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OTTAWA – The Harper government has been handed a lesson in why those who live in glass houses shouldn't throw stones.
Conservatives have been trying to deflect attention from the Senate expenses scandal by accusing opposition parties of ethical lapses of their own — including the fact that two New Democrat MPs have admitted they owe back taxes.
But it's now emerged that one of Stephen Harper's former top advisers also had tax troubles while he was working in the Prime Minister's Office.
Documents filed in court in Gatineau, Que., show that Dimitri Soudas received repeated notices from May 2008 to April 2011 that he owed Revenu Quebec $67,467 in back taxes, including interest.
The matter was finally settled following a court order in March 2012.
Soudas, Harper's former communications director, says the back taxes were the result of clerical errors in filling out his 2008 and 2009 tax forms and — while it took some time to sort out, including a challenge on the interest Revenu Quebec charged — he insists he has never tried to avoid paying his taxes.
"I believe that no tax is a good tax but … I have always paid my taxes. I have never refused to pay my taxes," he said in an interview Friday.
Soudas said his situation is entirely different from that of NDP MPs Tyrone Benskin and Hoang Mai, who "actually failed to pay their taxes to the point that their salaries may be garnished."
Despite Soudas's trouble, Conservative MPs continued Friday to raise the NDP's alleged tax evasion as a way to deflect opposition questions about Harper's former chief of staff's decision to personally pay the $90,000 tab for invalid expense claims racked up by Sen. Mike Duffy.
They maintained Harper has dealt more swiftly and decisively with the scandal than NDP Leader Tom Mulcair has dealt with the tax evaders in his midst.
"By contrast, the leader of the NDP has been aware of two of his senior critics trying to avoid their taxes," Pierre Poilievre, the government's designated hitter on the Senate scandal, told the Commons.
"One of them (Benskin) is the heritage critic who attempted to introduce a private member's bill that would absolve him from his tax liability. The other (Mai), amazingly, was his revenue critic. That is not the kind of leadership Canadians expect."
Mulcair stripped Benskin and Mai of their critic responsibilities when news of their back taxes broke. Both MPs have promised to pay the money owed.
The Conservative attacks were blunted, however, by the knowledge that one of their own has also owed back taxes in the past.
"How is this possible when PMO staff have taxes deducted at source?" wondered Liberal MP Hedy Fry.
"Did Mr. Soudas have a side deal like Mr. Duffy to get extra income from the Conservative party? Just what is going on in the PMO?"
Fry got no answers to her questions in the Commons. Soudas later said he had only one source of income during his years working for Harper.
Outside the Commons, opposition MPs accused the Tories of hypocrisy.
"People who live in glass houses shouldn't throw stones," said Liberal MP Marc Garneau.
"And I hope that the Conservatives will be a little more modest in the House of Commons in their attacks against the NDP for not paying their taxes because it's very, very clear that they're not angels themselves."
New Democrat Mathieu Ravignat accused the Conservatives of a double standard that he described as "kind of sad."
"It just underlines the hypocrisy of this government by bringing up taxes when, on their side, it is (also) an issue," he said.
"I think that what we need to do is refocus. The fact is that there's a lack of leadership going on, on this (Senate) issue. We need to do something to clean up the Senate. We need to know this scandal goes all the way into the Prime Minister's Office.
"We need the details."


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Lawyer for Phil Spector's wife calls divorce heartbreaking
An attorney for Phil Spector's wife called a divorce filing by the imprisoned music producer heartbreakingly bizarre and said she has provided the best possible care for him.
Attorney Aaron Abramowitz wrote in a statement Tuesday that Rachelle Spector has been devoted to her husband and has been providing him support and the best possible care while he is incarcerated.
"This whole situation is heartbreakingly bizarre," Abramowitz wrote. "It is regrettable that Mr. Spector has failed to recognize the efforts made by Rachelle in spending tens of thousands of dollars on his medical and dental costs while incarcerated."
Court records in Stockton, California, show Spector filed for divorce on March 18. A copy of his filing, which was first reported by celebrity website TMZ, was not immediately available.
Spector, 75, is housed at a prison facility in Stockton that provides medical and mental health care to the state's sickest inmates, including those with chronic conditions.
He is famous for revolutionizing rock music with his "Wall of Sound" that merged beautiful vocal harmonies with lavish orchestral arrangements to produce such pop hits as "Da Doo Ron Ron," `'Be My Baby," "He's a Rebel" and the Righteous Brothers' version of "You've Lost that Loving Feeling."
Abramowitz said Rachelle Spector obtained her pilots license to make it easier to visit her husband.
The Spectors met at a Hollywood restaurant in 2003, shortly after he was arrested in the shooting death of Lana Clarkson. The producer was later convicted of killing Clarkson and is serving sentence of 19 years to life.
The pair married in 2006, and Rachelle Spector has been running her husband's businesses while he is imprisoned. She also obtained a private investigator license to assist with her husband's appeal of the conviction.
Phil Spector's attorney, John H. McKinley, had no immediate comment on Abramowitz's statement Tuesday.
(Copyright 2016 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.)

subset: commoncrawl


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Milwaukee, WI
Hunzinger Construction performed a complete gut and remodel job for Madison Medical Affiliates downtown Milwaukee location. The new medical center was built in the northwest corner of an occupied office building and spanned two floors. The new medical center features extremely high-end finishes including wood columns, feature walls, crown molding, wood floors, custom cabinets, base, trim and doors. Custom handmade lighting and elaborate wood trimmed vestibule glass was also installed. The medical center features 6 private physicians' offices, 13 exam rooms, 2 nurses' stations, 2 reception areas joined by a unique stairway leading from floor 1 to floor 2, 2 clerical offices and open office space on the 1st floor.


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Pasta La Vista!June 1, 2013 at 7:42 pm | Posted in cooking, food, Recipe | Leave a comment
Tags: cheese, Food, Leftovers, Omelette, Pasta, Peas, Recipe
I've bored you with my bizarre pasta omelettes on a previous occasion, but hey, we all need reminding from time to time about weird eating experiences.
It's simple: snip up your fridge-cold leftover pasta (tagliatelle on this occasion for me) using scissors, à la Nigella, mix it with eggs (say 1 per 25g pasta) and season (add dried/ fresh herbs if you wish). The lower the heat level you use, and the slower you cook your omelette, the better the result.
I also had a hankering last night for a sort of sophisticated mushy peas, the sort of consistency Hugh Fearnley Poshboy might call 'smashed'. So I grabbed my stash out the freezer (everyone should always have frozen peas), boiled them up, mashed them slightly and mixed them with grated cheese. Nursery food at its finest.
Spaghetti OmeletteMay 14, 2012 at 11:37 am | Posted in cooking, food, Recipe | Leave a comment
Tags: Dinner, Pasta, Recipe
So you're thinking, 'What??? Spaghetti omelette?'. Admittedly, it sounds bizarre, but it's really not so far removed a concept from Spanish omelette, which I love. And if you're anything as bad at spaghestimating as I am (say, making enough pasta to feed 10 Alsatians & a Jack Russell), then this is the recipe for you.
1) Remove your pan of congealed spaghetti from the fridge. Snip the spaghetti up into 1cm chunks. This is essential: you will be able to mix your eggs into the pasta much more easily.
2) Add eggs: I went for 4. I would say 2 per 50g spaghetti is about right.
3) Add some vegetables/herbs. I'm being annoyingly vague, because it really is up to you. I'm not going to tell you to add onions if you detest them. I only added some fresh oregano and fresh ripped basil (ripping releases the flavour better than tearing), as my spaghetti was a courgette and basil carbonara in its first life.
3) Pour the mixture into an oiled pan and cook on medium until the base is firm and a good even cover. This will really depend on how much pasta you have: I had about 150-200g (cooked weight) and it took 20 minutes.
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text:
Marketing Strategy, With A Twist of Rebellion
At Marketing Doctor, we are strategic, passionate and influential. We will bring these attributes to our work with you and we know you will find our expertise and passion highly valuable.
Analytical Marketing, With Flair
The marketplace is filled with run of the mill advertising. Status quo, safe, predictable marketing, created by a perfectly nice team of professionals who have been doing the same thing for years. At Marketing Doctor, we push back on predictable, choosing instead to expand the boundaries of what is possible.
Your advertising is serious business.
But in order to make an impression,
it also needs to be lively and memorable.
In our world, and for our clients, run of the mill just isn't good enough.
Brilliant Marketing Minds + Best Practices
We specialize in striking the perfect balance between data-driven insights and creative design ideas. From this place of confident synergy, we'll create successful media campaigns for your business. Utilizing our continuing education in progressive marketing techniques and best practices, we will provide you with peace of mind, and the knowledge that you're in capable hands.
We Stand By Our Promise
You won't think twice about working with Marketing Doctor. By following the industry standard best practices, and integrating our knack for creating breathtaking campaigns, we ensure you'll see results and a quantitative ROI.
Trust us. We're the best in the business, and you will be too.


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41 Old Frankfort Way
Frankfort, IL 60423
Ambrosino's Italian Market & Deli
20495 S La Grange Rd Frankfort, IL
The Galway Tribes Irish Pub & Restaurant
9680 Lincolnway Ln Frankfort, IL
I take my girlfriend here every once in a while to enjoy a hassle-free breakfast. We never wait and always have a good meal. Portions are huge, too, so you will get your money's worth.5
Always have a great experience here. The food is great, I never have to wait, and the staff is very prompt. I definitely recommend to anyone who likes a classic breakfast experience.5


text:
Document Type:PRESOL
Posted Date:Aug 29, 2017
Maintenance Repair Shop Equipment
Set Aside:N/A
Department of the Navy, Naval Sea Systems Command, NUWC Keyport Division, 610 Dowell Street, Keyport, Washington, 98345-7610, United States
Sole Source Justification (redacted) RFQ N0025317Q0314 Naval Undersea Warfare Center Division Keyport intends to solicit and negotiate with only one source in accordance with FAR 13.106-1(b) (1). A firm fixed priced contract will be issued to Stratasys, Inc., or their authorized dealers, for FORTUS 900mc upgrades. This requirement is being issued as a combined synopsis/solicitation for commercial Items in accordance with FAR 12.6, as supplemented with additional information included in the attached solicitation. This announcement constitutes the only solicitation. The Defense Priorities and Allocations System (DPAS) applicable assigned rating for this requirement is DO-C9. The solicitation number issued as a request for quotation (RFQ) is N0025317Q0314 and is attached to this announcement. Provisions and clauses in effect through the latest Federal Acquisition Regulations are included in the attached solicitation. The applicable NAICS code for this requirement is 334419 and has a size standard of 750 employees or less. The government prefers FOB Destination pricing to NUWC Keyport, WA 98345-7610. Requirements and evaluation procedures are listed in the attached solicitation. This solicitation is required to be completely filled out and returned before the solicitation closes. Questions should be submitted via e-mail to: email@example.com or faxed to (360) 396-7036. No paper copies will be mailed. Failure to respond to this RFQ and associated amendments if applicable prior to the closing date and time established may render an offer non-responsive and result in rejection. To access the clauses/provisions to be completed, the Federal Acquisition Regulations (FAR) are available for download at http://www.acquisition.gov/far or download the FAR and Defense Federal Acquisition Regulations (DFARS) at: http://farsite.hill.af.mil. Offerors are also advised that these representations and certifications can be completed electronically via the SAM website at https://www.sam.gov
POC Jennifer L. Calkins, Phone: 3603153830
Link: FBO.gov Permalink


text:
WaterSafe Auckland services many universities in the Auckland area, delivering professional development at an undergraduate and postgraduate level, primarily for pre-service teachers.
WaterSafe Auckland can also provide aquatic education, training and practical experience for staff and managers of other tertiary institutions. For more information contact: Operations Manager, James Lea firstname.lastname@example.com
Extensive range of FREE resources to help you keep yourself and others safer in, on and around water.
If you'd like more information, resources or like to discuss your specific needs we'd love to hear from you.
Copyright © Drowning Prevention Auckland | Website Design by Quentosity | Web + Creativity x Genius


text:
International Paper Posts Loss
International Paper Co. swung to a first-quarter loss on a plant-shutdown charge as higher costs pressured margins.
"We started the quarter with an extreme run-up in fiber costs in North America, but ended with costs peaking in March and now moderating," said Chairman and Chief Executive John Faraci.
The paper-and-pulp company...


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2018-09-14 (5 Days Old)Total Views: 17 | Last 7 Days: 4
MUMBAI - Dadarao Bilhore smoothes the road surface, rests his shovel, looks to the sky and prays for his son, one of thousands of Indians killed every year in accidents caused by potholes.
FOX: What happened to $400G in GoFundMe cash? That will be made 'crystal clear,' New Jersey man says
FOX: Gregg Jarrett: If Rod Rosenstein defies Trump's order to declassify documents, he should be fired
FOX: What happened to $400G in GoFundMe cash? That will be made 'crystal clear,' New Jersey man says
Los Angeles Times: Six months after Stephon Clark's death, Black Lives Matter protesters climb into makeshift coffins outside police conference
Daily Mail: Video: Who is the current Premier League top scorer?
Daily Mail: Love Island's Wes Nelson steps out amid claims he will join Dancing on Ice line-up
Daily Mail: COLUMN-Nickel's "electric premium" crushed by trade...
Daily Mail: Oil prices fall amid surprise growth in U.S. crude stocks
Daily Mail: Sydney hotel evacuated after chemical leak
Daily Mail: Thugs kick Pomeranian puppy to death during walk in the park in 'disgusting, unacceptable' attack
NBC New York: Westchester Mom Accused of Killing Tot Appears in Court
NBC New York: Bodega Owner Fights Off Robber
NBC New York: What to Do If You Hit a Pothole
NBC New York: Woman Drives Over 2 NJ Airport Runways
NBC New York: NJ AG Says Cop Among Child Predators Snared in Sting
NBC New York: Cuomo Kicks Off General Election Campaign
CTV News: City council agrees on no smoking, cannabis use 10 metres within entrances
Reuters: Mexico's next anti-money laundering czar vows action after 'shameful' Odebrecht
FOX: California jury: Career criminal guilty of killing 2 teens
FOX: California jury: Career criminal guilty of killing 2 teens
CNN: NHL: How the sport plans to grow in China ahead of 2022 Winter Olympics
CNN: Authorities: Agent confesses to killings
CNN: Ford wants FBI investigation before testifying


text:
A Better ToiletFor A Cleaner World
Prototype Update, 17 November 2016
Ahmedabad, India
At the prototype site at CEPT University in Ahmedabad, we successfully ran 8 cycles of the drying unit processing real solid materials (human feces).
The photo below illustrates the results of the effective drying process. The end product that you see is a batch of "chips" that will be used as fuel in our combustion system.
North Carolina, United States
We also continue to test, develop, and refine our drying unit back in the US (in our testing lab at RTI International). As in Ahmedabad, we also use real solid materials in our tests.
This parallel testing and refinement of our system, allows us to adapt to any changes or obstacles we encounter during "real world" use.
Below, you can a view a video of our lab unit's automated drying cycle completing, and then restarting. There are also pictures of the resultant "chips", awaiting combustion.


text:
They always say that actions speak louder than words. But with spoken word pieces this powerful, we'd have to disagree.
Prince EA: Thinking about the end of the world is a bit scary. But not for Poet Prince EA, who draws awareness to many of the threats we face today in a society that has become consumed by technology and keeping up with the status quo. His pieces make you think, which is good since his primary mission is to create content with purpose, allowing listeners to recognize "the power, peace and equanimity within themselves."
Antix: A talented lyricist with an ear for a good beat, Antix (né Alexander Nimier) creates pieces often classified as rap and hip-hop. But there's so much more than meets the eye (and ear). His velvet voice backed my solemn cello strokes reveal a rising master wordsmith. "Once upon a time I knew a girl named Esmerelda." He pauses, "And I killed her when I told her that I never really felt her. She looked at me and smiled, and then she blew into the mist. And became one of those stories that don't really have no gist."
Marshall Davis Jones: A National Slam Team finalist and champion, Marshall Davis Jones draws inspiration from "one dark Friday night back in 2006," standing atop the Brooklyn Bridge and feeling as if he had "nothing left to contribute." Since that lonely night, he uses the art of spoken word to "heal and perhaps, make my life more meaningful," dedicating his life to "building bridges and bridging worlds, so that others may do the same."
[h/t Copywriting: Britt Feder]


text:
Thursday, March 15, 2012
Blogging Break
After an insightful email from my future-sister-in-law and, most importantly, after a long talk with my Hubby-Man, I have decided that I need to put blogging on the back burner and get some other things balanced better during my free time instead.
I also think we are going to put a pause on tot schooling because the planning/prep is taking up so much of my free time as well. And Boogie isn't enjoying it enough to justify the time I am putting into it. We will still do planned things if I find something he will really love, but I am not going to do any one thing on a regular basis. Except play at the train table, apparently :)
I hope I will be able to bounce on from time to time and share what the boys are doing, but I am not going to commit to link parties, weekly wrap up posts, or regular features at the moment. If I scheduled you for Lesson Learned, I would still love to publish your post! I just wont be scheduling any additional posts for awhile.
I will still be pinning, since I do that from my phone when Boogie is asleep while Bam Bam nurses, so please feel free to follow me on Pinterest. And, I will still be available through email if you would like to say hi :)
There are a couple other ideas I was going to post so I might get those up in the next couple days. If not, I will see you when I post the next Lesson Learned on Sunday!
18 comments:
I will miss you, but I totally understand. Hope you come back soon!ReplyDeleteReplies
Thank you, Amanda! As you can see, I haven't totally disappeared, but I have definitely cut back. I love seeing all the things you and J are up to when I blog browse on my phone. It is hard to comment on a smart phone, but know that I am thinking about how awesome you are every time you post :)Delete
Balance is so important and you have to do what is best for your family. I enjoy your pins on Pinterest, so I'll still be following.ReplyDelete
Thank you, Jen! You are so right. Balance isn't easy sometimes. I would rather be blogging than cooking and cleaning! But it blesses my husband and children when the house is clean and there is a thoughtful meal on the table. So, I have to do my best.Delete
I agree with the other ladies here! I will miss you in blogger world, but I completely understand! Life is too short to not enjoy your precious family. Balance is so very important too. Take care of YOU and YOURS! Hugs!!!ReplyDeleteReplies
Thanks, Trina! Life is definitely too short to spend on the computer and these little ones don't stay little for long. I hope I can continue to come on and share things and I want to be able to comment more, too. I love the community and miss it.Delete
Enjoy your break Sierra and I hope you come back soon!! I'll miss you, but TOTALLY understand the need for a blogging break! "See" you in pinterest!ReplyDeleteReplies
Thanks, Katie! I'll miss you, too, but will still be reading your posts and enjoying them! :)Delete
I agree with everyone else! You have a wonderful blog, but your kids are only little once--I'll still "see" you around!ReplyDeleteReplies
Thank you, Carla! They grow so fast!Delete
I will miss you too, but we understand you're doing what's best for your family!ReplyDeleteReplies
Thank you for the encouragement, Brittney. I loved following your rainbow muffin tin meals!Delete
Yes we will miss you but I so understand, life goes by fast and this is our chance.ReplyDeleteReplies
Thank you for your support, Sandra!Delete
Hope that you are just needing space to chill and its nothing more serious. will miss you.ReplyDeleteReplies
Thank you for being concerned! There has been A LOT going on here, some of it not as chill as I would like, but we are getting through one day at a time. You are so sweet. I love all the things you have been doing on your blog to grow it recently!Delete
I can so relate! Hope you enjoy your breakReplyDelete
Jada roo can do blogReplies
I'm sure you can, Andrea! Enjoy having two little ones! Gage is adorable!Delete
Thank you for commenting! I try to reply to every comment either by using the reply function (so please subscribe to the comment thread or check back) or email (if you are a "no-reply blogger", it is an easy change).
Have a great day!


text:
I just wanted to say THANK YOU for being such a wonderful company. I ordered a customized Rubix cube for my boyfriend from your website and I was...Read More ->
Thank you, thank you, thank you!!!!!
Saturday, December 17, 2011
I just wanted to let you know what a wonderful experience I have had dealing with you! From the time I ordered the first blanket to when I received the second blanket I ordered, I have been overwhelmed with your very quick and very nice replies, your flexibility in terms of changing the photo proofs even just a little bit. And the end result of both blankets is AMAZING!!!!!
And the quality of both the very plush blanket material and the photos/text are so high. I can't until my daughters open them on Xmas - they will love them!!! Thank you, thank you, thank you!!!!!


text:
Mercurial > cpdt > repo
view src/StackMachine.v @ 205:f05514cc6c0d
'make doc' works with 8.2
|Adam Chlipala <email@example.com>
|Fri, 06 Nov 2009 12:15:05 -0500
line wrap: on
line source
(* Copyright (c) 2008, Adam Chlipala * * This work is licensed under a * Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 * Unported License. * The license text is available at: * http://creativecommons.org/licenses/by-nc-nd/3.0/ *) (* begin hide *) Require Import List. Require Import Tactics. Set Implicit Arguments. (* end hide *) (** %\chapter{Some Quick Examples}% *) (** I will start off by jumping right in to a fully-worked set of examples, building certified compilers from increasingly complicated source languages to stack machines. We will meet a few useful tactics and see how they can be used in manual proofs, and we will also see how easily these proofs can be automated instead. I assume that you have installed Coq and Proof General. The code in this book is tested with Coq version 8.1pl3, though parts may work with other versions. As always, you can step through the source file %\texttt{%#<tt>#StackMachine.v#</tt>#%}% for this chapter interactively in Proof General. Alternatively, to get a feel for the whole lifecycle of creating a Coq development, you can enter the pieces of source code in this chapter in a new %\texttt{%#<tt>#.v#</tt>#%}% file in an Emacs buffer. If you do the latter, include a line [Require Import List Tactics.] at the start of the file, to match some code hidden in this rendering of the chapter source, and be sure to run the Coq binary %\texttt{%#<tt>#coqtop#</tt>#%}% with the command-line argument %\texttt{%#<tt>#-I SRC#</tt>#%}%, where %\texttt{%#<tt>#SRC#</tt>#%}% is the path to a directory containing the source for this book. In either case, you will need to run %\texttt{%#<tt>#make#</tt>#%}% in the root directory of the source distribution for the book before getting started. If you have installed Proof General properly, it should start automatically when you visit a %\texttt{%#<tt>#.v#</tt>#%}% buffer in Emacs. There are some minor headaches associated with getting Proof General to pass the proper command line arguments to the %\texttt{%#<tt>#coqtop#</tt>#%}% program. The best way to add settings that will be shared by many source files is to add a custom variable setting to your %\texttt{%#<tt>#.emacs#</tt>#%}% file, like this: %\begin{verbatim}%#
#(custom-set-variables ... '(coq-prog-args '("-impredicative-set" "-I" "/path/to/cpdt/src")) ... )#
#%\end{verbatim}% The extra arguments demonstrated here are the proper choices for working with the code for this book. The ellipses stand for other Emacs customization settings you may already have. It can be helpful to save several alternate sets of flags in your %\texttt{%#<tt>#.emacs#</tt>#%}% file, with all but one commented out within the %\texttt{%#<tt>#custom-set-variables#</tt>#%}% block at any given time. With Proof General, the portion of a buffer that Coq has processed is highlighted in some way, like being given a blue background. You step through Coq source files by positioning the point at the position you want Coq to run to and pressing C-C C-RET. This can be used both for normal step-by-step coding, by placing the point inside some command past the end of the highlighted region; and for undoing, by placing the point inside the highlighted region. *) (** * Arithmetic Expressions Over Natural Numbers *) (** We will begin with that staple of compiler textbooks, arithmetic expressions over a single type of numbers. *) (** ** Source Language *) (** We begin with the syntax of the source language. *) Inductive binop : Set := Plus | Times. (** Our first line of Coq code should be unsurprising to ML and Haskell programmers. We define an algebraic datatype [binop] to stand for the binary operators of our source language. There are just two wrinkles compared to ML and Haskell. First, we use the keyword [Inductive], in place of %\texttt{%#<tt>#data#</tt>#%}%, %\texttt{%#<tt>#datatype#</tt>#%}%, or %\texttt{%#<tt>#type#</tt>#%}%. This is not just a trivial surface syntax difference; inductive types in Coq are much more expressive than garden variety algebraic datatypes, essentially enabling us to encode all of mathematics, though we begin humbly in this chapter. Second, there is the [: Set] fragment, which declares that we are defining a datatype that should be thought of as a constituent of programs. Later, we will see other options for defining datatypes in the universe of proofs or in an infinite hierarchy of universes, encompassing both programs and proofs, that is useful in higher-order constructions. *) Inductive exp : Set := | Const : nat -> exp | Binop : binop -> exp -> exp -> exp. (** Now we define the type of arithmetic expressions. We write that a constant may be built from one argument, a natural number; and a binary operation may be built from a choice of operator and two operand expressions. A note for readers following along in the PDF version: coqdoc supports pretty-printing of tokens in LaTeX or HTML. Where you see a right arrow character, the source contains the ASCII text %\texttt{%#<tt>#->#</tt>#%}%. Other examples of this substitution appearing in this chapter are a double right arrow for %\texttt{%#<tt>#=>#</tt>#%}% and the inverted 'A' symbol for %\texttt{%#<tt>#forall#</tt>#%}%. When in doubt about the ASCII version of a symbol, you can consult the chapter source code. %\medskip% Now we are ready to say what these programs mean. We will do this by writing an interpreter that can be thought of as a trivial operational or denotational semantics. (If you are not familiar with these semantic techniques, no need to worry; we will stick to "common sense" constructions.) *) Definition binopDenote (b : binop) : nat -> nat -> nat := match b with | Plus => plus | Times => mult end. (** The meaning of a binary operator is a binary function over naturals, defined with pattern-matching notation analogous to the %\texttt{%#<tt>#case#</tt>#%}% and %\texttt{%#<tt>#match#</tt>#%}% of ML and Haskell, and referring to the functions [plus] and [mult] from the Coq standard library. The keyword [Definition] is Coq's all-purpose notation for binding a term of the programming language to a name, with some associated syntactic sugar, like the notation we see here for defining a function. That sugar could be expanded to yield this definition: [[ Definition binopDenote : binop -> nat -> nat -> nat := fun (b : binop) => match b with | Plus => plus | Times => mult end. ]] In this example, we could also omit all of the type annotations, arriving at: [[ Definition binopDenote := fun b => match b with | Plus => plus | Times => mult end. ]] Languages like Haskell and ML have a convenient %\textit{%##principal typing##%}% property, which gives us strong guarantees about how effective type inference will be. Unfortunately, Coq's type system is so expressive that any kind of "complete" type inference is impossible, and the task even seems to be hard heuristically in practice. Nonetheless, Coq includes some very helpful heuristics, many of them copying the workings of Haskell and ML type-checkers for programs that fall in simple fragments of Coq's language. This is as good a time as any to mention the preponderance of different languages associated with Coq. The theoretical foundation of Coq is a formal system called the %\textit{%##Calculus of Inductive Constructions (CIC)##%}%, which is an extension of the older %\textit{%##Calculus of Constructions (CoC)##%}%. CIC is quite a spartan foundation, which is helpful for proving metatheory but not so helpful for real development. Still, it is nice to know that it has been proved that CIC enjoys properties like %\textit{%##strong normalization##%}%, meaning that every program (and, more importantly, every proof term) terminates; and %\textit{%##relative consistency##%}% with systems like versions of Zermelo Fraenkel set theory, which roughly means that you can believe that Coq proofs mean that the corresponding propositions are "really true," if you believe in set theory. Coq is actually based on an extension of CIC called %\textit{%##Gallina##%}%. The text after the [:=] and before the period in the last code example is a term of Gallina. Gallina adds many useful features that are not compiled internally to more primitive CIC features. The important metatheorems about CIC have not been extended to the full breadth of these features, but most Coq users do not seem to lose much sleep over this omission. Commands like [Inductive] and [Definition] are part of %\textit{%##the vernacular##%}%, which includes all sorts of useful queries and requests to the Coq system. Finally, there is %\textit{%##Ltac##%}%, Coq's domain-specific language for writing proofs and decision procedures. We will see some basic examples of Ltac later in this chapter, and much of this book is devoted to more involved Ltac examples. %\medskip% We can give a simple definition of the meaning of an expression: *) Fixpoint expDenote (e : exp) : nat := match e with | Const n => n | Binop b e1 e2 => (binopDenote b) (expDenote e1) (expDenote e2) end. (** We declare explicitly that this is a recursive definition, using the keyword [Fixpoint]. The rest should be old hat for functional programmers. *) (** It is convenient to be able to test definitions before starting to prove things about them. We can verify that our semantics is sensible by evaluating some sample uses. *) Eval simpl in expDenote (Const 42). (** [= 42 : nat] *) Eval simpl in expDenote (Binop Plus (Const 2) (Const 2)). (** [= 4 : nat] *) Eval simpl in expDenote (Binop Times (Binop Plus (Const 2) (Const 2)) (Const 7)). (** [= 28 : nat] *) (** ** Target Language *) (** We will compile our source programs onto a simple stack machine, whose syntax is: *) Inductive instr : Set := | IConst : nat -> instr | IBinop : binop -> instr. Definition prog := list instr. Definition stack := list nat. (** An instruction either pushes a constant onto the stack or pops two arguments, applies a binary operator to them, and pushes the result onto the stack. A program is a list of instructions, and a stack is a list of natural numbers. We can give instructions meanings as functions from stacks to optional stacks, where running an instruction results in [None] in case of a stack underflow and results in [Some s'] when the result of execution is the new stack [s']. [::] is the "list cons" operator from the Coq standard library. *) Definition instrDenote (i : instr) (s : stack) : option stack := match i with | IConst n => Some (n :: s) | IBinop b => match s with | arg1 :: arg2 :: s' => Some ((binopDenote b) arg1 arg2 :: s') | _ => None end end. (** With [instrDenote] defined, it is easy to define a function [progDenote], which iterates application of [instrDenote] through a whole program. *) Fixpoint progDenote (p : prog) (s : stack) {struct p} : option stack := match p with | nil => Some s | i :: p' => match instrDenote i s with | None => None | Some s' => progDenote p' s' end end. (** There is one interesting difference compared to our previous example of a [Fixpoint]. This recursive function takes two arguments, [p] and [s]. It is critical for the soundness of Coq that every program terminate, so a shallow syntactic termination check is imposed on every recursive function definition. One of the function parameters must be designated to decrease monotonically across recursive calls. That is, every recursive call must use a version of that argument that has been pulled out of the current argument by some number of [match] expressions. [expDenote] has only one argument, so we did not need to specify which of its arguments decreases. For [progDenote], we resolve the ambiguity by writing [{struct p}] to indicate that argument [p] decreases structurally. *) (** ** Translation *) (** Our compiler itself is now unsurprising. [++] is the list concatenation operator from the Coq standard library. *) Fixpoint compile (e : exp) : prog := match e with | Const n => IConst n :: nil | Binop b e1 e2 => compile e2 ++ compile e1 ++ IBinop b :: nil end. (** Before we set about proving that this compiler is correct, we can try a few test runs, using our sample programs from earlier. *) Eval simpl in compile (Const 42). (** [[ = IConst 42 :: nil : prog ]] *) Eval simpl in compile (Binop Plus (Const 2) (Const 2)). (** [[ = IConst 2 :: IConst 2 :: IBinop Plus :: nil : prog ]] *) Eval simpl in compile (Binop Times (Binop Plus (Const 2) (Const 2)) (Const 7)). (** [[ = IConst 7 :: IConst 2 :: IConst 2 :: IBinop Plus :: IBinop Times :: nil : prog ]] *) (** We can also run our compiled programs and check that they give the right results. *) Eval simpl in progDenote (compile (Const 42)) nil. (** [[ = Some (42 :: nil) : option stack ]] *) Eval simpl in progDenote (compile (Binop Plus (Const 2) (Const 2))) nil. (** [[ = Some (4 :: nil) : option stack ]] *) Eval simpl in progDenote (compile (Binop Times (Binop Plus (Const 2) (Const 2)) (Const 7))) nil. (** [[ = Some (28 :: nil) : option stack ]] *) (** ** Translation Correctness *) (** We are ready to prove that our compiler is implemented correctly. We can use a new vernacular command [Theorem] to start a correctness proof, in terms of the semantics we defined earlier: *) Theorem compile_correct : forall e, progDenote (compile e) nil = Some (expDenote e :: nil). (* begin hide *) Abort. (* end hide *) (* begin thide *) (** Though a pencil-and-paper proof might clock out at this point, writing "by a routine induction on [e]," it turns out not to make sense to attack this proof directly. We need to use the standard trick of %\textit{%##strengthening the induction hypothesis##%}%. We do that by proving an auxiliary lemma: *) Lemma compile_correct' : forall e p s, progDenote (compile e ++ p) s = progDenote p (expDenote e :: s). (** After the period in the [Lemma] command, we are in %\textit{%##the interactive proof-editing mode##%}%. We find ourselves staring at this ominous screen of text: [[ 1 subgoal ============================ forall (e : exp) (p : list instr) (s : stack), progDenote (compile e ++ p) s = progDenote p (expDenote e :: s) ]] Coq seems to be restating the lemma for us. What we are seeing is a limited case of a more general protocol for describing where we are in a proof. We are told that we have a single subgoal. In general, during a proof, we can have many pending subgoals, each of which is a logical proposition to prove. Subgoals can be proved in any order, but it usually works best to prove them in the order that Coq chooses. Next in the output, we see our single subgoal described in full detail. There is a double-dashed line, above which would be our free variables and hypotheses, if we had any. Below the line is the conclusion, which, in general, is to be proved from the hypotheses. We manipulate the proof state by running commands called %\textit{%##tactics##%}%. Let us start out by running one of the most important tactics: *) induction e. (** We declare that this proof will proceed by induction on the structure of the expression [e]. This swaps out our initial subgoal for two new subgoals, one for each case of the inductive proof: [[ 2 subgoals n : nat ============================ forall (s : stack) (p : list instr), progDenote (compile (Const n) ++ p) s = progDenote p (expDenote (Const n) :: s) ]] [[ subgoal 2 is: forall (s : stack) (p : list instr), progDenote (compile (Binop b e1 e2) ++ p) s = progDenote p (expDenote (Binop b e1 e2) :: s) ]] The first and current subgoal is displayed with the double-dashed line below free variables and hypotheses, while later subgoals are only summarized with their conclusions. We see an example of a free variable in the first subgoal; [n] is a free variable of type [nat]. The conclusion is the original theorem statement where [e] has been replaced by [Const n]. In a similar manner, the second case has [e] replaced by a generalized invocation of the [Binop] expression constructor. We can see that proving both cases corresponds to a standard proof by structural induction. We begin the first case with another very common tactic. *) intros. (** The current subgoal changes to: [[ n : nat s : stack p : list instr ============================ progDenote (compile (Const n) ++ p) s = progDenote p (expDenote (Const n) :: s) ]] We see that [intros] changes [forall]-bound variables at the beginning of a goal into free variables. To progress further, we need to use the definitions of some of the functions appearing in the goal. The [unfold] tactic replaces an identifier with its definition. *) unfold compile. (** [[ n : nat s : stack p : list instr ============================ progDenote ((IConst n :: nil) ++ p) s = progDenote p (expDenote (Const n) :: s) ]] *) unfold expDenote. (** [[ n : nat s : stack p : list instr ============================ progDenote ((IConst n :: nil) ++ p) s = progDenote p (n :: s) ]] We only need to unfold the first occurrence of [progDenote] to prove the goal: *) unfold progDenote at 1. (** [[ n : nat s : stack p : list instr ============================ (fix progDenote (p0 : prog) (s0 : stack) {struct p0} : option stack := match p0 with | nil => Some s0 | i :: p' => match instrDenote i s0 with | Some s' => progDenote p' s' | None => None (A:=stack) end end) ((IConst n :: nil) ++ p) s = progDenote p (n :: s) ]] This last [unfold] has left us with an anonymous fixpoint version of [progDenote], which will generally happen when unfolding recursive definitions. Fortunately, in this case, we can eliminate such complications right away, since the structure of the argument [(IConst n :: nil) ++ p] is known, allowing us to simplify the internal pattern match with the [simpl] tactic: *) simpl. (** [[ n : nat s : stack p : list instr ============================ (fix progDenote (p0 : prog) (s0 : stack) {struct p0} : option stack := match p0 with | nil => Some s0 | i :: p' => match instrDenote i s0 with | Some s' => progDenote p' s' | None => None (A:=stack) end end) p (n :: s) = progDenote p (n :: s) ]] Now we can unexpand the definition of [progDenote]: *) fold progDenote. (** [[ n : nat s : stack p : list instr ============================ progDenote p (n :: s) = progDenote p (n :: s) ]] It looks like we are at the end of this case, since we have a trivial equality. Indeed, a single tactic finishes us off: *) reflexivity. (** On to the second inductive case: [[ b : binop e1 : exp IHe1 : forall (s : stack) (p : list instr), progDenote (compile e1 ++ p) s = progDenote p (expDenote e1 :: s) e2 : exp IHe2 : forall (s : stack) (p : list instr), progDenote (compile e2 ++ p) s = progDenote p (expDenote e2 :: s) ============================ forall (s : stack) (p : list instr), progDenote (compile (Binop b e1 e2) ++ p) s = progDenote p (expDenote (Binop b e1 e2) :: s) ]] We see our first example of hypotheses above the double-dashed line. They are the inductive hypotheses [IHe1] and [IHe2] corresponding to the subterms [e1] and [e2], respectively. We start out the same way as before, introducing new free variables and unfolding and folding the appropriate definitions. The seemingly frivolous [unfold]/[fold] pairs are actually accomplishing useful work, because [unfold] will sometimes perform easy simplifications. *) intros. unfold compile. fold compile. unfold expDenote. fold expDenote. (** Now we arrive at a point where the tactics we have seen so far are insufficient. No further definition unfoldings get us anywhere, so we will need to try something different. [[ b : binop e1 : exp IHe1 : forall (s : stack) (p : list instr), progDenote (compile e1 ++ p) s = progDenote p (expDenote e1 :: s) e2 : exp IHe2 : forall (s : stack) (p : list instr), progDenote (compile e2 ++ p) s = progDenote p (expDenote e2 :: s) s : stack p : list instr ============================ progDenote ((compile e2 ++ compile e1 ++ IBinop b :: nil) ++ p) s = progDenote p (binopDenote b (expDenote e1) (expDenote e2) :: s) ]] What we need is the associative law of list concatenation, available as a theorem [app_ass] in the standard library. *) Check app_ass. (** [[ app_ass : forall (A : Type) (l m n : list A), (l ++ m) ++ n = l ++ m ++ n ]] We use it to perform a rewrite: *) rewrite app_ass. (** changing the conclusion to: [[ progDenote (compile e2 ++ (compile e1 ++ IBinop b :: nil) ++ p) s = progDenote p (binopDenote b (expDenote e1) (expDenote e2) :: s) ]] Now we can notice that the lefthand side of the equality matches the lefthand side of the second inductive hypothesis, so we can rewrite with that hypothesis, too: *) rewrite IHe2. (** [[ progDenote ((compile e1 ++ IBinop b :: nil) ++ p) (expDenote e2 :: s) = progDenote p (binopDenote b (expDenote e1) (expDenote e2) :: s) ]] The same process lets us apply the remaining hypothesis. *) rewrite app_ass. rewrite IHe1. (** [[ progDenote ((IBinop b :: nil) ++ p) (expDenote e1 :: expDenote e2 :: s) = progDenote p (binopDenote b (expDenote e1) (expDenote e2) :: s) ]] Now we can apply a similar sequence of tactics to that that ended the proof of the first case. *) unfold progDenote at 1. simpl. fold progDenote. reflexivity. (** And the proof is completed, as indicated by the message: [[ Proof completed. ]] And there lies our first proof. Already, even for simple theorems like this, the final proof script is unstructured and not very enlightening to readers. If we extend this approach to more serious theorems, we arrive at the unreadable proof scripts that are the favorite complaints of opponents of tactic-based proving. Fortunately, Coq has rich support for scripted automation, and we can take advantage of such a scripted tactic (defined elsewhere) to make short work of this lemma. We abort the old proof attempt and start again. *) Abort. Lemma compile_correct' : forall e s p, progDenote (compile e ++ p) s = progDenote p (expDenote e :: s). induction e; crush. Qed. (** We need only to state the basic inductive proof scheme and call a tactic that automates the tedious reasoning in between. In contrast to the period tactic terminator from our last proof, the semicolon tactic separator supports structured, compositional proofs. The tactic [t1; t2] has the effect of running [t1] and then running [t2] on each remaining subgoal. The semicolon is one of the most fundamental building blocks of effective proof automation. The period terminator is very useful for exploratory proving, where you need to see intermediate proof states, but final proofs of any serious complexity should have just one period, terminating a single compound tactic that probably uses semicolons. The proof of our main theorem is now easy. We prove it with four period-terminated tactics, though separating them with semicolons would work as well; the version here is easier to step through. *) Theorem compile_correct : forall e, progDenote (compile e) nil = Some (expDenote e :: nil). intros. (** [[ e : exp ============================ progDenote (compile e) nil = Some (expDenote e :: nil) ]] At this point, we want to massage the lefthand side to match the statement of [compile_correct']. A theorem from the standard library is useful: *) Check app_nil_end. (** [[ app_nil_end : forall (A : Type) (l : list A), l = l ++ nil ]] *) rewrite (app_nil_end (compile e)). (** This time, we explicitly specify the value of the variable [l] from the theorem statement, since multiple expressions of list type appear in the conclusion. [rewrite] might choose the wrong place to rewrite if we did not specify which we want. [[ e : exp ============================ progDenote (compile e ++ nil) nil = Some (expDenote e :: nil) ]] Now we can apply the lemma. *) rewrite compile_correct'. (** [[ e : exp ============================ progDenote nil (expDenote e :: nil) = Some (expDenote e :: nil) ]] We are almost done. The lefthand and righthand sides can be seen to match by simple symbolic evaluation. That means we are in luck, because Coq identifies any pair of terms as equal whenever they normalize to the same result by symbolic evaluation. By the definition of [progDenote], that is the case here, but we do not need to worry about such details. A simple invocation of [reflexivity] does the normalization and checks that the two results are syntactically equal. *) reflexivity. Qed. (* end thide *) (** * Typed Expressions *) (** In this section, we will build on the initial example by adding additional expression forms that depend on static typing of terms for safety. *) (** ** Source Language *) (** We define a trivial language of types to classify our expressions: *) Inductive type : Set := Nat | Bool. (** Now we define an expanded set of binary operators. *) Inductive tbinop : type -> type -> type -> Set := | TPlus : tbinop Nat Nat Nat | TTimes : tbinop Nat Nat Nat | TEq : forall t, tbinop t t Bool | TLt : tbinop Nat Nat Bool. (** The definition of [tbinop] is different from [binop] in an important way. Where we declared that [binop] has type [Set], here we declare that [tbinop] has type [type -> type -> type -> Set]. We define [tbinop] as an %\textit{%##indexed type family##%}%. Indexed inductive types are at the heart of Coq's expressive power; almost everything else of interest is defined in terms of them. ML and Haskell have indexed algebraic datatypes. For instance, their list types are indexed by the type of data that the list carries. However, compared to Coq, ML and Haskell 98 place two important restrictions on datatype definitions. First, the indices of the range of each data constructor must be type variables bound at the top level of the datatype definition. There is no way to do what we did here, where we, for instance, say that [TPlus] is a constructor building a [tbinop] whose indices are all fixed at [Nat]. %\textit{%##Generalized algebraic datatypes (GADTs)##%}% are a popular feature in GHC Haskell and other languages that removes this first restriction. The second restriction is not lifted by GADTs. In ML and Haskell, indices of types must be types and may not be %\textit{%##expressions##%}%. In Coq, types may be indexed by arbitrary Gallina terms. Type indices can live in the same universe as programs, and we can compute with them just like regular programs. Haskell supports a hobbled form of computation in type indices based on multi-parameter type classes, and recent extensions like type functions bring Haskell programming even closer to "real" functional programming with types, but, without dependent typing, there must always be a gap between how one programs with types and how one programs normally. *) (** We can define a similar type family for typed expressions. *) Inductive texp : type -> Set := | TNConst : nat -> texp Nat | TBConst : bool -> texp Bool | TBinop : forall arg1 arg2 res, tbinop arg1 arg2 res -> texp arg1 -> texp arg2 -> texp res. (** Thanks to our use of dependent types, every well-typed [texp] represents a well-typed source expression, by construction. This turns out to be very convenient for many things we might want to do with expressions. For instance, it is easy to adapt our interpreter approach to defining semantics. We start by defining a function mapping the types of our languages into Coq types: *) Definition typeDenote (t : type) : Set := match t with | Nat => nat | Bool => bool end. (** It can take a few moments to come to terms with the fact that [Set], the type of types of programs, is itself a first-class type, and that we can write functions that return [Set]s. Past that wrinkle, the definition of [typeDenote] is trivial, relying on the [nat] and [bool] types from the Coq standard library. We need to define a few auxiliary functions, implementing our boolean binary operators that do not appear with the right types in the standard library. They are entirely standard and ML-like, with the one caveat being that the Coq [nat] type uses a unary representation, where [O] is zero and [S n] is the successor of [n]. *) Definition eq_bool (b1 b2 : bool) : bool := match b1, b2 with | true, true => true | false, false => true | _, _ => false end. Fixpoint eq_nat (n1 n2 : nat) {struct n1} : bool := match n1, n2 with | O, O => true | S n1', S n2' => eq_nat n1' n2' | _, _ => false end. Fixpoint lt (n1 n2 : nat) {struct n1} : bool := match n1, n2 with | O, S _ => true | S n1', S n2' => lt n1' n2' | _, _ => false end. (** Now we can interpret binary operators: *) Definition tbinopDenote arg1 arg2 res (b : tbinop arg1 arg2 res) : typeDenote arg1 -> typeDenote arg2 -> typeDenote res := match b in (tbinop arg1 arg2 res) return (typeDenote arg1 -> typeDenote arg2 -> typeDenote res) with | TPlus => plus | TTimes => mult | TEq Nat => eq_nat | TEq Bool => eq_bool | TLt => lt end. (** This function has just a few differences from the denotation functions we saw earlier. First, [tbinop] is an indexed type, so its indices become additional arguments to [tbinopDenote]. Second, we need to perform a genuine %\textit{%##dependent pattern match##%}% to come up with a definition of this function that type-checks. In each branch of the [match], we need to use branch-specific information about the indices to [tbinop]. General type inference that takes such information into account is undecidable, and Coq avoids pursuing special heuristics for the problem, instead asking users to write annotations, like we see above on the line with [match]. The [in] annotation restates the type of the term being case-analyzed. Though we use the same names for the indices as we use in the type of the original argument binder, these are actually fresh variables, and they are %\textit{%##binding occurrences##%}%. Their scope is the [return] clause. That is, [arg1], [arg2], and [arg3] are new bound variables bound only within the return clause [typeDenote arg1 -> typeDenote arg2 -> typeDenote res]. By being explicit about the functional relationship between the type indices and the match result, we regain decidable type inference. The same tricks suffice to define an expression denotation function in an unsurprising way: *) Fixpoint texpDenote t (e : texp t) {struct e} : typeDenote t := match e in (texp t) return (typeDenote t) with | TNConst n => n | TBConst b => b | TBinop _ _ _ b e1 e2 => (tbinopDenote b) (texpDenote e1) (texpDenote e2) end. (** We can evaluate a few example programs to convince ourselves that this semantics is correct. *) Eval simpl in texpDenote (TNConst 42). (** [[ = 42 : typeDenote Nat ]] *) Eval simpl in texpDenote (TBConst true). (** [[ = true : typeDenote Bool ]] *) Eval simpl in texpDenote (TBinop TTimes (TBinop TPlus (TNConst 2) (TNConst 2)) (TNConst 7)). (** [[ = 28 : typeDenote Nat ]] *) Eval simpl in texpDenote (TBinop (TEq Nat) (TBinop TPlus (TNConst 2) (TNConst 2)) (TNConst 7)). (** [[ = false : typeDenote Bool ]] *) Eval simpl in texpDenote (TBinop TLt (TBinop TPlus (TNConst 2) (TNConst 2)) (TNConst 7)). (** [[ = true : typeDenote Bool ]] *) (** ** Target Language *) (** Now we want to define a suitable stack machine target for compilation. In the example of the untyped language, stack machine programs could encounter stack underflows and "get stuck." This was unfortunate, since we had to deal with this complication even though we proved that our compiler never produced underflowing programs. We could have used dependent types to force all stack machine programs to be underflow-free. For our new languages, besides underflow, we also have the problem of stack slots with naturals instead of bools or vice versa. This time, we will use indexed typed families to avoid the need to reason about potential failures. We start by defining stack types, which classify sets of possible stacks. *) Definition tstack := list type. (** Any stack classified by a [tstack] must have exactly as many elements, and each stack element must have the type found in the same position of the stack type. We can define instructions in terms of stack types, where every instruction's type tells us what initial stack type it expects and what final stack type it will produce. *) Inductive tinstr : tstack -> tstack -> Set := | TINConst : forall s, nat -> tinstr s (Nat :: s) | TIBConst : forall s, bool -> tinstr s (Bool :: s) | TIBinop : forall arg1 arg2 res s, tbinop arg1 arg2 res -> tinstr (arg1 :: arg2 :: s) (res :: s). (** Stack machine programs must be a similar inductive family, since, if we again used the [list] type family, we would not be able to guarantee that intermediate stack types match within a program. *) Inductive tprog : tstack -> tstack -> Set := | TNil : forall s, tprog s s | TCons : forall s1 s2 s3, tinstr s1 s2 -> tprog s2 s3 -> tprog s1 s3. (** Now, to define the semantics of our new target language, we need a representation for stacks at runtime. We will again take advantage of type information to define types of value stacks that, by construction, contain the right number and types of elements. *) Fixpoint vstack (ts : tstack) : Set := match ts with | nil => unit | t :: ts' => typeDenote t * vstack ts' end%type. (** This is another [Set]-valued function. This time it is recursive, which is perfectly valid, since [Set] is not treated specially in determining which functions may be written. We say that the value stack of an empty stack type is any value of type [unit], which has just a single value, [tt]. A nonempty stack type leads to a value stack that is a pair, whose first element has the proper type and whose second element follows the representation for the remainder of the stack type. This idea of programming with types can take a while to internalize, but it enables a very simple definition of instruction denotation. We have the same kind of type annotations for the dependent [match], but everything else is like what you might expect from a Lisp-like version of ML that ignored type information. Nonetheless, the fact that [tinstrDenote] passes the type-checker guarantees that our stack machine programs can never go wrong. *) Definition tinstrDenote ts ts' (i : tinstr ts ts') : vstack ts -> vstack ts' := match i in (tinstr ts ts') return (vstack ts -> vstack ts') with | TINConst _ n => fun s => (n, s) | TIBConst _ b => fun s => (b, s) | TIBinop _ _ _ _ b => fun s => match s with (arg1, (arg2, s')) => ((tbinopDenote b) arg1 arg2, s') end end. (** Why do we choose to use an anonymous function to bind the initial stack in every case of the [match]? Consider this well-intentioned but invalid alternative version: [[ Definition tinstrDenote ts ts' (i : tinstr ts ts') (s : vstack ts) : vstack ts' := match i in (tinstr ts ts') return (vstack ts') with | TINConst _ n => (n, s) | TIBConst _ b => (b, s) | TIBinop _ _ _ _ b => match s with (arg1, (arg2, s')) => ((tbinopDenote b) arg1 arg2, s') end end. ]] The Coq type-checker complains that: [[ The term "(n, s)" has type "(nat * vstack ts)%type" while it is expected to have type "vstack (Nat :: t)" ]] Recall from our earlier discussion of [match] annotations that we write the annotations to express to the type-checker the relationship between the type indices of the case object and the result type of the [match]. Coq chooses to assign to the wildcard [_] after [TINConst] the name [t], and the type error is telling us that the type checker cannot prove that [t] is the same as [ts]. By moving [s] out of the [match], we lose the ability to express, with [in] and [return] clauses, the relationship between the shared index [ts] of [s] and [i]. There %\textit{%##are##%}% reasonably general ways of getting around this problem without pushing binders inside [match]es. However, the alternatives are significantly more involved, and the technique we use here is almost certainly the best choice, whenever it applies. *) (** We finish the semantics with a straightforward definition of program denotation. *) Fixpoint tprogDenote ts ts' (p : tprog ts ts') {struct p} : vstack ts -> vstack ts' := match p in (tprog ts ts') return (vstack ts -> vstack ts') with | TNil _ => fun s => s | TCons _ _ _ i p' => fun s => tprogDenote p' (tinstrDenote i s) end. (** ** Translation *) (** To define our compilation, it is useful to have an auxiliary function for concatenating two stack machine programs. *) Fixpoint tconcat ts ts' ts'' (p : tprog ts ts') {struct p} : tprog ts' ts'' -> tprog ts ts'' := match p in (tprog ts ts') return (tprog ts' ts'' -> tprog ts ts'') with | TNil _ => fun p' => p' | TCons _ _ _ i p1 => fun p' => TCons i (tconcat p1 p') end. (** With that function in place, the compilation is defined very similarly to how it was before, modulo the use of dependent typing. *) Fixpoint tcompile t (e : texp t) (ts : tstack) {struct e} : tprog ts (t :: ts) := match e in (texp t) return (tprog ts (t :: ts)) with | TNConst n => TCons (TINConst _ n) (TNil _) | TBConst b => TCons (TIBConst _ b) (TNil _) | TBinop _ _ _ b e1 e2 => tconcat (tcompile e2 _) (tconcat (tcompile e1 _) (TCons (TIBinop _ b) (TNil _))) end. (** One interesting feature of the definition is the underscores appearing to the right of [=>] arrows. Haskell and ML programmers are quite familiar with compilers that infer type parameters to polymorphic values. In Coq, it is possible to go even further and ask the system to infer arbitrary terms, by writing underscores in place of specific values. You may have noticed that we have been calling functions without specifying all of their arguments. For instance, the recursive calls here to [tcompile] omit the [t] argument. Coq's %\textit{%##implicit argument##%}% mechanism automatically inserts underscores for arguments that it will probably be able to infer. Inference of such values is far from complete, though; generally, it only works in cases similar to those encountered with polymorphic type instantiation in Haskell and ML. The underscores here are being filled in with stack types. That is, the Coq type inferencer is, in a sense, inferring something about the flow of control in the translated programs. We can take a look at exactly which values are filled in: *) Print tcompile. (** [[ tcompile = fix tcompile (t : type) (e : texp t) (ts : tstack) {struct e} : tprog ts (t :: ts) := match e in (texp t0) return (tprog ts (t0 :: ts)) with | TNConst n => TCons (TINConst ts n) (TNil (Nat :: ts)) | TBConst b => TCons (TIBConst ts b) (TNil (Bool :: ts)) | TBinop arg1 arg2 res b e1 e2 => tconcat (tcompile arg2 e2 ts) (tconcat (tcompile arg1 e1 (arg2 :: ts)) (TCons (TIBinop ts b) (TNil (res :: ts)))) end : forall t : type, texp t -> forall ts : tstack, tprog ts (t :: ts) ]] *) (** We can check that the compiler generates programs that behave appropriately on our sample programs from above: *) Eval simpl in tprogDenote (tcompile (TNConst 42) nil) tt. (** [[ = (42, tt) : vstack (Nat :: nil) ]] *) Eval simpl in tprogDenote (tcompile (TBConst true) nil) tt. (** [[ = (true, tt) : vstack (Bool :: nil) ]] *) Eval simpl in tprogDenote (tcompile (TBinop TTimes (TBinop TPlus (TNConst 2) (TNConst 2)) (TNConst 7)) nil) tt. (** [[ = (28, tt) : vstack (Nat :: nil) ]] *) Eval simpl in tprogDenote (tcompile (TBinop (TEq Nat) (TBinop TPlus (TNConst 2) (TNConst 2)) (TNConst 7)) nil) tt. (** [[ = (false, tt) : vstack (Bool :: nil) ]] *) Eval simpl in tprogDenote (tcompile (TBinop TLt (TBinop TPlus (TNConst 2) (TNConst 2)) (TNConst 7)) nil) tt. (** [[ = (true, tt) : vstack (Bool :: nil) ]] *) (** ** Translation Correctness *) (** We can state a correctness theorem similar to the last one. *) Theorem tcompile_correct : forall t (e : texp t), tprogDenote (tcompile e nil) tt = (texpDenote e, tt). (* begin hide *) Abort. (* end hide *) (* begin thide *) (** Again, we need to strengthen the theorem statement so that the induction will go through. This time, I will develop an alternative approach to this kind of proof, stating the key lemma as: *) Lemma tcompile_correct' : forall t (e : texp t) ts (s : vstack ts), tprogDenote (tcompile e ts) s = (texpDenote e, s). (** While lemma [compile_correct'] quantified over a program that is the "continuation" for the expression we are considering, here we avoid drawing in any extra syntactic elements. In addition to the source expression and its type, we also quantify over an initial stack type and a stack compatible with it. Running the compilation of the program starting from that stack, we should arrive at a stack that differs only in having the program's denotation pushed onto it. Let us try to prove this theorem in the same way that we settled on in the last section. *) induction e; crush. (** We are left with this unproved conclusion: [[ tprogDenote (tconcat (tcompile e2 ts) (tconcat (tcompile e1 (arg2 :: ts)) (TCons (TIBinop ts t) (TNil (res :: ts))))) s = (tbinopDenote t (texpDenote e1) (texpDenote e2), s) ]] We need an analogue to the [app_ass] theorem that we used to rewrite the goal in the last section. We can abort this proof and prove such a lemma about [tconcat]. *) Abort. Lemma tconcat_correct : forall ts ts' ts'' (p : tprog ts ts') (p' : tprog ts' ts'') (s : vstack ts), tprogDenote (tconcat p p') s = tprogDenote p' (tprogDenote p s). induction p; crush. Qed. (** This one goes through completely automatically. Some code behind the scenes registers [app_ass] for use by [crush]. We must register [tconcat_correct] similarly to get the same effect: *) Hint Rewrite tconcat_correct : cpdt. (** We ask that the lemma be used for left-to-right rewriting, and we ask for the hint to be added to the hint database called [cpdt], which is the database used by [crush]. Now we are ready to return to [tcompile_correct'], proving it automatically this time. *) Lemma tcompile_correct' : forall t (e : texp t) ts (s : vstack ts), tprogDenote (tcompile e ts) s = (texpDenote e, s). induction e; crush. Qed. (** We can register this main lemma as another hint, allowing us to prove the final theorem trivially. *) Hint Rewrite tcompile_correct' : cpdt. Theorem tcompile_correct : forall t (e : texp t), tprogDenote (tcompile e nil) tt = (texpDenote e, tt). crush. Qed. (* end thide *)


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Dwarf Hamsters
Dwarf Hamster Basics
Basic Facts:
Dwarf hamsters have different care needs than Syrian or big hamsters. They are nocturnal and they live 2 to 3 years. They are generally social creatures, and can live with littermates in a large clean cage, with ample food.
If they start to fight seriously or if they ever injure each other, they need to be separated and live apart. Make sure a knowledgeable person double checks that they are the same sex, or get them spayed or neutered by an expert hamster surgeon if they are the opposite sex.
A dwarf hamster is an intelligent living creature, not a "learner" pet or a child's toy. Adults are responsible for their health and safety.
Dwarf hamsters should only be handled by gentle children who are old enough to understand how to be gentle, and only while the child is seated and under close adult supervision.
When a hamster is woken up, or first wakes up, s/he may be cranky. Allow him/her a chance to perk up before handling to avoid being nipped. Dwarfs often do not like being picked up by a hand directly from the cage, and may bite. To avoid this, let the hamster climb into a ball, cup or toy, then lift the hammie out. Once they are out of the cage, allow them to climb onto your flat palm at their own speed. This takes patience when they first meet you. They may try to dig through your hand or nip lightly to make sure that you are not food (make sure your hands are clean and do not smell like food). This light nipping is not the same as an aggression bite. When first handling a new dwarf, do so over a soft surface, close to the ground in case they bite and you drop them accidentally. Always wash your hands before handling your hamster to avoid transferring germs to them from the outside world.
Hamsters need temperatures between 65 and 85 degrees Fahrenheit at all times. In winter, if it is below this temperature, they can go into false hibernation, and appear to be dead. If the hamster appears to be dead, before burial move it to a warmer location, and wait until the body is warm to ensure s/he is not hibernating. In summer make sure the hammies stay cool. Keep a frozen water bottle in the freezer to use as emergency cage air conditioning in case of power outages or AC malfunction. It's a great idea to hang a thermometer on the outside of the hamster cage so that you can monitor the temperature.
Dwarf hamsters are very prone to diabetes and need a specific diet to ensure a happy healthy life. If they are not fed this diet they are likely to develop diabetes and may be surly and aggressive. They should eat 50% washed veggies (organic preferable) and 50% sugar-, corn-, fruit-, carrot-, and pea-free hamster food and grain mix (approximately 1/8 to ¼ cup daily). Any food containing sugar in any form, including fruits corn, carrots or peas will harm dwarf hamsters over time. When introducing new foods, do so slowly, one at a time, and check the hamster poop the following day to make sure their stools are solid. If they appear soft, discontinue all fresh foods until they are solid again. Dwarfs will not eat all of the dry food every day, but they enjoy hiding it, and need excess to feel secure. Dwarfs also benefit from a small amount of oat or timothy hay, especially when they are shedding. Healthy Handfuls by Oxbow or Hazel Hamster (with corn and peas picked out) are two of the better hamster foods. When choosing a hamster food, make sure that there is no sugar, including corn syrup.
Cane molasses is fine if it is lower on the ingredient list, since it is high in B vitamins. Hamsters should never get fruit seeds or pits as these contain arsenic. Hams should never have raw potatoes, yucca, onions, garlic, or food that is spoiled, slimy or moldy. The hamster diet can be supplemented with roasted unsalted soybeans (i.e. Genisoy brand), lentils, cooked beans, tofu, egg, cheese, nuts, sesame seeds and seeds with shells. Grain mixes can include rolled oats, rye, barley, wheatberries, whole quinoa, amaranth, teff, whole grain pasta, puffed whole grain cereals. A health food store bulk section is a great place to look for hamster grains. If hamsters are ill or elderly, baby food sometimes gets them to eat. Fresh foods like veggies and tofu should be removed after a few hours and thrown away.
The hamster needs a bowl big enough to sit in comfortably, as hammies like to sit on top of their food when they eat. The bowl should be sturdy ceramic, and it needs to be rinsed and dried out daily, with excess food thrown out (or to the birds).
Hamsters need fresh water every day, so the bottles they use can be fairly small. They need to have two bottles, because they often become stuck and the hamster cannot go without water. Check the bottles once or twice per day by tapping on the ball to make sure water can easily come out. Also check the bedding under the bottles to make sure the bottles are not leaking. Dwarf hamsters with diabetes will consume massive amounts of water. This is an early clue that your dwarf may have diabetes. If the cage is much wetter than usual or is moldy, this is also a sign of diabetes. Diabetic dwarfs must have access to lots of water as they need it to help flush their kidneys, which are required to work hard to cope with the diabetes.
Weekly, the bowl and water bottles need to be washed with mild soap and rinsed well.
Hamsters should not have salt licks or mineral wheels.
Hamsters should never have store bought treats, (with the exception of treats from Oxbow), as they contain too much sugar. They should never have cookies, sticky foods, honey, chocolate, soda, avocados or most people food. They can have nuts or seeds. Dwarfs without diabetes can have a tiny piece of fruit the size of a baby pinkie nail once a week maximum. Diabetics should never have fruit, carrots, beets or peas (any sweet veggie). If hamsters start to gain too much weight, especially diabetics, eliminate seeds from their diet until the weight is lost, and then add back in moderately.
Hamsters are master climbers and escape artists. In spite of their tiny size, in nature they have a five-mile range, so any housing we supply for them is going to be too small. Get the largest house you can possible afford and take care of. The minimum for a hamster house is 3 levels, 12″ wide, by 2 feet long, by 2 feet high. Anything smaller is inhumane and will lead to cage aggression and biting. The cage sides should be sturdy metal wire or glass, not plastic, since hamsters will happily chew out of a plastic cage in a single night. Plastic toys and tubes can be used inside of a cage, but not as a means of containing hamsters. Wires should be ¼" apart maximum, and smaller for baby hamsters. The cage bottom should be solid, not bars, and all wire floor surfaces should be covered with cardboard or paper, to make cleaning easier and prevent injuries. Babies should have solid walls and not wires, as they will walk out from between the wires. The cage needs to be placed away from direct sunlight and sources of heat, which can cause the hammies to overheat while they sleep, and away from drafts, which contribute to illness. Hamsters should not be kept in children's bedrooms or anywhere accessible to children without adult supervision.
Hamsters must run many miles (yes, miles) every day or they will develop cage paralysis. This means they must have a wheel at least 5″ in diameter at all times. Smaller wheels are alright for babies, but not when the hammies are full grown. The wheel must have a solid bottom or fine mesh, not rungs. Wheels with rungs break hamster legs and should never be used. Make sure the wheel will be easy to clean. A detachable wheel that is not connected to the cage is best. Hamsters are nocturnal, so check the wheel before you buy to make sure the sound of running will not disturb your sleep. Vegetable oil can be used to grease the joint to decrease squeaking or sounds.
Hamster balls are a great way for the hamster to get free time to explore and get exercise. The ball should be about 5″ in diameter. Make sure to always tape the ball shut with fresh tape or the hammie will escape. Hamsters should have daily ball time in 20-minute sessions. Hamsters will generally let you know when they are bored in the ball, because they will stop to eat, groom or sleep. When they do, take them out of the ball. Listen while your hammie is in the ball to make sure they are not trapped in a corner or by a cord. If there are children in the house, make absolutely sure that they never kick or throw the ball with the hamster in it, as this will kill the hamster. Young children should not handle the hamster ball ever. Diabetic hamsters or hamsters starting to develop diabetes may not like the ball, since they do not have access to water while inside it. Do not force them into it if they resist.
Hamsters need a paper-based bedding, such as Carefresh, Paper Shavings, SoftSorbent, Yesterdays News or Cagetech. Cedar bedding is deadly. Pine bedding is potentially harmful. Aspen may be fine, but why chance it? Use paper bedding, about three inches deep so the hammies can burrow. In winter, provide extra bedding to ensure the hammie stays warm enough, and consider putting towels or blankets around the bottom and sides of the cage to ensure warmth. Never use any hamster fluff or cotton bedding material, as hammies can ingest it and die. Use paper towel, toilet paper, or paper napkins torn into strips for the hammies to make their nests. Tiny boxes (without tape or plastic parts) or toilet tubes make wonderful hammie hideaways. The cage needs to be cleaned weekly, unless the hammie has diabetes, in which case it needs to be checked for moisture daily, and cleaned. The mold that grows on wet hamster bedding is highly toxic. Leaving a hamster in a filthy cage is animal cruelty. Don't force your hamster to live in filth. The cage should be cleaned only with white vinegar or mild soap and water, no harsh cleaners. If the hamster has been ill, you can use bleach to disinfect, but only when the hamster is far enough away to be unaffected by the fumes. Hamsters are easily harmed by airborne chemical cleaners and other household chemicals. If you use them in your home, move the hammies to a safe, fume-free area before using the chemicals. Some hamsters will use hamster litter boxes or Hamster Potty. If you use them, make sure to use only hamster litter by Hamster Potty or Small Animal Litter by Kaytee, never cat litter. If your hamster is ever dirty it is because s/he is sick or the cage is dirty. Hamsters clean themselves and should never be bathed. If they are ill and need to be cleaned, use a warm damp cloth and carefully dry the hammie with a soft towel. Keep them warm while they dry completely.
Toys and Hideaways:
Plastic pigloos, plastic tubes, plastic toys, wooden houses, cardboard boxes and tubes (plastic tape removed), are all fine. Clean them weekly when the cage is cleaned and throw them away if they get dirty or splintered. Snack Shaks are not recommended for dwarfs because they contain sugar.
Chew Toys:
Hamsters need to wear down and sharpen their teeth constantly, so they need to have wire bars or wooden chews available to chew on. Apple twigs or willow chews seem the most popular.
Veterinary Care:
Hamsters deserve medical care, just as every other living being does. The "cost" of an animal should never determine its right to a long healthy life. Find a dwarf hamster vet before you need one. Usually with a hamster this will need to be a late night vet, because that is when a change in health or behavior is noticeable in these nocturnal animals. By the time a hamster seems ill, they are generally very ill and need prompt medical care. Never use Dritail, because a hamster with wet tail (diarrhea) should be rushed to a vet for rehydration (injection of Lactated Ringers solution) and medicine immediately, if s/he is to survive. Use the skin pinch test regularly to determine if your hamster needs rehydration. Gently pinch the skin between the shoulders and release it. If it stays up in a tent or retracts back to normal shape slowly the hamster is incredibly dehydrated. Use this test daily on diabetic hamsters. Keep unflavored children's Pedialyte in the house in case of emergencies. If you can get your hamster to drink some on the way to the vet it may save the hamster's life.
Do the pinch test when the hammie is healthy so you have something to compare it to in case your hammie gets sick. Be aware of your hamster's normal eating, drinking, pooping, peeing, sleeping and activity patterns so that you can tell when they change. Inspect your hammie on a weekly basis to help catch changes early. Common dwarf hamster illnesses can include diabetes, kidney problems, wet tail, dehydration, malocclusion (overgrowth of the teeth), cheek pouch impaction (something stuck in the pouch), upper respiratory infections, broken bones, mites, cuts, abscesses, eye injury, fungus, and tumors. All of these conditions, including diabetes and tumors, are treatable when caught early. If you ever feel like your hamster is not acting normally, trust your instincts and get to a vet immediately. Please check the Dwarf Hamster Diabetes care sheet for additional information on warning signs, testing and treating diabetic dwarfs.


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Horizon Counseling was founded in 2008, and is located at 2156 Wooddale Blvd in Baton Rouge.
Horizon Counseling is located at 2156 Wooddale Blvd, Baton Rouge, LA. This location is in the Lobdell/Woodale neighborhood. This business specializes in Other Organizations and Social Services.


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Short Courses: October 29
Meeting: October 30-31
The DIA Annual Canadian Meeting will deliver a comprehensive overview of the current bio-pharma and device landscape in Canada, while sharing insights into Canada's broader role in global healthcare product development. From policy updates and priorities shared directly from Health Canada, to sessions on international work sharing and partnerships to key regulatory and clinical considerations for drugs and devices, you will have the exclusive opportunity to address the current issues and opportunities in Canada and across the globe.
Bringing together key stakeholders from the drug (innovator and generic/biosimilar)/, device and Patient Self Care industries, regulatory agencies, and academia, this meeting will discuss/analyze the relevant challenges and opportunities for professionals working in the field in Canada.
This year's meeting will feature preconference short courses, plenary sessions, multi-track breakout sessions and multiple networking opportunities.
Travel Once, Learn Twice!
This year the DIA Annual Canadian Meeting will be co-located with DIA's Canadian Pharmacovigilance and Risk Management Conference. Maximize your education and time by attending both! Save* $150 when you register for both!
*You must register for both events at the same time.
Content Preview Webinar
What to Expect When You're Inspected | September 24 | 11:00AM-12:00PM ET
Gain insight on the most common regulatory agencies expectations and discuss how to prepare for and manage the actual inspection and learn follow-up activities required for close-out, as well as real-life lessons learned through being involved and conducting audits.
On-Demand Webinar
Plain Language Labeling for Over-the-Counter Drugs: Implementing Health Canada's Guidance for Industry
This webinar will review Health Canada's requirements for Plain Language Labeling (PLL) for over-the-counter medicines, which just came into force in June 2017. We will walk through key recently finalized and revised guidance documents to help industry comply with these requirements and identify strategies to help industry add Drug Facts Tables to packaging while minimizing the need for packaging increases.
Learning objectives
At the conclusion of this meeting,, participants should be able to:
- Describe the current and evolving regulatory environment in Canada
- Summarize methods and approaches in various aspects of clinical trials, patient engagement, and market access
- Discuss more in-depth, approaches on international harmonization, worksharing, and adoption of guidelines
- Review the various levels of transparency and post-market activities that are underway
Program Committee
Karen Feltmate • President
Marc F. Poitras, PhD, MBA • Scientific Manager, Marketed Pharmaceuticals and Medical Devices Bureau
Health Canada, Canada
Marilena Bassi, MA • Director of the Bureau of Policy
Health Canada, Canada
Lisa Chartrand • Director, Regulatory Affairs and Quality Management
Hoffmann-La Roche Limited, Canada
Loretta Del Bosco • Director, Regulatory Affairs Quality Assurance Operations
AbbVie Corporation, Canada
Fiona Frappier, PhD • Senior Policy Analyst
Health Canada, Canada
Lorella Garofalo, PhD • Director, Regulatory Affairs; Worldwide Safety and Regulatory-Innovative
Pfizer Canada Inc, Canada
Melissa Hunt, MSc • Acting Director
Health Canada, Canada
Keith McIntosh • Executive Director, Scientific & Regulatory Affairs
Innovative Medicines Canada, Canada
Rania Mouchantaf, PhD • Manager
Marketed Health Product Directorate, Health Canada, Canada
Lissa Murseli • Manager
Health Canada, Canada
Polina Ostrovsky, MPH • Policy Analyst
Health Canada, Canada
Kristin Willemsen, MS • Director of Scientific & Regulatory Affairs
Consumer Health Products Canada, Canada
Ashley Zakhem • Policy Analyst
Health Canada, Canada
Contact us
Registration Questions?Send Email
Preconference Short Courses
Policy and Regulatory Development at the Health Products and Food Branch (HPFB): From Conception to Realization and the Role of Stakeholders
Regulatory Renewal: Statistical Principles as Part of Regulatory Decision-Making
Co-Located Conference
Canadian Pharmacovigilance and Risk Management Strategies Conference
*Save $150 when you register for both at the same time!
Content Preview Webinar
What to Expect When You're Inspected
September 24 | 11:00AM-12:00PM ET


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|more about hitched
1 definition found From Webster's Revised Unabridged Dictionary (1913) [web1913]: Hitch \Hitch\, v. t. [imp. & p. p. {Hitched}; p. pr & vb n. {Hitching}.] 1. To hook; to catch or fasten as by a hook or a knot; to make fast unite, or yoke; as to hitch a horse, or a halter. 2. To move with hitches; as he hitched his chair nearer. {To hitch up}. a To fasten up b To pull or raise with a jerk; as a sailor hitches up his trousers. c To attach, as a horse, to a vehicle; as hitch up the gray mare. [Colloq.]
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There are two questions to ask when assessing whether the U.S. should intervene in Syria: Is there a legitimate national security interest at risk here? And if so, is U.S. intervention in Syria the best approach to protect our interests?
The answer to the first question is a "maybe." International conventions such as the Geneva Protocol from 1925 (signed by Syria 1968) prohibit the use of Weapons of Mass Destruction. The use of Weapons of Mass Destruction (especially by a government against its own population) is reprehensible and threatens not only regional stability, but the well-being of people around the globe.
However, sweeping statements by our own politicians such as drawing "red lines" for foreign policy doctrine might threaten national security even more than the current turmoil in the Middle East. Rather than empower the U.S. to respond to difficult situations, such statements narrow tactical and military options, and have caused credibility problems in the past such as when Reagan stated the U.S. would not withdraw from Lebanon.
President Obama's "red line" claim has put him in a difficult position: If Congress does not follow his recommendation and deliver upon his previous threats, Obama's credibility is damaged. As tough of a loss as that may be for the President, it would be a victory for the U.S. One of the great differences between the U.S. and those countries threatening our security is that no single person can decide the fate of the entire nation. Future U.S. Presidents should come to finally understand that ex-ante military doctrines are not theirs to set, and they should consult Congress before declaring how the country will react to particular actions.
The move of President Obama to involve Congress in deciding whether to intervene in Syria or not was the right thing to do. Presenting this move as a surprise and not involving Congress from the very beginning is the actual scandal and exemplary of the lack of respect for our tripartite system of checks and balances cultivated by this administration.
As for the question of whether U.S. intervention is the best approach to stabilize the situation in the Middle East, the answer is a very likely "no." Intervening will lead to a litany of unintended consequences, and likely fail to accomplish its stated purpose of sending a statement to Assad and other regimes in the region and around the world that Weapons of Mass Destruction will not be tolerated. At this point, intervention would serve the political interests of the President more than the security interests of the U.S.
It is not about isolationism but about being aware of the unintended consequences of interventionism. Many problems in the Middle East can be at least be partially seen as unintended consequences of former interventions, military aid, or intelligence campaigns. An entire decade of war has not stabilized the region at all but rather brought more instability, political uncertainty, and terror to the Middle East and Northern Africa.
Claims by some that less military intervention abroad means being disconnected to other cultures or indifferent to atrocities overseas are just not correct. The notion of not creating bigger fires in the Middle East has nothing to do with isolationism practiced in the early 20th, century but with a 21st century understanding of the interconnectedness of the world that suggests greater military intervention and greater violence might not lead to peace and stability.
Hawkish Republicans and bellicose Democrats (following the administration) are trying to continue the neoconservative heritage of the past ten years and thus lead us to a second decade of war.
The pro-interventionist alliance of Democrats and Republicans is another illustration how the mainstream parts of both parties try to push for more policing around the world and neglect the people's opinion on these issues. It is now up to the American public, dovish Democrats, and non-interventionist Republicans to prevent another war. Real liberal Democrats are hopefully starting to understand that the Obama administration practices a style of foreign policy which is diametrically opposed to their fundamental ideas.
It's about time to finally overcome the neoconservative direction of U.S. foreign policy. Congress and the President have to understand that stability in the Middle East can't be brought by additional U.S.-led intervention.


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10 and while Apollonius was going up with his armed forces to seize the money, angels on horseback with lightning flashing from their weapons appeared from heaven, instilling in them great fear and trembling.
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Rogue Community College tax credit program
To request course information, please complete this form. You may receive information from just one program, or several. Before making decisions about your future, compare programs carefully.
Think about what career is best suited for you, and where you want to study. Request more information now.
Think about what career is best suited for you, and where you want to study. Request more information now.
To request course information, please complete this form. Before making decisions about your future, compare programs carefully.
Think about what career is best suited for you, and where you want to study. Request more information now.
Think about what career is best suited for you, and where you want to study. Request more information now.
To request course information, please complete this form.
Think about what career is best suited for you, and where you want to study. Request more information now.
Think about what career is best suited for you, and where you want to study. Request more information now.
Learn about Rogue Community College tax credit program, registering in a technical training program, and taking tests for free online. Which college degrees give you the best chances of finding employment after graduation? Given the breadth of business specialties, you may find your niche in management, human resources, sales, or advertising. Technical training is only the first step towards a rewarding career. If you complete the tax credit program, for example, there are a variety of concentrations that may appeal to you, such as tax credit management, tax audit screening, or tax planner training. Please use the form above to request admissions info for Rogue Community College.
The Internal Revenue Service (IRS) is a bureau of the Department of the Treasury. In the 2015 fiscal year, the IRS processed 240 million tax returns and collected roughly $3.3 trillion in revenue, spending 35¢ for every $100 it collected. Income tax credits are available to help with estate planning. The Earned Income Tax Credit (EITC or EIC) provides a subsidy for low-income, working families. The EITC is a refundable tax credit, which means that it can reduce your tax liability beyond zero and pay out the remaining amount as a tax refund. Because of this, people who aren't normally required to file a tax return may want to do so in order to reap the estate planning benefits of the earned income tax credit.
Although the IRS prefers that you find a way to pay your taxes in full, if you are unable to pay on time, you may wish to consult a tax planner, so as not to trigger a tax audit. With an installment agreement, you gradually pay off your tax liability by making monthly payments. An offer in compromise (OIC) allows you to settle your IRS tax debt for less than the full amount owed. With an OIC, you offer to pay a portion of your taxes right away and the IRS agrees to drop the remaining balance. If the IRS determines that you are unable to pay your tax debt, your account may be reported as not collectible. This means that the IRS will temporarily delay collection until your estate planning situation improves. However, your tax debt will continue to increase because the IRS charges ongoing penalties and interest.
Budget & Policy Analyst / Budget & Polic...
City of Norfolk, VA
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SaaS software company
Business Analyst w/Light Project Management. Fast growing SaaS company in a specialized aviation vertical scheduling and management of corporate business jets..
7 days ago CITY CARRIER ASSISTANT
United States Postal Service
Subject to business needs. Collects mail from street letter boxes and accepts letters from mailing from customers.
4 days ago Customer Account Representative I
GM Financial
Develop effective internal and external business relationships. Support center and company initiatives and demonstrate an understanding of business needs.
4 days ago Crew - Site 11696 - North Hills
JAE Restaurant Group
This person is also responsible for a visual check of all cooked products on the grill to see that proper quality standards are maintained.
5 hours ago
Certificate Courses Online
It isn't necessary to be enrolled in a degree program in order to sign up for online courses. You can audit classes at your own pace without the pressure of a classroom. If you remain true to your career interests, your overall earnings will increase as you gain experience. In fact, many self-made entrepreneurs started working in a technical field that they were good at.
Your business plan is a snapshot of your financial goals. Before launching a business start-up, research your target industry and competitors, and if you need outside funding, give special attention to financial projections. Make use of templates online to assist you in writing an original business plan. Working capital is always in short supply, but has to be enough to cover the first six months at a minimum. To begin, you must obtain a Tax ID number, register your business name, and seek a business license.
Online Tests - Free Practice!This section offers practice tests in a variety of business areas. Each of the following multiple-choice tests has 10 questions to work on. No sign-up is required, just straight to the test.
Other colleges near Grants Pass, Oregon:Take a few moments to browse other colleges and universities near Grants Pass. It's a good idea to compare all schools in your target area, as well as consider taking some of your classes online. By continuing your education, you can improve your salary prospects or train for a more interesting position. Financial aid deadlines are typically set well in advance of regular admission dates, so be sure to apply early. You may request free information from several different schools below, without making a commitment.
|College Guide
|In-state Tuition
|Out-of-state Tuition
|Student Body Size
|Request Info
|Rogue Community College
Grants Pass, OR
|$ (low)
|$ (low)
|Program Info
|University of Portland
Portland, OR
|Program Info
|Western Seminary
Portland, OR
|$ (low)
|$ (low)
|Program Info
|Lane Community College
Eugene, OR
|$ (low)
|very large
|Program Info
|Linfield College
McMinnville, OR
|Program Info
|Central Oregon Community College
Bend, OR
|$ (low)
|Program Info
|Clatsop Community College
Astoria, OR
|$ (low)
|Program Info
|Blue Mountain Community College
Pendleton, OR
|$ (low)
|Program Info
|Clackamas Community College
Oregon City, OR
|$ (low)
|Program Info
|Pacific Northwest College of Art
Portland, OR
|Program Info
|Columbia Gorge Community College
The Dalles, OR
|$ (low)
|$ (low)
|Program Info
|Treasure Valley Community College
Ontario, OR
|$ (low)
|$ (low)
|Program Info
Business & Medical JobsAs the economy improves, many firms are beginning to hire. Companies are in need of candidates that can fill a particular job position, so set up an introductory meeting to ask questions about the firm's history, and current business opportunities. They are watching for those candidates who are trying harder than others, thus your first task is to set yourself apart. Hiring managers typically post new jobs on targeted job sites, which we have sampled. Browse current job openings below, by clicking on the type of position that you'd like to pursue.
|Links below are updated hourly:
|Starting Salary
(up to)
|10 Year Salary
(up to)
|Casino Dealers
|Computer Programmers
|EMT, Paramedics
|Financial Analysts
|Flight Attendants
|Graphic Design
|Hotel Jobs
|Human Resources
|Private Investigators
|Property Management
|Public Relations
|Retail Sales
|Teaching Jobs
|Website Design
Rogue Community College tax credit programApply to several colleges and universities simultaneously, and if you have the grades and test scores, give yourself a fighting chance to get into a top-rated program by doing something outstanding in high school or community college. It isn't as hard as you might think to get an article written in your local newspaper. An advanced degree will stick with you for a long time, so apply yourself and work hard for a few years, graduating from the best school that you can get into.
Rogue Community College tax credit program
3345 Redwood Hwy
Grants Pass, OR 97527
3345 Redwood Hwy
Grants Pass, OR 97527