Dreamy briefly looks back and sees the bear cubs again by the riverside, but as he turns to head back to the village, he trips over and sees a crystal lying on the ground. He again hears Papa Smurf tell him that it was just a dream. But then Dreamy starts to wonder if it really was a dream.
Background Information
- The episode title is an allusion to the Rudyard Kipling short story The Man Who Would Be King, which became a 1975 film.
- This episode makes reference to three others: "The Astro Smurf", "The Last Smurfberry", and "Handy's Kite".
- As to whether Dreamy's adventure actually happened, the only possible explanation comes from the "non-canonical" Smurf story "The Smurfs And The Magic Flute", where Homnibus uses a technique called "hypno-kinesis" which causes Sir Johan and Peewit to magically appear near the Smurf Village while also still being in Homnibus' hovel. But since in this story there's no wizard that causes Dreamy to fall asleep and appear in the land of the Pookies, this explanation is uncertain at best.
- In the syndicated version of the episode, the part where Smurfette's vision in the waterfall shows Dreamy the past adventures he has been on has been edited out.


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Mazel 2010 Award Nominees & Winners:
Wig of the Year:
Kim Zolciak
Donald Trump
Brett Michaels
Wendy Williams (Winner)
People's Champion of the Year:
Levi Johnston
Bristol Palin
Oprah Winfrey
Jimmy McMillan (Winner)
Non-Homo-Sapien of the Year:
Barbara Streisand's chickens
NeNe's puppy Playa
Sir Jiggy VanderPump (Winner)
Grandma Wrinkles
Most Rational Person of the Year: Rachel Maddow
Resignation of the Year:
Lindsay Lohan's lawyer Shawn Chapman
Kanye West's media trainer Susie Arons
Tiger Woods' coach Hank Haney
JetBlue flight attendant Steven Slater (Winner)
Employee of the Year:
Flipping Out's Zoila (Winner)
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Movement of the Year:
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Dan Savage & Terry Miller - It Gets Better Project (Winner)
Various Celebrities - Digital Death Movement
Tom Brady, Michele Bunchin & Sporty Spice - Earth Hour Movement
Viewer's Choice Mazel of the Year:
Repeal of DADT [21% of vote]
Ben Weiner [30% of vote]
Betty White [39% of vote] (Winner)
Chilean Miners [10% of vote]
Although Andy addressed this episode as Watch What Happens: Live's 50th episode, it is actually the 51st episode in the series. However, he could have simply been referencing the fact that Watch What Happens: Live had aired 50 episodes and was over a year old at the time.
This episode premiered at the series' new timeslot of 11:00pm (ET) instead of its original timeslot of 12:00am (ET).
This episode premiered at a special date and time of Wednesday at 12:00am (ET) instead of the series' normal timeslot of Fridays at 12:00am (ET).
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Eastside Hydroponics550 Ohio Pike Cincinnati, Ohio USA
Eastside Hydroponics Bad Attitude from Owner of Eastside Hydroponics Cincinnati Ohio
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Fix it the right way.
Corporate Advocacy Program™
My name is Bill. I've gone many times over the years to Eastside Hydroponics to speak with Sarah about various kinds of fertilizers and seeds and I recently went to Eastside Hydroponics to speak with her.
She wasn't there and when I asked the owner if she was available he got very irritated with me and even a little bit verbally abusive. It was all I could do to keep my own temper in check and just walk out the store. I occasionally also see her in the supermarket and when I did just a couple days ago, she let me know that she moved on to her own business up in Blue Ash.
But, what really got me was just how verbally abusive this man, the owner whose name I don't know, was to me. I was totally shocked at the way he spoke with me.
I do know this, however, I'll never go back to that store ...EVER.
This report was posted on Ripoff Report on 09/28/2013 05:23 PM and is a permanent record located here: http://www.ripoffreport.com/reports/eastside-hydroponics/cincinnati-ohio-45245/eastside-hydroponics-bad-attitude-from-owner-of-eastside-hydroponics-cincinnati-ohio-1088045. The posting time indicated is Arizona local time. Arizona does not observe daylight savings so the post time may be Mountain or Pacific depending on the time of year.
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Inside the Hornet's Head(2005)
An Anthology of Jewish American Writing
An anthology of stories edited by Jerome Charyn
When compiler Jerome Charyn first read Saul Bellow's The Adventures of Augie March, a world of letters opened up to him. It was his first exposure to the full potential of language, rendered breathlessly. In those pages he felt the terror and delight and buzz and ceaseless clatter of the inside of a hornet's head. Here, he shares with us nineteen stories, including one from Augie March, that evoke similar feelings of passion and pain and joy. Selected from some of America's most celebrated Jewish writers, as well as a few lesser known ones, Inside the Hornet's Head is a moving, daring, appealing, and indispensable work.
Similar Books by other authors...
Used availability for Jerome Charyn's Inside the Hornet's Head
See all available used copies of this book at Abebooks UK or Abebooks US
Paperback Editions
October 2005 : USA Paperback
|Title: Inside the Hornet's Head: An Anthology of Jewish American Writing
Author(s): Jerome Charyn
ISBN: 1-56025-740-7 / 978-1-56025-740-0 (USA edition)
Publisher: Da Capo Press
Availability: Amazon Amazon UK Amazon CA
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text:
CAN BUS | Cypress Semiconductor
Hello friends,
I want to run CAN BUS interface with car.so I dont know how can i do that.if there anybody that know please help me to do?
and if there anybody have any example please realese here?
thanks for regard...
I want to know exactly how work parameter and items in CAN component in psoc creator.datasheet is not obvious for me...
please help me...
There are two examples (click on the right to CAN component -> Find code example)
CAN_Full_Example and CAN_Basic_Example.
You must have two PSoC5LP board for experiment with these examples.
Ideal - if you have a logic analyzer (saleae ljgic or another with CAN support)
You can use SN55HVD251 or PIN for Tx in Resistive pull up mode if no have CAN / LIN Expansion board.
Hi Pavloven.I checked example before but I have one psoc5lp.should have i 2 psoc5lp?
Exactly i want to know how can i connect and get data from car with can bus for example speed or motor detail.so can you help me or give me data or example project for doing that project?it is very important for me...
thanks for attention...
You need to have two nodes for data transfer. If you already have a transmitting CAN node other than PSoC, then you can use one PSoC 5LP with CAN transceiver kit: http://www.cypress.com/documentation/development-kitsboards/cy8ckit-017-...
If you want to just receive the data then you can refer 'CAN_Full_Example' mentioned in interaction #3 above. This example is receiving switch status and ADC data from another node and displaying on LCD. You can modify this project according to your need.
Also you need to take care of Baudrate settings. If your car CAN bus has specific baudrate then you need to configure CAN component accordingly. We recommend you to refer Getting started with CAN application note in the following link:
Kindly have a look at above. Let us know if you need any clarification.
Thanks and Regards
Hi pavloven and Hars.I buy another psoc5lp but i cant to run can bus interface with psoc creator example.I connected tx and rx pin(with pullup resistor)together and program twice psoc5lp kit.but I have no data transciever on can bus.so how can i test easy interfacing with 2 psoc by can bus?
please help me and tanks rof your regrding
It is worked.i programed basic examples on first psoc5lp and full example on second psoc5lp.so my mistake was pin configuration.explanation of mr pavloven is very helpful.so now i want to run this project with car so how can i do it?
Hi friends.Is there anybody that know how can hears CAN BUS from car on computer???
for example change CAN to RS232 to see data on hercules or other software.because i want to calculate data transciever from CAN BUS by psoc5lp and i dont know car parameter ID to recieave them...
please help me...
You need some CAN Analyzer like OBD-II PIDs to get the car parameter ID
Hi friends.i want to ask a question.I am running CAN interface on psoc5lp prototype kit.and connect with pca82c250 can controller.so my problem is to read data from vehicle.i cant read data with my psoc project.
is there any body that know what is my problem and how can i solve it?
my program and address data can bus and clock is set on vehicle specification...
I can get data correctly when i use another psoc5lp as vehicle device for send data ...but when i connect with vehicle(can simulator) i cant get data...
what can i do to solved this problem?
thanks for attention...


text:
Merely a week ago most would have agreed that a Trump Presidency, as entertaining as it may have been, was a bridge too far for the eccentric billionaire. Now, have multiple revelation regarding FBI investigations into Hillary Clinton, many new polls have put that prospect of a Trump White House back on the table. According to the latest polls, here are 20 possible outcomes that give The Donal what he needs to move into 1600 Pennsylvania Ave.
1 – The "Live Free or Get High" Scenario..
Key States: New Hampshire and Colorado
Polls trending towards: TRUMP
Two recent polls have Trump and Clinton dead-locked in both CO and NH. Remember, Trump won NH in the primary with record-setting turnout and a massive swatch on first-time voters. Its also helpful that there is a hyper-competitive senate race going on there with incumbent Republican Kelly Ayotte edging out he opponent. If NH goes stays too-close-to-call early in the night, that will be the first sign that the "Live Free or Get High" scenario is in play.


text:
Reactive systems over cospans
- Curtis Barker
- 2 years ago
- Views:
1 Reactive systems over cospans Vladimiro Sassone University of Sussex Paweł Sobociński Università di Pisa Abstract The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we offer a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and König s rewriting via borrowed contexts and opens the way to a unified treatment of several applications. Introduction Some of the most important operational techniques, developed through research on concurrency, involve the use of labelled transition systems (LTS) and the accompanying notions of operational preorders and equivalences, bisimulation being chief among these, in order to reason about process equivalence. Some basic concepts, common to many applications where such operational techniques apply, include the notions of term, context and reaction. Such notions began to be studied in the seminal work of Berry and Boudol [3] on the chemical abstract machine. More recently, Leifer and Milner s [] introduced the framework of reactive systems, aimed at providing a general setting where such notions can be studied. Reactive systems can be seen as a generalisation of ground termrewriting systems, where a collection of ground rewrite rules is closed under a set of reactive contexts to obtain the rewrite relation. ontexts are themselves organised as the arrows of a category. Leifer and Milner s chief contribution was to utilise a universal categorical construction, dubbed relative pushout Research partly supported by EU FET- MYTHS: Models and Types for Security in Mobile istributed Systems, IST--367 and AILE: Architectures for Mobility, IST--3747; E RTN SERAVIS; and BRIS, Basic Research in omputer Science (www.brics.dk), funded by the anish National Research Foundation, University of Aarhus. (RPO), in order to equip each reactive system with an LTS, whose labels can be characterised as the smallest contexts that allow reactions to occur an idea originally due to Sewell [9]. Such LTSs are very well-behaved; in particular, bisimilarity is a congruence with respect to all contexts, provided that has enough RPOs. In [6], the authors proposed an approach based on a -dimensional generalisation of RPOs, the groupoidal relative pushout (RPO), which has been shown in [5] to encompass previous approaches addressing these issues. Of course, one retains the congruence theorems (bisimilarity, trace and failures equivalences) in the more general setting. Several constructions of RPOs have been proposed in the literature for particular categories of models. For instance, Milner explicitly constructed such bicolimits for bigraphs [3] in full detail, but there has been little work on understanding how such constructions may be performed in other models. Indeed, the main applications our theory of reactive systems have so far involved relatively simple examples [6, 5]. In the paper we address this by giving a construction of RPOs for a wide range of models those which can be expressed as certain cospans over adhesive categories. The class of adhesive categories, introduced in [9], includes many categories where the objects are variants of graphs for instance, the category raph of graphs and graph homomorphisms is adhesive. An important application of our results is Ehrig and König s rewriting via borrowed contexts, an extension of the double-pushout (PO) graph transformation approach with a contextual semantics that allows transfer of concepts and techniques from the field of process algebra to graphs. The labels of their LTS are the so-called borrowedcontexts certain contexts which allow a PO transformation to be performed. Other applications include a partial treatment of Milner s bigraphs [3], a model introduced to model various fundamental notions arising from the study of process calculi such as the pi-calculus, as well as a Petri net-based model Milner actually constructs ordinary RPOs in a precategory this is equivalent to constructing RPOs in the bicategory which results from taking support translations as -cells (see [5]).
2 $ $ take money S pour coffee insert money $ Bob $ drink coffee insert money $ take money Bob Figure. Example of a contextual system. of open systems [7], related to open nets []. S drink coffee pour coffee Before a formal presentation of the technical details of our results, we shall first allow ourselves a certain amount of informality in order to illustrate the intuition and the motivation behind the construction introduced in this paper. A cospan in an adhesive category is for us a generalised graphical context between interfaces; starting with objects I, J and of an adhesive category A (the reader could takea=raph for concreteness), we can treat as a context with inner interface I and outer interface J by providing ι o homomorphisms I c J. This resulting cospan is treated as an arrow of a new category ospan(a) with the same objects asa indeed such cospans may be composed; intuitively, by glueing together along the common interface; concretely, by constructing a pushout. ue to the nature of pushouts, the composition is, in general, not associative on the nose, but rather, up to a unique coherent isomorphism which means that ospan(a) is, in general, a bicategory []. Starting with any category A with pushouts, the process Aospan(A) can be thought of as a kind of a canonical contextualisation operation, turning objects of a one category into the arrows of another (bi)category. Incidently, the dual situation, that of spans over graphical structures, has been studied by Katis et al [8] roughly, they argue that spans over graphs can be seen as generalised automata. For an idealised example of cospans, consider the simple model of a coffee vending machine, illustrated by the leftmost diagram of Fig.. It has an outer interface consisting of two nodes, $ and, which one can think of as a money slot and the coffee out-tray. These are the parts of the coffee machine accessible to the environment, the internal components, represented by S, are invisible. The middle diagram represents a coffee drinker. He expects to see a money slot and a coffee out-tray, which are his inner interfaces. As the outer interface of the coffee machine and the inner interface of the coffee drinker match, one may compose them and obtain the system pictured in the rightmost diagram. There are several examples of cospans relevant for computer science. For instance bigraphs are cospans in an adhesive category of place-link graphs with outer interface maps mono, and graph contexts in the sense of Ehrig and König [5] are cospans in raph with both interface maps mono. Examples of reactive systems over such cospan categories include, therefore, the theory of bigraphical reactive systems of Milner [3] and the theory of double-pushout (PO) graph transformation [4]. The main result of the paper is the construction of R- POs in a class of cospan bicategories over adhesive categories, which in turn allows the derivation of LTSs for all reactive systems based on such bicategories. Specifically, we require that the inner interface map of every cospan is mono. Although technical in nature, the linearity condition does have an intuitive account. As alluded in the coffee drinker example, one can consider a cospan as a black box, with an inner interface and an outer interface. The environment cannot see the internals of the system and only interacts with it through the outer interface. The fact that the outer interface need not be linear means that the system is free to connect the outer interface arbitrarily to its internal representation. For example, the coffee machine could have two extra buttons in its outer interface; the café latte button and the cappuccino button. The machine internals could connect both these buttons to the same internal trigger for coffee with milk; the point is that the system controls its outer interface and is able to equate parts of it. On the other hand, the system cannot control what is plugged into one of its slots. Thus, an assumption of input-linearity is essentially saying that the system does not have the right to assume that two components coming in through the inner interface can be confused. Applying the construction to mono cospans in raph yields Ehrig and König s [5] construction of rewriting via borrowed contexts which confirms that their approach is an instance of the general methodology of reactive systems; we shall show that their labels actually arise from RPOs and thus satisfy a universal property. As a consequence, their congruence theorem follows automatically from the theory of reactive systems. Finally, because we require only the left leg of the cospan to be mono, we are able to generalise their results. Since Milner s bigraphs can be seen as output-linear cospans, the construction does not apply. However, we provide LTS semantics for a different class of bigraphs: the input-linear cospans over the same category. The construction has also been applied in order to derive LTS semantics for a compositional model of Petri nets [7]. Structure of the paper. The paper begins with two sections summarising the background theory necessary for our construction. First, in we recall Leifer and Milner s theory of reactive systems and relative pushouts together with the generalisation of the theory previously worked out by the authors. Secondly, in we recall about adhesive categories and cospan bicategories. Our main construction appears in 3. In 4, we provide a detailed exposition of the
3 relevance to Ehrig and König s [5] and mention other applications. Preliminaries. Throughout the paper we assume a basic knowledge of category theory, as well as basic acquaintance with the concepts of -categories and bicategories. Here we mention only that a bicategory [] can be described, roughly, as a -category where associativity and identity laws of horizontal composition hold up to isomorphisms. We shall denote all associativity isomorphisms by a, as for example, a : h(g f ) (hg) f. The isomorphisms are required to respect well-known coherence axioms []. We use id X to denote the identity at X, while f and stand, respectively, for identity -cells and vertical composition. Reactive Systems and RPOs Here we briefly recall an extension of Leifer and Milner s notion of reactive system to categories with -dimensional structure, as previously introduced by the authors [6]. The basic idea of a reactive system is to bring together a collection of contexts, which form the arrows of a category, with a set of reaction rules on terms. From the reaction rules one generates a reaction relation by contextual closure. Using certain pushouts, one equips a reactive system with an LTS on which bisimilarity is a congruence with respect to all contexts. Apart from trivial examples, it is the norm that the contexts of a reactive system have some notion of isomorphism often referred to as structural congruence in the field of process calculi. It turns out that ignoring such structure is often problematic (cf. [6]) and one solution is to include the isomorphism/structural congruence as part of the structure; i.e., to consider -categories of contexts instead of categories. uided by examples, we usually consider only isomorphic -cells. In order to generate an LTS and extend the congruence results still, one then needs to consider bipushouts (rather than pushouts) [6]. In this paper we consider cospans as contexts; since the composition is associative up to isomorphism, we shall need to work in bicategories instead of -categories. Apart from changing the definition of reactive system, this generalisation poses no difficulty bicolimits are naturally a bicategorical notion. efinition. (Reactive System). A reactive system consists of. a bicategoryb with all -cells iso;. a collectionof arrows ofbcalled the reactive contexts; it is required to be closed under -cells and be composition-reflecting (see below); 3. a distinguished object B; arrows with domain are often referred to as terms; 4. a set of pairs of terms, the reaction rulesr. The terms l, r of any given pair l, r R have the same codomain as arrows ofb. The reactive contexts are those inside which evaluation may occur. omposition-reflecting means that dd implies d and d, while the closure property means that given d and an isomorphismρ: d d inbimplies d. The reaction relation is defined by taking a a if there is l, r R, d,α: dl a andα : a dr. This represents that, up to structural congruence α, a is the left-hand side l of a reduction rule in a reactive context d, while a is, up to structural congruenceα, the right-hand side r in the same context. Leifer and Milner [] developed the derivation of a canonical LTS associated to any given reactive system. The derivation uses a universal construction, dubbed relativepushout (RPO), which is a pushout in a slice category. Bisimulation on the resulting LTS is a congruence, provided that the underlying category of the reactive system has enough RPOs; we shall make the meaning of enough precise below. A groupoidal-relative pushout (RPO) is the generalisation of an RPO to categories with -dimensional structure. We recall the definition below, and due to lack of space refer the reader to [6] for a full presentation. Note that although RPOs are introduced there in the setting of - categories (-categories with iso -cells), the development is easily transferred to bicategories with iso -cells it suffices to introduce the coherent associativity isomorphisms where necessary. In order to increase readability, we leave these out within the definition below. efinition. (RPO). A candidate for square (i) is a tuple I 5, e, f, g,β,γ,δ such thatδb gβ γa=α. In other words, the -cellsγ,βandδ, illustrated in diagram (ii), paste together to giveα. A groupoidal-relative-pushout (RPO) is a candidate which satisfies a universal property, namely, for any other candidate I 6, e, f, g,β,γ,δ there exists a mediating morphism, that is a quadruple h : I5 I 6,ϕ : e he,ψ : h f f,τ : g h g illustrated in diagrams (iii) and (iv). The equations that need to be satisfied are:.τe g ϕ γ =γ ;.δ g ψ τ f=δ; and 3.ψb hβ ϕa=β. Such a mediating morphism must be essentially unique, namely, for any other mediating morphism h,ϕ,ψ,τ there must exist a unique -cellξ : h h which makes the two mediating morphisms compatible, i.e.:.ξe ϕ=ϕ ;.ψ ξ f=ψ ; and 3.τ g ξ=τ. 3
4 c d α a b (i) c γ a e g I 5 β (ii) δ f b d e I 6 ϕ h e I 5 ψ (iii) f f g I 6 h τ (iv) RPOs are used to classify the smallest contexts necessary for a reaction to be performed. The redex squares which satisfy this property are known as groupoidal-idempushouts, or IPOs. efinition.3 (IPO). iagram (i) of efinition. is a -idem-pushout (IPO) if, c, d, id I4,α, c, d is its RPO. We are now in a position to define the LTS which has such smallest contexts as labels. efinition.4 (LTS). For a reactive system andbits underlying bicategory, define LTS() as follows: the states of LTS() are terms; there is a transition a f a if there exists a -cellα, a rule l, r R, and a reactive context d such that the diagram below is a IPO and a is iso to dr. f d α a l In previous work [6, 5], we have considered an abstract LTS where the terms and transitions are quotiented by isomorphism; this is the norm in specific calculi, for instance in S or the pi-calculus the states are processes, i.e., terms modulo structural congruence. For simplicity, we leave the terms and transitions unquotiented here, that is, we deal with the concrete transition system, using the terminology of []. Both versions have the same congruence properties. efinition.5. A reactive system is said to have redex- RPOs when every redex-square (), with a and f arbitrary, d a reactive context and l a part of a reaction rule l, r R, has a RPO. The following is a slight extension of a theorem for - categories which can be found in [6]. Theorem.6. Let be a reactive system with redex- RPOs. Then bisimilarity on LTS() is a congruence with respect to all the contexts of. For category theorists, a RPO can be described concisely as a bipushout in a pseudo-slice category. g I 5 () g A m n f Figure. Pushout diagram. Adhesive categories and cospans Adhesive categories. In order to construct RPOs in cospan bicategories we shall need the notion of adhesive categories, we refer the reader to [9] for an introduction; here we shall only mention some properties of adhesivity which we shall be need in the later exposition. In 3, we assume that the underlying category of the cospan bicategory is adhesive and use the structure of adhesive categories repeatedly in the construction of RPOs. Adhesive categories can be described by a slogan: pushouts along monomorphisms exist and are wellbehaved. The class of adhesive categories includes Set, raph, as well as any elementary topos. It is closed under product, slice, coslice and functor category. As explained in [9], many graphical structures relevant to computer science form adhesive categories. We shall need the following properties of adhesive categories for our constructions. The proof of the following lemma can be found in [9]. Lemma.. LetAbe an adhesive category.. Monos are stable under pushout ina. In other words, in the diagram of Fig., if m is mono then n is mono.. A pushout ina(fig. ) is also a pullback diagram, if m is mono. 3. If it exists, a pushout complement 3 of m, g, with m mono, is unique up to a compatible isomorphism; more precisely, if f, n and f : B, n : B are pushout complements, then there exists an iso ϕ : B B such thatϕ f=f and n ϕ=n. Recall that, given an object X, a subobject [µ : Y X] is an equivalence class of monomorphisms into X, where the equivalence relation is generated from the canonical preorder on monomorphisms into X: µ µ if there exists k : Y Y such thatµ k=µ. Subobject intersection and union refers to a meet and join of subobjects (if it exists) in this preorder. Any category with pullbacks has binary subobject intersection. Binary subobject unions in adhesive categories are calculated by pushing out along their intersection. 3 iven m : A and g : A, we say that B is a pushout complement of m, g when there exist f : B and n : B such that the resulting diagram (Fig. ) is a pushout diagram. B 4
5 ι + I o o Figure 3. omposition of cospans. ospan bicategories. We shall assume that is a category with chosen pushouts. That is, for arrows m : A and f : B, there exists unique chosen object A+ B and arrows A A+ B and B A+ B such that the resulting square is a pushout. The bicategory of cospans ospan() has the same objects as, but arrows from to are cospans. o ι. We will denote such cospans o ι :, and omitι (resp. o ) when (resp. ) is initial. We shall sometimes refer to and as, respectively, the inner and outer interfaces of o ι. Intuitively, we can think of a cospan as a generalised context, where are the internals, (the image via o of) represents the public view of, and (the image viaι of) the view of afforded to the holes in it. A -cell h: o ι o ι : in ospan() is an arrow h: insatisfying hι = ι and ho = o. The isomorphic -cells provide a canonical notion of structural congruence. We shall denote the bicategory of cospans which has the -cells limited to isomorphisms by ospan (). iven cospans o ι : and o ι :, their composition is the cospan obtained by taking the pushout of o andι, as illustrated by Fig. 3. Note that in the resulting composition, is forgotten. omposition is associative up to a unique isomorphism. It is easy to check that the associativity isomorphisms satisfy the coherence axioms, and thus yield a bicategory To perform our construction we need a certain linearity restriction. In particular, the notion of input-linear cospan. efinition. (Linearity). A cospan o ι is said to be input-linear whenι is a mono, output-linear when o is mono, and linear when it is both input-linear and outputlinear. A simple corollary of the first part of Lemma. is that the composition of two input-linear cospans over an adhesive category yields an input-linear cospan. Similarly, composition preserves output-linearity and linearity. efinition.3. Assuming that A is adhesive, let IL(A) be the bicategory consisting of input-linear cospans and - isomorphisms. Similarly, let L(A) be the bicategory of linear cospans and -isomorphisms. ι 3 RPOs for cospans In this section we present a general construction of RPOs for a class of reactive systems over cospan bicategories. onstruction. The following result is the main original contribution of this paper. Several implications of Theorem 3. and of the construction which constitutes its proof are considered in 4. Theorem 3.. IfAis adhesive, IL(A) has RPOs. The remainder of this section presents a proof of the above theorem. We first outline an algorithm for the construction of the desired minimal candidate. Because of space constraints, we have omitted most technical details; these can be found in the second author s Ph.. thesis [] and in [8]. An arbitrary square in IL(A), as illustrated in diagram (i) below, amounts to a commutative diagram (ii) in A, withαan isomorphism. A α (i) B o o ι i i ι A+ α B+ I3 o A o B A i i B efinition 3. (Frame of reference). iven a diagram (i) in IL(), by a frame of reference we mean an arbitrary object X equipped with isomorphismsω l : A+ I X and ω r : B+ I3 X such thatω r ω l =α. Letω A =ω l i A A+ : A X,ω =ω l i A+ : X,ω B =ω r i B B+ : B X andω =ω r i B+ : X. ι A (ii) learly, a frame of reference for (i) always exists. For instance, one can let X be B+ I3,ω r be the identity andω l be α. It follows easily that diagram (iii), below, is commutative. Notice that both of the squares in diagram (iii) are actually pushouts. ι B o I o 4 ι ω ι ω X ω o A A ω B o B A I ι B B ι A (iii) Sinceω A andω B are readily seen to be mono, being pushouts of monos in an adhesive category (Lemma.), we are able to obtain the subobject union an object Y= 5
6 A B and monomorphismsµ : Y X,ǫ : A Yand ǫ : B Y satisfyingµǫ =ω A andµǫ =ω B. Notice that sinceµis mono andµǫ ι A =ω A ι A =ω B ι B = µǫ ι B we have thatǫ ι A =ǫ ι B. We obtain the commutative diagram (iv). ω A X µ A ǫ Y ι A (iv) ǫ ιb ω B B E σ o E ρ ω I 5 ι π σ F ρ ω X Y µ (v) π A E γ I 5 δ F β B (vi) Algorithm 3.3 (RPO onstruction in IL(A)). The construction of the components of the minimal candidate is outlined below. They are illustrated in diagrams (v) and (vi). We obtain:. as the pullback ofω : Xandω : X;. E as the pullback ofµ : Y X andω : X; 3. F as the pullback ofµ : Y X andω : X; 4. I 5 as the pullback ofρ : F andπ : ; notice that due to the properties of pullbacks, we obtain a morphism o E : I 5 E such that all the faces of (v) are pullbacks. The following two lemmas show that the construction of Algorithm 3.3 indeed results in a RPO, and complete the proof of Theorem 3.. Lemma 3.4. The construction as outlined in Algorithm 3.3 provides a candidate for square (i). Proof. In order to prove the lemma, we are required to:. demonstrate the existence of appropriate inner and outer interfaces for each of E, F and ;. show that there exist isomorphismsβ : A+ I E B+ I3 F,γ : E+ I5 andδ: F+ I5 ; 3. show that these isomorphisms paste together in way which results in a -cell equal toα : A+ I B+ I3. We omit the details, and refer the reader to [8, ]. Lemma 3.5. The candidate constructed using Algorithm 3.3 satisfies the universal property of a RPO. More γ γ Figure 4. RPOs in IL(Set). precisely, given any other candidate for diagram (i), as illustrated in diagram (xiii), there exists a mediating morphism: γ δ E I 6 F β A B (xiii) ι a cospan I 5 H o H H I 6 (an arrow H : I 5 I 6 of IL(A)) and isomorphismsϕ : E E+ I5 H,ψ : F+ I5 H F andτ : H+ I6 in which form -cells of IL(A) and which satisfy the required equations: (E+ I5 τ)a(ϕ+ I6 )γ =γ, δ (ψ+ I6 )a(f+ I5 τ )=δ and (B+ I3 ψ)a(β+ I5 H)a(A+ I ϕ)=β. Moreover, the mediating morphism H, ϕ, ψ, τ is required to be essentially unique (see efinition.). This means that for any other mediating morphism H,ϕ,ψ,τ which satisfies analogous equations, there exists a unique isomorphismξ : H H which makes the two mediating morphisms compatible: (E+ I5 ξ)ϕ=ϕ, ψ(f+ I5 ξ )=ψ and Proof. Omitted, see [8, ]. τ (ξ+ I6 )=τ. Examples. First, with the aid of a simple example, we shall demonstrate that it is critical that one fixes a particular isomorphismα : A+ I B+ I3. Indeed, consider the two diagrams in IL(Set) in the first row of Fig. 4; the arrow denotes the cospan id id, while 6
7 o o o The RPO is illustrated in the interior of the diagram. One can compare this blowing up of the outer interface in the RPO with the phenomenon of forking as described by Leifer [, Fig..4]. c a ι d a a a a a o A ι E a b c a, a, a, a, a, a, a, a, d a a o E ι A ι ι B a a b Figure 5. RPO IL(raph) denotes the cospan!, andγ : is the bijection which swaps the two elements. We illustrate the two resulting candidates in the second row of Fig. 4: id is the identity cospan id id, whereas is the cospan id and is the cospan γ. Intuitively, in the first case, the two lower arrows correspond to the same element. Thus the context contains redundant information which can be factored out resulting in a candidate which is just the identity context. onversely, they are different in the second case, meaning that the context has to be kept in the minimal candidate. We shall give one more example with IL(raph) as our category of contexts in order to illustrate some of the effects of allowing non-mono outer interfaces. In the accompanying Fig. 5, we label the nodes of the graphs in order to clarify the action of various graph morphisms, which we leave unlabelled. We also do not draw the -cells as the labelling on the nodes makes these clear. The exterior maps of Fig. 5 correspond to two different ways of decomposing c d a b d a c a ι F o B a b ι 4 Applications In this sections we shall examine some of the applications of Theorem 3. and Algorithm 3.3. ue to space restrictions, we shall concentrate on the application Ehrig and König s rewriting via borrowed contexts and briefly summarise applications to bigraphs and Petri nets. 4. Rewriting via borrowed contexts Our results both shed light on and extend Ehrig and König s rewriting via borrowed contexts [5]. First, we shall show that borrowed contexts correspond to IPOs, and therefore satisfy a universal property. onsequently, the theory of rewriting via borrowed contexts falls within the framework of reactive systems [, 6, 5] and therefore the various congruence properties and constructions carry over. In particular, Ehrig and König s congruence theorem can be seen as an application of the congruence of bisimilarity theorem for reactive systems. Finally, due to the generality of Theorem 3., we relax some of the technical conditions imposed by Ehrig and König and thereby introduce the notion of extended borrowed contexts (efinition 4.7). We begin with a brief account of a variant of doublepushout (PO) graph transformation [4], working at the level of an arbitrary adhesive categorya. efinition 4. (Rewrite Rule). A rewrite rule p is a span L l K r R () ina. No assumptions are made about either l or r. Here L and R represent respectively the left and righthand side of the rule, while K is information which remains unaffected by the rewrite. A redex in an object is identified by matching a rule s left-hand side, which is done via a morphism f : L. efinition 4. (rammar). An grammar is a pair, P whereis a category and P is a set of rewrite rules. A grammar is said to be adhesive whenis adhesive. efinition 4.3 (Rewrite rule application). Object rewrites to with rule p, in symbols p, f, if there exist an object E and morphisms so that the two squares in the Fig. 6 are pushouts. We shall write if there exist p P and f : L such that p, f. 7
8 L f l K r R v g E w Figure 6. Rewrite rule application (PO). Using the conclusion of the third part of Lemma., one can show that in adhesive grammars, the application of leftlinear rewrite rules is functional, so that p, f and p, f implies that (cf. [9]). Any grammar =, P can be seen translated into a reactive system on ospan(). Let denote the empty graph, and the setrcontain for each rewrite rule p () a pair L l K, R h r K. We choose all arrows of ospan() be reactive. Let denote the resulting reaction relation. The translation preserves semantics, as demonstrated by the following lemma, which is similar to a previously published result [6] and can be considered folklore. We use the shorthand to mean that and are cospans with empty inner and outer interfaces. It is crucial for us because it serves as a foundation for relating the theory of PO transformation systems and reactive systems over cospans. Lemma 4.4. iff. In order to apply Theorem 3., we need restrict to graph transformation systems which correspond to reactive systems over input-linear cospans. efinition 4.5 (Input-Linear Rewrite Application). Object rewrites to input-linearly with rule p, in symbols il p, f, if p, f and in addition f, g and h of Fig. 6 are mono. It follows that starting with an adhesive grammar = A, P and an input-linear rewrite relation il, we may construct a corresponding reactive system A over the bicategory of input-linear cospans IL(A). learly, Lemma 4.4 specialises, and thus semantics is preserved. Now, using the construction of RPOs of Theorem 3., we obtain an LTS; let LTS() = LTS(A). Using the congruence theorem for bisimilarity from [6] on such an LTS, we obtain that bisimilarity on LTS() is a congruence. A rewrite rule () is called linear when both l and r are mono. If we restrict our view to PO rewriting systems with linear rewrite rules and input-linear rewrites then we are in a position to compare the resulting LTS with rewriting via borrowed contexts, which requires these extra assumptions. Precisely, given an adhesive grammar = A, P, where P consists of linear rewrite rules, let RB() be the LTS o J L l r I R () ǫ () ι (3) ǫ + σ θ H (4) ι F σ F (5) K o Figure 7. Borrowed context. derived via rewriting with borrowed contexts as defined in [5]. Recall that the states of RB() are graphs with a mono outer interface. The transitions are labelled by mono cospans of graphs; there is a transition o H o H precisely when there exists a diagram as illustrated in Fig. 7 with all arrows mono, L l r I R P, regions ( 4) pushouts and region (5) a pullback. Theorem 4.6. LTS() = RB(). Proof. The proof consists of showing that borrowed contexts correspond to contexts obtained from IPOs. From borrowed contexts to IPOs. iven a borrowed context diagram as illustrated in Fig. 7, we shall show that one may construct a IPO (i). F J K α (i) L I σ θ F ιf K o F K F σ + + (ii) σ Assume without loss of generality that L+ I = +. Let α : F+ J + be the unique isomorphism such that αi i =σ : F + andαi =ǫ : +. Since square () of Fig. 7 is a pushout of monos and we are in an adhesive category, it is also a pullback (Lemma.). This implies that L = +. The cube which results from an application of Algorithm 3.3 is illustrated in (ii), in the construction we use only the fact that square (5) of Fig. 7 is a pullback. Thus, the RPO of redex square (i) is K, F,, id, id, id,α, meaning that it is a IPO. From IPOs to borrowed contexts. Suppose that ιf H o H is a transition in LTS(). then F ι F must be a part of an IPO diagram. Since every IPO can be constructed as a RPO, we have a redex diagram as σ o 8
9 L L (v) ǫ F Y ǫ γ δ F I 5 β L (iii) o I 5 F σ (vi) Y σ o i o R R θ H i F ǫ (vii) (iv) F Y σ θ o L L i ǫ (viii) the outside of diagram (iii), with L o L, R o R being a reaction rule, corresponding via the translation of Lemma 4.4 o L o R to the rewrite rule L R. The candidate I 5, F,,,β,γ,δ illustrated is the RPO obtained via the construction of Algorithm 3.3. We also have H o H o i R o R, which in other words means that diagram (iv) is a pushout with o H : I 5 H equal toθ o. Recall that from the construction, we have that diagram (v) is a pushout, diagram (vi) is a pullback, diagrams (vii) and (v) are pushouts. iagrams (iv) through to (viii) paste together to give the required borrowed context. We end this section with an extension of borrowed contexts suggested by the linearity conditions imposed in the construction of Algorithm 3.3. efinition 4.7 (Extended Borrowed ontexts). iven an adhesive grammar =, P with an arbitrary set of rules P, we shall construct a labelled transition system with: States: raphs with outer interfaces, J o is arbitrary; Y σ o where Transitions: ospans of graphs J ι F F K where ι F is mono and is arbitrary. We derive a transition ιf H o H if there exists a commutative diagram as in Fig. 7, where (), (), (3) and (4) are pushouts, while square (5) is a pullback. The indicated morphisms are assumed to be mono, the others are arbitrary. As a corollary of the translation between borrowed contexts and IPOs of Theorem 4.6 and the congruence we have that bisimilarity on the labelled transition system resulting from efinition 4.7 is a congruence with respect to arbitrary input-linear graph contexts. 4. Bigraphs and Petri nets Bigraphs are a graphical formalism originally introduced by Milner [3] in order model dynamic systems with independent locality and connectivity structures [7]. Bigraphs can be seen as output-linear cospans over a certain adhesive category, as we discuss below. It follows that by considering an input-linear variant a model which yet incorporates many of bigraphs fundamental features we meet the requirements of our framework. Using Algorithm 3.3, we are then able to derive an LTS for any reactive system on such bigraphical structures. Such an LTS coincides with Milner s on the bigraphs in the intersection of the respective definitions. Here we offer only a brief discussion, the reader is referred to [8, ] for details. We introduce the adhesive category of place-link graphs, which can be considered bigraphs without interfaces. Interfaces will be handled by considering the bicategory of cospans over such category. Fixed an alphabet of controls Σ, we define a place-graph to be a directed graph with nodes labelled overσ. Here edges represent (a generalisation of) the nesting of locations. The connectivity of each K Σ is determined by an arity function ar :Σ N,so that K has ports numbered,..., ar(k). By set of ports of we indicate the disjoint union of all the ports associated to all the nodes of. efinition 4.8 (Place-Link raphs). A place-link (pl) graph is a place-graph together with a link map l: P S, where P is the set of ports of. The role of l and S is to jointly describe the connections between ports. A place-link (pl) morphism is a graph morphism which preserve node labels and port connections. Let PLraph Σ be the category of pl-graphs and pl-graph morphisms over Σ. It is easy to construct a categoryx Σ so that PLraph Σ is a presheaf category Set X Σ and, as such, is adhesive. We can then conclude as follows. orollary 4.9. IL(PLraph Σ ) has RPOs, calculated using Algorithm 3.3. There are two aspects of our bicategory of pl-graphs that generalise the theory of bigraphs. Firstly, interfaces here need not be discrete, i.e., specify just nodes to be merged and ports to be connected, but allow for more complex forms of composition. Secondly, place graphs are usually forests of trees, and their input (resp. output) interfaces reach only leaves (resp. roots), while we allow all directed graphs. One can, however, prove that orollary 4.9 remains valid when the arrows of IL(PLraph Σ ) are restricted to such bigraphs. The main difference with bigraphs remains the inputvs output-linearity issue, which has the interesting effect of banning name aliasing in respectively the inner and the 9
10 outer interface. We leave a deeper analysis of this dichotomy as future work. Petri nets provide another application of our framework, described in [7]. The model consists of adding an elementary notion of interface to Petri nets, similarly to other proposals in the literature, as e.g. [, 4]. Specifically, we equip each net with two ordered subsets of places: the inner and the outer interface. This, together with morphisms that respect net topologies and interfaces, yields a bicategory INet, which can easily be recast in terms of cospans over an adhesive category. Formally, let MNet be the category of marked Petri nets and structure-preserving homomorphisms. As MNet is adhesive, we have the following result, where RPOs are calculated via Algorithm 3.3. orollary 4.. IL(MNet) has RPOs, INet consists of the linear cospans with discrete interfaces in IL(MNet) and, once again, the existence of R- POs is not affected by this restriction. Then, considering the usual Petri token game as a reactive system over INet, we automatically derive an LTS for Petri nets with interfaces over which bisimulation is congruence. As it turns out, such a bisimulation admits a very simple characterisation consisting of only three kinds of transitions: p τ p, if p results from p through an internal firing; p +i p if p results from p by adding a token at its ith outer place; and p i p if p results from p by removing a token from its ith outer place. We remark that this is the same bisimulation as derived by Milner using a bigraphbased representation of Petri nets with interfaces [4]. 5 onclusion We have constructed groupoidal relative pushouts (RPOs) in a general framework of generalised contexts and interfaces, represented by cospan bicategories over adhesive categories. This allows us to systematically derive a compositional semantics for each reactive system in the framework, in the form of a LTS determining a bisimulation congruence. We have shown in detail how Ehrig and König s rewriting via borrowed contexts [5] falls within the framework and can be obtained as an application of our theory, and mentioned two others, a variant of Milner s bigraphs and a compositional approach to Petri nets [7]. As future work, we plan to investigate conditions under which a general construction of RPOs exist for outputlinear cospan bicategories. Acknowledgements. The authors would like to thank Vincent anos and the anonymous referees for their helpful comments. References [] P. Baldan, A. orradini, H. Ehrig, and R. Heckel. ompositional modeling of reactive systems using open nets. In ONUR, volume 54 of LNS. Springer,. [] J. Bénabou. Introduction to bicategories. In Midwest ategory Seminar, volume 4 of LNM, pages 77. Springer, 967. [3]. Berry and. Boudol. The chemical abstract machine. Theoretical omputer Science, 96:7 48, 99. [4] H. Ehrig,. Engels, H.-J. Kreowski, U. Montanari, and. Rozenberg, editors. raph rammars and omputing by raph Transformation, Vol. -3. World Scientific, 999. [5] H. Ehrig and B. König. eriving bisimulation congruences in the PO approach to graph rewriting. In FOSSAS 4, volume 987 of LNS, pages Springer, 4. [6] F. adducci and R. Heckel. An inductive view of graph transformation. In WAT 97, pages 3 37, 997. [7] O. H. Jensen and R. Milner. Bigraphs and mobile processes. Technical Report 57, University of ambridge, 3. [8] P. Katis, N. Sabadini, and R. F.. Walters. Bicategories of processes. J. Pure Appl. Algebra, 5:4 78, 997. [9] S. Lack and P. Sobociński. Adhesive categories. In FOS- SAS 4, volume 987 of LNS. Springer, 4. [] J. Leifer. Operational congruences for reactive systems. Phd thesis, University of ambridge,. [] J. Leifer and R. Milner. eriving bisimulation congruences for reactive systems. In ONUR, volume 877 of LNS, pages Springer,. [] S. MacLane and R. Paré. oherence for bicategories and indexed categories. J. Pure Appl. Algebra, pages 59 8, 985. [3] R. Milner. Bigraphical reactive systems. In oncur, volume 54 of LNS, pages Springer,. [4] R. Milner. Bigraphs for Petri nets. In Lectures on oncurrency and Petri Nets 3, volume 398 of LNS, pages Springer, 4. [5] V. Sassone and P. Sobociński. eriving bisimulation congruences: -categories vs precategories. In FOSSAS 3, volume 6 of LNS. Springer, 3. Full version to appear in Theor. omp. Sci. [6] V. Sassone and P. Sobociński. eriving bisimulation congruences using -categories. Nord. J. omput., ():63 83, 3. [7] V. Sassone and P. Sobociński. A congruence for Petri nets. In Workshop on Petri Nets and raph Transformation, 4. Available at the authors web pages. [8] V. Sassone and P. Sobociński. ongruences for contextual graph-rewriting. Technical Report RS-4, BRIS, 4. [9] P. Sewell. From rewrite rules to bisimulation congruences. Theoretical omputer Science, 74( ):83 3,. [] P. Sobociński. eriving process congruences from reaction rules. Ph thesis, BRIS, University of Aarhus, 4.
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text: Remember the last time when we told you how to prep up for the sale season and how to get the best out the numerous sales? Well, today, we have tried to make your lives a little bit easier by scouting some of the amazing sales online and compiling a list of pieces that you should be adding to your cart right now. Ready, set, go!


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Journal of Multilingual Education Research (JMER) is the official journal of the New York State Association for Bilingual Education. Its distinct orientation reflects what is most important to researchers, specialists, and educators in the fields of multilingualism and multilingual education. JMER is a vehicle to disseminate changes and growth of knowledge in a variety of national language education issues that have local and regional relevance. It responds to the emerging needs and interests of teachers, administrators, teacher educators, researchers, counselors, psychologists, advocates, and community leaders whose work focuses on the successful education of multilingual students.
Current Volume: Volume 6 (2015) Bilingual Special Education: Exploring Pedagogical, Research, and Policy ImplicationsImplementing effective practices to address the needs of culturally and linguistically diverse learners with disabilities in Pre K-12 schools is a challenge for many educators and school systems. However, developing effective and efficient practices in a multilingual classroom creates opportunities for a 21st century teacher to be a major catalyst for social change.
Current Bilingual Special Education demands comprehensive understanding of various key issues including, but not limited to: the nature of diversity in special education and distinguishing between language differences and disorders; bridging schools with special education programs and the multilingual families and community of the students they serve; strategic methods to support multilingual learners as a way to preventing under- and over-representation in special education; and special education within an international context.
Given these knowledge needs, the overarching theme of JMER's special themed issue on bilingual special education is: Exploring the pedagogical, research, and policy implications of the most current research in bilingual special education for this field in the 21st century.
This issue of JMER focuses on bilingual special education, an educational field that works with students from diverse culturally and linguistically diverse backgrounds with special needs.
Front Matter
Bilingual Special Education: Investigating and Implementing Evidence-Based Practices in Schools
Diane Rodríguez
Articles on Theory and Research
Reframing Venerable Standpoints about Language and Learning Differences: The Need for Research on the Literate Lives of Latina/o Language Minority Students
Taucia González and Alfredo J. Artiles
Trends and Issues in Bilingual Special Education Teacher Preparation: A Literature Review
Peishi Wang and Sara B. Woolf
Survey of Educator Attitude Regarding Inclusive Education within a Southern Arizona School District
Bradford Harkins and Todd Fletcher
Understanding parental engagement in Hispanic mothers of children with autism spectrum disorder: Application of a process-model of cultural competence
Elizabeth Ijalba
Disentangling Language Differences from Disability: A Case Study of District-Preservice Collaboration
Julie Esparza Brown and Phyllis Campbell Ault
Article on Practice
Dual Language Program Meets Integrated Collaborative Teaching
Bethany Hatheway, Deborah Shea, and Monica Winslow
Book/Multimedia Review
English Language Learners: Differentiating Between Language Acquisition and Learning Disabilities
Patricia Martínez- Álvarez
Notes on Contributors to This Issue
Diane Rodríguez


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Choosing life insurance is just like making any other financial decision. Typically, you will find that taking time to make the right decision will generally yield better results than if you make an uninformed quick decision. As they say, "If you are going to do it, you should really do it right."
Here are some questions you might want to ask yourself before committing to buying life insurance.
They can help to ensure you not only choose the right life insurance product, but they may also save you some money too!
How much coverage do I need?
Finding out how much cover you need is the key to getting the right level of life insurance. There is a remarkable number of people out there who are either under-insured or over-insured. Being under-insured means you won't have enough coverage should you need to make a claim, and being over-insured means you are probably paying too much.
Use an online calculator to give you a rough idea of how much coverage you need, or speak to a financial adviser or insurance expert for advice.
What kind of policy is right for me?
With life insurance, there is not just one single option. Instead, there are many different products out there. From accidental death insurance, to income protection insurance, to funeral insurance, and much more. Do some research to find out what different products are on offer, and work out which one is best for you.
Bear in mind that some insurance providers will let you tailor your policy, allowing you to get the most suitable policy at the most suitable price.
How do I choose an insurance provider that is right for me?
There are many different providers out there, and it can be difficult choosing the right one. Again, do some research and find out what you can about the insurer. Read independent online reviews, and find out what other people think. Try to choose an insurer that has an "A" rating or higher.
Where can I find the best deals?
Many people start their search for life insurance online on comparison websites. This can be a useful place to start, as you can compare multiple options in one place at the same time. Be aware of the comparison criteria used on the website, and also remember that the price given will usually be an estimate, and not what you will actually pay.
What do I do once I have a shortlist?
Once you have checked out all the options online and made a shortlist of policies you like, it's time to get down to the nitty gritty. This is the time to make more thorough comparisons, and to find out more information about each policy. Read the small print to find out if there are any exclusions that may affect you, or anything in the policy that shows it is not as good as it seems.
How can I save money?
When you're looking at life insurance options, be sure to check for any special offers. Some providers offer a certain amount of cash back if no claims are made within a certain time. Others may offer a discount for buying online. Some may offer one or two months free each year. Just be sure to choose a policy that is right for you – don't choose one just because it has a great offer but not-so-great insurance.
How can I reduce my premiums?
One of the best ways to reduce your premiums is to get healthy! You can quit smoking, cut down on alcohol, do more exercise, or reduce your cholesterol or blood pressure if they are high. Becoming more healthy can have a huge effect on your premiums, and can save you a huge amount of money over the life of the policy.
What is the best payment option?
Insurers often offer different payment options. You may find that making annual payments will be cheaper than monthly payments, but it will really depend on whether you can afford to pay a large sum up front, or you want to spread the cost throughout the year.
Do I need to review my life insurance once I have it?
Reviewing your life insurance regularly is one of the most effective ways to save money, and also to make sure your policy still suits your lifestyle. Try to review your life insurance annually, and also when your lifestyle changes significantly – such as, having a child.
How about you all? What strategies/methods do you use to 1) find the best life insurance policy and 2) ensure you are saving the most money?
Share your experiences by commenting below!
***Photo courtesy of http://www.flickr.com/photos/diggersf/709831439/


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Hollywood 1324; ca. 1937; One piece frock features front closing with slide fastener or buttons and loops. High or low neck and simulated welt pockets. Front skirt panel in one with blouse section. Skirt may have plain gored back or a full back shirred at waistline. Long or short sleeves.
Featured in Hollywood Patterns, April 1937
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