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Just enter your email and we’ll take care of the rest:. Please enter a valid email address. Please select a newsletter. Sign up. Firaxis delays Marvel’s Midnight Suns, maybe until Khalid , People spent much less time watching gaming streams this spring, report says By K. Holt , Bonifacic , People spent much less time watching gaming streams this spring, report says Facebook Gaming saw a far bigger decline than Twitch and YouTube Gaming, according to Streamlabs and Stream Hatchet.

We have two newsletters, why not sign up for both? Just enter your email and we’ll take care of the rest: Please enter a valid email address Please select a newsletter Subscribe. A promotional video was issued for the song as well. The group played several shows, covering Bowie’s Ziggy Stardust -era songs and released one internet-only album since deleted.

Vivian Campbell has played with two side bands in recent years, Clock and the Riverdogs , and recorded a solo album, Two Sides of If , released in They have released two studio albums of covers, one of original material and one live album since their incarnation in The band pays tribute to Dio by playing songs from their original tenure in the band and released an album titled Heavy Crown in February Phil Collen formed a blues project by the name of Delta Deep with vocalist Debbi Blackwell Cook which released an eponymous debut in From Wikipedia, the free encyclopedia.

British rock band. This article is about the band. For their self-titled album, see Def Leppard album. Glam metal hard rock heavy metal arena rock pop rock.

Vocalist Joe Elliott left and bassist Rick Savage right , pictured in , are the sole remaining original members of Def Leppard. See also: Phil Collen and Pyromania album. See also: Rick Allen drummer. See also: Hysteria Def Leppard album. Main articles: Adrenalize , Retro Active , and Slang album.

Def Leppard album. Main article: Songs from the Sparkle Lounge. Main articles: Mirror Ball Tour and Viva! Current members Joe Elliott — lead vocals, occasional rhythm guitar, keyboards, piano —present Rick Savage — bass guitar, keyboards, backing vocals —present Rick Allen — drums, percussion, backing vocals —present Phil Collen — guitars, backing vocals —present Vivian Campbell — guitars, backing vocals —present Former members Tony Kenning — drums — Pete Willis — guitars, backing vocals — Steve Clark — guitars, backing vocals —; until his death.

Main article: List of awards and nominations received by Def Leppard. Main article: Def Leppard discography. The New Zealand Herald. Retrieved 27 September Hysteria with Def Leppard’s Joe Elliott”. Sheffield Star. Archived from the original on 21 December Retrieved 20 December Retrieved 1 March Retrieved 8 January Rock on the Net.

Retrieved 22 July Retrieved 25 November Planet Rock. Retrieved 13 December Music Sales Group. Rolling Stone. Archived from the original on 29 October Turnaround, ISBN Jeffrey Def Leppard: Arena Rock Band. Steve Clark Biography Allmusic.

The Billboard book of number one hits 4th ed. New York: Billboard Books. ISBN The Guardian. Retrieved 7 October The N. Iron Pages Books 3 ed. Berlin, Germany: I. Retrieved 17 April Official Charts Company. Retrieved 13 August Oxford Music Online. Oxford University Press. Hachette UK. Retrieved 29 April Retrieved 27 March Retrieved 28 May Ultimate Classic Rock. Cover Story. Retrieved 20 February Archived from the original on 11 September Retrieved 17 November Omnibus Press.

Retrieved 5 August Spin magazine. February The Tombstone Tourist: Musicians. Retrieved 30 March The Rough Guide to Rock. ProQuest Retrieved 4 February Retrieved 15 December Archived from the original on 12 October Retrieved 23 October Guitar Center’s Hollywood Rockwalk.

Retrieved 23 December Retrieved 28 March Retrieved 27 April Archived from the original on 18 December Archived from the original on 14 December Retrieved 3 February Retrieved 3 May Archived from the original on 23 February Retrieved 23 February Archived from the original on 5 March Retrieved 7 March Archived from the original on 24 August Retrieved 13 July Archived from the original on 20 March Triple M.

Archived from the original on 1 February Retrieved 26 January Archived from the original on 13 February Retrieved 10 February Archived from the original on 12 March Retrieved 11 March Retrieved 12 November The Hollywood Reporter.

King Features. Retrieved 5 June Retrieved 27 June Retrieved 15 November Virgin media, 10 June Retrieved 3 September Archived from the original on 12 February Retrieved 12 February Grand Forks Herald. Retrieved 28 August Big, Winger Singers Step In”. Retrieved 30 March — via Twitter. Live from Detroit”.

Retrieved 3 June Retrieved 19 January Retrieved 25 October Retrieved 14 December Retrieved 18 December Def Leppard. Def Leppard Official Website. Retrieved 10 June Retrieved 16 March Retrieved 29 May Retrieved 19 March Tuscaloosa News. Guitar World. Archived from the original on 4 October Retrieved 15 April Retrieved 9 October Archived from the original on 21 January Retrieved 14 September Retrieved 13 February Retrieved 21 October Archived from the original on 27 September Retrieved 30 April That Metal Show.

Season 3. Episode 5. Archived from the original on 26 May Retrieved 2 October Archived from the original on 31 May Archived from the original on 31 March Yorkshire Post. Retrieved 4 November Retrieved 2 April Retrieved 22 April The New York Times. Archived from the original on 23 June U Discover Music. Retrieved 2 February Brave Words.

Metal Head Zone. Retrieved 20 January

In his biography, Cousins claims that he did his best Laurence Olivier impersonation for the song’s intro. The album received mostly positive reviews. He also stated that the band’s ambition “would never allow [them] to be tunnel-visioned”, but he concluded that On Through the Night “can be categorized as a grower of an album since the more superficial elements that would appeal to the mainstream will initially distract some listeners from what is actually an incredibly tight musical and vocal performance.

Most of the songs on the album were dropped from the band’s live setlists after , although “Rock Brigade” and “Wasted” would see periodic revivals after Also, the non-album track from the same era entitled “Good Morning Freedom” would be played live in during the opening to the “Viva Hysteria” shows. From Wikipedia, the free encyclopedia. Def Leppard. Startling Studios Ascot, Berkshire. Side one No. Title Writer s Solos Length 1.

Clark Elliott Savage Willis. Side two No. Title Writer s Solos Length 7. Official Charts Company. Retrieved 13 August Retrieved 30 April Rolling Stone. A weekly roundup of our favorite tech deals.

A daily dose of the news you need. Just enter your email and we’ll take care of the rest:. Please enter a valid email address.

Please select a newsletter. Sign up. Firaxis delays Marvel’s Midnight Suns, maybe until Khalid , Here is a solution:. The innermost statements, forward and turn are indented twice to show that they are inside the for loop, which is inside the function definition.

Wrapping a piece of code up in a function is called encapsulation. One of the benefits of encapsulation is that it attaches a name to the code, which serves as a kind of documentation. Another advantage is that if you re-use the code, it is more concise to call a function twice than to copy and paste the body! Adding a parameter to a function is called generalization because it makes the function more general: in the previous version, the square is always the same size; in this version it can be any size.

The next step is also a generalization. Instead of drawing squares, polygon draws regular polygons with any number of sides. The next step is to write circle , which takes a radius, r , as a parameter. Here is a simple solution that uses polygon to draw a sided polygon:. Thus, polygon draws a sided polygon that approximates a circle with radius r.

One limitation of this solution is that n is a constant, which means that for very big circles, the line segments are too long, and for small circles, we waste time drawing very small segments. One solution would be to generalize the function by taking n as a parameter.

This would give the user whoever calls circle more control, but the interface would be less clean. The interface of a function is a summary of how it is used: what are the parameters? What does the function do? And what is the return value? In this example, r belongs in the interface because it specifies the circle to be drawn. Rather than clutter up the interface, it is better to choose an appropriate value of n depending on circumference :.

When I wrote circle , I was able to re-use polygon because a many-sided polygon is a good approximation of a circle. One alternative is to start with a copy of polygon and transform it into arc. The result might look like this:. We could generalize polygon to take an angle as a third argument, but then polygon would no longer be an appropriate name!

This process—rearranging a program to improve interfaces and facilitate code re-use—is called refactoring. Once you start coding, you understand the problem better. Sometimes refactoring is a sign that you have learned something.

A development plan is a process for writing programs. The steps of this process are:. Once you get the program working, identify a coherent piece of it, encapsulate the piece in a function and give it a name. Repeat steps 1—3 until you have a set of working functions. Copy and paste working code to avoid retyping and re-debugging.

Look for opportunities to improve the program by refactoring. For example, if you have similar code in several places, consider factoring it into an appropriately general function. This approach lets you design as you go along. Documentation can be accessed in the REPL or in a notebook by typing? Docstrings are often triple-quoted strings, also known as multiline strings because the triple quotes allow the string to span more than one line. A docstring contains the essential information someone would need to use this function.

It explains concisely what the function does without getting into the details of how it does it. It explains what effect each parameter has on the behavior of the function and what type each parameter should be if it is not obvious. Writing this kind of documentation is an important part of interface design. A well-designed interface should be simple to explain; if you have a hard time explaining one of your functions, maybe the interface could be improved. An interface is like a contract between a function and a caller.

The caller agrees to provide certain parameters and the function agrees to do certain work. For example, polyline requires four arguments: t has to be a turtle; n has to be an integer; len should be a positive number; and angle has to be a number, which is understood to be in degrees. These requirements are called preconditions because they are supposed to be true before the function starts executing. Conversely, conditions at the end of the function are postconditions.

Postconditions include the intended effect of the function like drawing line segments and any side effects like moving the turtle or making other changes. Preconditions are the responsibility of the caller.

If the caller violates a properly documented! If the preconditions are satisfied and the postconditions are not, the bug is in the function. If your pre- and postconditions are clear, they can help with debugging. The process of replacing something unnecessarily specific like a number with something appropriately general like a variable or parameter. A description of how to use a function, including the name and descriptions of the arguments and return value.

The process of modifying a working program to improve function interfaces and other qualities of the code. You can do the arithmetic by hand or add print statements to the code. The version of arc in Refactoring is not very accurate because the linear approximation of the circle is always outside the true circle.

As a result, the turtle ends up a few pixels away from the correct destination. My solution shows a way to reduce the effect of this error.

Read the code and see if it makes sense to you. If you draw a diagram, you might see how it works. Write an appropriately general set of functions that can draw flowers as in Turtle flowers. Write an appropriately general set of functions that can draw shapes as in Turtle pies. The letters of the alphabet can be constructed from a moderate number of basic elements, like vertical and horizontal lines and a few curves.

Design an alphabet that can be drawn with a minimal number of basic elements and then write functions that draw the letters. The main topic of this chapter is the if statement, which executes different code depending on the state of the program. But first I want to introduce two new operators: floor division and modulus. For example, suppose the run time of a movie is minutes. You might want to know how long that is in hours. Conventional division returns a floating-point number:.

Floor division returns the integer number of hours, rounding down:. The modulus operator is more useful than it seems. Also, you can extract the right-most digit or digits from a number. A boolean expression is an expression that is either true or false. Although these operations are probably familiar to you, the Julia symbols are different from the mathematical symbols.

Conditional statements give us this ability. The simplest form is the if statement:. The boolean expression after if is called the condition. If it is true, the indented statement runs. If not, nothing happens. Statements like this are called compound statements. There is no limit on the number of statements that can appear in the body. The syntax looks like this:. If the remainder when x is divided by 2 is 0, then we know that x is even, and the program displays an appropriate message.

If the condition is false, the second set of statements runs. Since the condition must be true or false, exactly one of the alternatives will run. The alternatives are called branches , because they are branches in the flow of execution. Sometimes there are more than two possibilities and we need more than two branches. One way to express a computation like that is a chained conditional :. Again, exactly one branch will run.

There is no limit on the number of elseif statements. Each condition is checked in order. If the first is false, the next is checked, and so on. If one of them is true, the corresponding branch runs and the statement ends.

Even if more than one condition is true, only the first true branch runs. One conditional can also be nested within another.

We could have written the example in the previous section like this:. The outer conditional contains two branches. The first branch contains a simple statement. The second branch contains another if statement, which has two branches of its own. Those two branches are both simple statements, although they could have been conditional statements as well.

Although the non-compulsory indentation of the statements makes the structure apparent, nested conditionals become difficult to read very quickly.

It is a good idea to avoid them when you can. Logical operators often provide a way to simplify nested conditional statements. For example, we can rewrite the following code using a single conditional:. It is legal for one function to call another; it is also legal for a function to call itself.

It may not be obvious why that is a good thing, but it turns out to be one of the most magical things a program can do. For example, look at the following function:. If n is 0 or negative, it outputs the word, “Blastoff! A function that calls itself is recursive ; the process of executing it is called recursion. For simple examples like this, it is probably easier to use a for loop. But we will see examples later that are hard to write with a for loop and easy to write with recursion, so it is good to start early.

In Stack Diagrams , we used a stack diagram to represent the state of a program during a function call. The same kind of diagram can help interpret a recursive function.

For a recursive function, there might be more than one frame on the stack at the same time. As usual, the top of the stack is the frame for Main. It is empty because we did not create any variables in Main or pass any arguments to it.

The four countdown frames have different values for the parameter n. It does not make a recursive call, so there are no more frames. If a recursion never reaches a base case, it goes on making recursive calls forever, and the program never terminates.

This is known as infinite recursion , and it is generally not a good idea. Here is a minimal program with an infinite recursion:. In most programming environments, a program with infinite recursion does not really run forever. Julia reports an error message when the maximum recursion depth is reached:.

This stacktrace is a little bigger than the one we saw in the previous chapter. When the error occurs, there are recurse frames on the stack! If you encounter an infinite recursion by accident, review your function to confirm that there is a base case that does not make a recursive call.

And if there is a base case, check whether you are guaranteed to reach it. The programs we have written so far accept no input from the user. They just do the same thing every time. Julia provides a built-in function called readline that stops the program and waits for the user to type something.

Before getting input from the user, it is a good idea to print a prompt telling the user what to type:. A semi-colon ; allows to put multiple statements on the same line. In the REPL only the last statement returns its value. If you expect the user to type an integer, you can try to convert the return value to Int64 :. When a syntax or runtime error occurs, the error message contains a lot of information, but it can be overwhelming.

The most useful parts are usually:. Syntax errors are usually easy to find, but there are a few gotchas. In general, error messages indicate where the problem was discovered, but the actual error might be earlier in the code, sometimes on a previous line.

The same is true of runtime errors. Suppose you are trying to compute a signal-to-noise ratio in decibels. The formula is. To find the error, it might be useful to print the value of ratio, which turns out to be 0. The problem is in line 3, which uses floor division instead of floating-point division. A statement that consists of a header and a body. The body is terminated with the keyword end. Eventually, an infinite recursion causes a runtime error.

Write a script that reads the current time and converts it to a time of day in hours, minutes, and seconds, plus the number of days since the epoch.

If you are given three sticks, you may or may not be able to arrange them in a triangle. For example, if one of the sticks is 12 inches long and the other two are one inch long, you will not be able to get the short sticks to meet in the middle. For any three lengths, there is a simple test to see if it is possible to form a triangle:.

If any of the three lengths is greater than the sum of the other two, then you cannot form a triangle. Otherwise, you can. Write a function that prompts the user to input three stick lengths, converts them to integers, and uses istriangle to check whether sticks with the given lengths can form a triangle.

What is the output of the following program? Draw a stack diagram that shows the state of the program when it prints the result. Write a docstring that explains everything someone would need to know in order to use this function and nothing else. Read the following function and see if you can figure out what it does see the examples in Case Study: Interface Design. Then run it and see if you got it right. The Koch curve is a fractal that looks something like A Koch curve. Write a function called koch that takes a turtle and a length as parameters, and that uses the turtle to draw a Koch curve with the given length.

Write a function called snowflake that draws three Koch curves to make the outline of a snowflake. The Koch curve can be generalized in several ways. Many of the Julia functions we have used, such as the math functions, produce return values. In this chapter you will learn to write fruitful functions. Calling the function generates a return value, which we usually assign to a variable or use as part of an expression.

The functions we have written so far are void. Speaking casually, they have no return value; more precisely, their return value is nothing. In this chapter, we are finally going to write fruitful functions. The first example is area , which returns the area of a circle with the given radius:. We have seen the return statement before, but in a fruitful function the return statement includes an expression. The value returned by a function is the value of the last expression evaluated, which, by default, is the last expression in the body of the function definition.

On the other hand, temporary variables like a and explicit return statements can make debugging easier. Sometimes it is useful to have multiple return statements, one in each branch of a conditional:. As soon as a return statement runs, the function terminates without executing any subsequent statements.

Code that appears after a return statement, or any other place the flow of execution can never reach, is called dead code. In a fruitful function, it is a good idea to ensure that every possible path through the program hits a return statement. This function is incorrect because if x happens to be 0, neither condition is true, and the function ends without hitting a return statement. If the flow of execution gets to the end of a function, the return value is nothing , which is not the absolute value of 0.

To deal with increasingly complex programs, you might want to try a process called incremental development. The goal of incremental development is to avoid long debugging sessions by adding and testing only a small amount of code at a time. By the Pythagorean theorem, the distance is:.

The first step is to consider what a distance function should look like in Julia. In other words, what are the inputs parameters and what is the output return value?

In this case, the inputs are two points, which you can represent using four numbers. The return value is the distance represented by a floating-point value. But it is syntactically correct, and it runs, which means that you can test it before you make it more complicated.

I chose these values so that the horizontal distance is 3 and the vertical distance is 4; that way, the result is 5, the hypotenuse of a triangle. When testing a function, it is useful to know the right answer.

At this point we have confirmed that the function is syntactically correct, and we can start adding code to the body. The next version stores those values in temporary variables and prints them with the show macro. If so, we know that the function is getting the right arguments and performing the first computation correctly. If not, there are only a few lines to check. Again, you would run the program at this stage and check the output which should be Finally, you can use sqrt to compute and return the result:.

If that works correctly, you are done. The print statements we wrote are useful for debugging, but once you get the function working, you should remove them.

Code like that is called scaffolding because it is helpful for building the program but is not part of the final product. When you start out, you should add only a line or two of code at a time. As you gain more experience, you might find yourself writing and debugging bigger chunks. Either way, incremental development can save you a lot of debugging time. Start with a working program and make small incremental changes. At any point, if there is an error, you should have a good idea where it is.

Once the program is working, you might want to remove some of the scaffolding or consolidate multiple statements into compound expressions, but only if it does not make the program difficult to read. Use incremental development to write a function called hypotenuse that returns the length of the hypotenuse of a right triangle given the lengths of the other two legs as arguments.

Record each stage of the development process as you go. As you should expect by now, you can call one function from within another. Assume that the center point is stored in the variables xc and yc , and the perimeter point is in xp and yp. The first step is to find the radius of the circle, which is the distance between the two points.

We just wrote a function, distance, that does that:. The temporary variables radius and result are useful for development and debugging, but once the program is working, we can make it more concise by composing the function calls:.

Any program ever written could be rewritten using only the language features you have learned so far actually, you would need a few commands to control devices like the mouse, disks, etc.

Proving that claim is a nontrivial exercise first accomplished by Alan Turing, one of the first computer scientists some would argue that he was a mathematician, but a lot of early computer scientists started as mathematicians. Accordingly, it is known as the Turing Thesis. A recursive definition is similar to a circular definition, in the sense that the definition contains a reference to the thing being defined. A truly circular definition is not very useful:.

If you saw that definition in the dictionary, you might be annoyed. If you can write a recursive definition of something, you can write a Julia program to evaluate it.

The first step is to decide what the parameters should be. In this case it should be clear that factorial takes an integer:. Otherwise, and this is the interesting part, we have to make a recursive call to find the factorial of n-1 and then multiply it by n :.

The flow of execution for this program is similar to the flow of countdown in Recursion. If we call fact with the value 3 :. The return value, 1 , is multiplied by n , which is 1 , and the result is returned. The return value, 1 , is multiplied by n , which is 2 , and the result is returned.

The return value 2 is multiplied by n , which is 3 , and the result, 6 , becomes the return value of the function call that started the whole process. Stack diagram shows what the stack diagram looks like for this sequence of function calls. The return values are shown being passed back up the stack. In each frame, the return value is the value of result , which is the product of n and recurse.

In the last frame, the local variables recurse and result do not exist, because the branch that creates them does not run. Julia provides the function factorial to calculate the factorial of an integer number.

Following the flow of execution is one way to read programs, but it can quickly become overwhelming. When you come to a function call, instead of following the flow of execution, you assume that the function works correctly and returns the right result.

In fact, you are already practicing this leap of faith when you use built-in functions. You just assume that they work because the people who wrote the built-in functions were good programmers. The same is true when you call one of your own functions. For example, in Boolean Functions , we wrote a function called isdivisible that determines whether one number is divisible by another. Once we have convinced ourselves that this function is correct—by examining the code and testing—we can use the function without looking at the body again.

The same is true of recursive programs. If you try to follow the flow of execution here, even for fairly small values of n , your head explodes. But according to the leap of faith, if you assume that the two recursive calls work correctly, then it is clear that you get the right result by adding them together. It looks like an infinite recursion.

How can that be? But if n is not an integer, we can miss the base case and recurse forever. In the first recursive call, the value of n is 0. In the next, it is From there, it gets smaller more negative , but it will never be 0. We have two choices. We can try to generalize the factorial function to work with floating-point numbers, or we can make fact check the type of its argument.

We can use the built-in operator isa to verify the type of the argument. The first base case handles nonintegers; the second handles negative integers. In both cases, the program prints an error message and returns nothing to indicate that something went wrong:. If we get past both checks, we know that n is positive or zero, so we can prove that the recursion terminates. This program demonstrates a pattern sometimes called a guardian. The first two conditionals act as guardians, protecting the code that follows from values that might cause an error.

The guardians make it possible to prove the correctness of the code. In Catching Exceptions we will see a more flexible alternative to printing an error message: raising an exception. Breaking a large program into smaller functions creates natural checkpoints for debugging.

If a function is not working, there are three possibilities to consider:. To rule out the first possibility, you can add a print statement at the beginning of the function and display the values of the parameters and maybe their types.

Or you can write code that checks the preconditions explicitly. If the parameters look good, add a print statement before each return statement and display the return value. If possible, check the result by hand.

Consider calling the function with values that make it easy to check the result as in Incremental Development. If the function seems to be working, look at the function call to make sure the return value is being used correctly or used at all! Adding print statements at the beginning and end of a function can help make the flow of execution more visible.

For example, here is a version of fact with print statements:. If you are confused about the flow of execution, this kind of output can be helpful. It takes some time to develop effective scaffolding, but a little bit of scaffolding can save a lot of debugging. A program development plan intended to avoid debugging by adding and testing only a small amount of code at a time.

A programming pattern that uses a conditional statement to check for and handle circumstances that might cause an error. Write a function named ack that evaluates the Ackermann function. Use your function to evaluate ack 3, 4 , which should be What happens for larger values of m and n?

Recursively, a word is a palindrome if the first and last letters are the same and the middle is a palindrome. The following are functions that take a string argument and return the first, last, and middle letters:. Test these functions out.

What happens if you call middle with a string with two letters? One letter? What about the empty string, which is written “” and contains no letters? Write a function called ispalindrome that takes a string argument and returns true if it is a palindrome and false otherwise.

Remember that you can use the built-in function length to check the length of a string. Write a function called ispower that takes parameters a and b and returns true if a is a power of b.

Write a function called gcd that takes parameters a and b and returns their greatest common divisor. This chapter is about iteration, which is the ability to run a block of statements repeatedly. We saw a kind of iteration, using recursion, in Recursion. We saw another kind, using a for loop, in Simple Repetition. But first I want to say a little more about variable assignment. As you may have discovered, it is legal to make more than one assignment to the same variable.

A new assignment makes an existing variable refer to a new value and stop referring to the old value. State diagram shows what reassignment looks like in a state diagram.

At this point I want to address a common source of confusion. But this interpretation is wrong. First, equality is a symmetric relationship and assignment is not. Also, in mathematics, a proposition of equality is either true or false for all time. The third line changes the value of a but does not change the value of b , so they are no longer equal. Reassigning variables is often useful, but you should use it with caution. If the values of variables change frequently, it can make the code difficult to read and debug.

A common kind of reassignment is an update, where the new value of the variable depends on the old. Updating a variable by adding 1 is called an increment ; subtracting 1 is called a decrement.

Computers are often used to automate repetitive tasks. Repeating identical or similar tasks without making errors is something that computers do well and people do poorly. In a computer program, repetition is also called iteration.

We have already seen two functions, countdown and printn , that iterate using recursion. Because iteration is so common, Julia provides language features to make it easier. One is the for statement we saw in Simple Repetition. Another is the while statement. Here is a version of countdown that uses a while statement:. You can almost read the while statement as if it were English. When you get to 0, display the word Blastoff!

The body of the loop should change the value of one or more variables so that the condition becomes false eventually and the loop terminates. Otherwise the loop will repeat forever, which is called an infinite loop. In the case of countdown , we can prove that the loop terminates: if n is zero or negative, the loop never runs.

Otherwise, n gets smaller each time through the loop, so eventually we have to get to 0. The condition for this loop is n! Each time through the loop, the program outputs the value of n and then checks whether it is even or odd.

If it is even, n is divided by 2. For example, if the argument passed to sequence is 3, the resulting values of n are 3, 10, 5, 16, 8, 4, 2, 1. Since n sometimes increases and sometimes decreases, there is no obvious proof that n will ever reach 1, or that the program terminates.

For some particular values of n , we can prove termination. For example, if the starting value is a power of two, n will be even every time through the loop until it reaches 1. The previous example ends with such a sequence, starting with The hard question is whether we can prove that this program terminates for all positive values of n. So far, no one has been able to prove it or disprove it! Rewrite the function printn from Recursion using iteration instead of recursion. In that case you can use the break statement to jump out of the loop.

The loop condition is true , which is always true, so the loop runs until it hits the break statement. Each time through, it prompts the user with an angle bracket. If the user types done , the break statement exits the loop.

Many of the Julia functions we have used, such as the math functions, produce return values. In this chapter you will learn to write fruitful functions. Calling the function generates a return value, which we usually assign to a variable or use as part of an expression. The functions we have written so far are void. Speaking casually, they have no return value; more precisely, their return value is nothing. In this chapter, we are finally going to write fruitful functions. The first example is area , which returns the area of a circle with the given radius:.

We have seen the return statement before, but in a fruitful function the return statement includes an expression. The value returned by a function is the value of the last expression evaluated, which, by default, is the last expression in the body of the function definition.

As soon as a return statement runs, the function terminates without executing any subsequent statements. Code that appears after a return statement, or any other place the flow of execution can never reach, is called dead code. In a fruitful function, it is a good idea to ensure that every possible path through the program hits a return statement. This function is incorrect because if x happens to be 0, neither condition is true, and the function ends without hitting a return statement.

If the flow of execution gets to the end of a function, the return value is nothing , which is not the absolute value of 0. To deal with increasingly complex programs, you might want to try a process called incremental development. The goal of incremental development is to avoid long debugging sessions by adding and testing only a small amount of code at a time. By the Pythagorean theorem, the distance is:. The first step is to consider what a distance function should look like in Julia.

In other words, what are the inputs parameters and what is the output return value? In this case, the inputs are two points, which you can represent using four numbers.

The return value is the distance represented by a floating-point value. But it is syntactically correct, and it runs, which means that you can test it before you make it more complicated. I chose these values so that the horizontal distance is 3 and the vertical distance is 4; that way, the result is 5, the hypotenuse of a triangle. When testing a function, it is useful to know the right answer. At this point we have confirmed that the function is syntactically correct, and we can start adding code to the body.

The next version stores those values in temporary variables and prints them with the show macro. If so, we know that the function is getting the right arguments and performing the first computation correctly. If not, there are only a few lines to check. Again, you would run the program at this stage and check the output which should be Finally, you can use sqrt to compute and return the result:.

If that works correctly, you are done. The print statements we wrote are useful for debugging, but once you get the function working, you should remove them. Code like that is called scaffolding because it is helpful for building the program but is not part of the final product. When you start out, you should add only a line or two of code at a time. As you gain more experience, you might find yourself writing and debugging bigger chunks.

Either way, incremental development can save you a lot of debugging time. Start with a working program and make small incremental changes. At any point, if there is an error, you should have a good idea where it is. Once the program is working, you might want to remove some of the scaffolding or consolidate multiple statements into compound expressions, but only if it does not make the program difficult to read.

Use incremental development to write a function called hypotenuse that returns the length of the hypotenuse of a right triangle given the lengths of the other two legs as arguments. Record each stage of the development process as you go. As you should expect by now, you can call one function from within another. Assume that the center point is stored in the variables xc and yc , and the perimeter point is in xp and yp.

The first step is to find the radius of the circle, which is the distance between the two points. We just wrote a function, distance, that does that:. The temporary variables radius and result are useful for development and debugging, but once the program is working, we can make it more concise by composing the function calls:.

Functions can return booleans, which is often convenient for hiding complicated tests inside functions. We have only covered a small subset of Julia, but you might be interested to know that this subset is a complete programming language, which means that anything that can be computed can be expressed in this language. Any program ever written could be rewritten using only the language features you have learned so far actually, you would need a few commands to control devices like the mouse, disks, etc.

Accordingly, it is known as the Turing Thesis. A recursive definition is similar to a circular definition, in the sense that the definition contains a reference to the thing being defined. A truly circular definition is not very useful:. If you saw that definition in the dictionary, you might be annoyed. If you can write a recursive definition of something, you can write a Julia program to evaluate it. The first step is to decide what the parameters should be. In this case it should be clear that factorial takes an integer:.

Otherwise, and this is the interesting part, we have to make a recursive call to find the factorial of n-1 and then multiply it by n :. The flow of execution for this program is similar to the flow of countdown in Recursion. If we call fact with the value 3 :. The return value, 1 , is multiplied by n , which is 1 , and the result is returned. The return value, 1 , is multiplied by n , which is 2 , and the result is returned. The return value 2 is multiplied by n , which is 3 , and the result, 6 , becomes the return value of the function call that started the whole process.

Stack diagram shows what the stack diagram looks like for this sequence of function calls. The return values are shown being passed back up the stack. In each frame, the return value is the value of result , which is the product of n and recurse. In the last frame, the local variables recurse and result do not exist, because the branch that creates them does not run.

Julia provides the function factorial to calculate the factorial of an integer number. Following the flow of execution is one way to read programs, but it can quickly become overwhelming. When you come to a function call, instead of following the flow of execution, you assume that the function works correctly and returns the right result. In fact, you are already practicing this leap of faith when you use built-in functions.

You just assume that they work because the people who wrote the built-in functions were good programmers. The same is true when you call one of your own functions. For example, in Boolean Functions , we wrote a function called isdivisible that determines whether one number is divisible by another.

Once we have convinced ourselves that this function is correct—by examining the code and testing—we can use the function without looking at the body again.

It looks like an infinite recursion. How can that be? But if n is not an integer, we can miss the base case and recurse forever. In the first recursive call, the value of n is 0.

In the next, it is From there, it gets smaller more negative , but it will never be 0. We have two choices. We can try to generalize the factorial function to work with floating-point numbers, or we can make fact check the type of its argument.

If we get past both checks, we know that n is positive or zero, so we can prove that the recursion terminates. This program demonstrates a pattern sometimes called a guardian. The first two conditionals act as guardians, protecting the code that follows from values that might cause an error. The guardians make it possible to prove the correctness of the code. In Catching Exceptions we will see a more flexible alternative to printing an error message: raising an exception.

Breaking a large program into smaller functions creates natural checkpoints for debugging. If a function is not working, there are three possibilities to consider:.

To rule out the first possibility, you can add a print statement at the beginning of the function and display the values of the parameters and maybe their types. Or you can write code that checks the preconditions explicitly.

If the parameters look good, add a print statement before each return statement and display the return value. If possible, check the result by hand. Consider calling the function with values that make it easy to check the result as in Incremental Development.

If the function seems to be working, look at the function call to make sure the return value is being used correctly or used at all! Adding print statements at the beginning and end of a function can help make the flow of execution more visible. For example, here is a version of fact with print statements:. If you are confused about the flow of execution, this kind of output can be helpful. It takes some time to develop effective scaffolding, but a little bit of scaffolding can save a lot of debugging.

A program development plan intended to avoid debugging by adding and testing only a small amount of code at a time. A programming pattern that uses a conditional statement to check for and handle circumstances that might cause an error. Write a function named ack that evaluates the Ackermann function. Use your function to evaluate ack 3, 4 , which should be What happens for larger values of m and n?

Test these functions out. What happens if you call middle with a string with two letters? One letter? What about the empty string, which is written “” and contains no letters? Write a function called ispalindrome that takes a string argument and returns true if it is a palindrome and false otherwise.

Remember that you can use the built-in function length to check the length of a string. Write a function called ispower that takes parameters a and b and returns true if a is a power of b. Write a function called gcd that takes parameters a and b and returns their greatest common divisor. This chapter is about iteration, which is the ability to run a block of statements repeatedly.

We saw a kind of iteration, using recursion, in Recursion. We saw another kind, using a for loop, in Simple Repetition. But first I want to say a little more about variable assignment. As you may have discovered, it is legal to make more than one assignment to the same variable. A new assignment makes an existing variable refer to a new value and stop referring to the old value. State diagram shows what reassignment looks like in a state diagram.

A common kind of reassignment is an update, where the new value of the variable depends on the old. Updating a variable by adding 1 is called an increment ; subtracting 1 is called a decrement. Computers are often used to automate repetitive tasks. Repeating identical or similar tasks without making errors is something that computers do well and people do poorly. In a computer program, repetition is also called iteration. We have already seen two functions, countdown and printn , that iterate using recursion.

Because iteration is so common, Julia provides language features to make it easier. One is the for statement we saw in Simple Repetition. Another is the while statement. Here is a version of countdown that uses a while statement:.

You can almost read the while statement as if it were English. When you get to 0, display the word Blastoff! The body of the loop should change the value of one or more variables so that the condition becomes false eventually and the loop terminates.

Otherwise the loop will repeat forever, which is called an infinite loop. In the case of countdown , we can prove that the loop terminates: if n is zero or negative, the loop never runs. Otherwise, n gets smaller each time through the loop, so eventually we have to get to 0. The condition for this loop is n!

Each time through the loop, the program outputs the value of n and then checks whether it is even or odd. If it is even, n is divided by 2. For example, if the argument passed to sequence is 3, the resulting values of n are 3, 10, 5, 16, 8, 4, 2, 1. Since n sometimes increases and sometimes decreases, there is no obvious proof that n will ever reach 1, or that the program terminates.

So far, no one has been able to prove it or disprove it! Rewrite the function printn from Recursion using iteration instead of recursion. In that case you can use the break statement to jump out of the loop. The loop condition is true , which is always true, so the loop runs until it hits the break statement. Each time through, it prompts the user with an angle bracket. If the user types done , the break statement exits the loop. Otherwise the program echoes whatever the user types and goes back to the top of the loop.

The break statement exits the loop. When a continue statement is encountered inside a loop, control jumps to the beginning of the loop for the next iteration, skipping the execution of statements inside the body of the loop for the current iteration. If i is divisible by 3, the continue statement stops the current iteration and the next iteration starts.

Only the numbers in the range 1 to 10 not divisible by 3 are printed. Loops are often used in programs that compute numerical results by starting with an approximate answer and iteratively improving it. If we repeat the process with the new estimate, it gets even closer:. Here is a loop that starts with an initial estimate, x , and improves it until it stops changing:.

For most values of a this works fine, but in general it is dangerous to test float equality. Rather than checking whether x and y are exactly equal, it is safer to use the built-in function abs to compute the absolute value, or magnitude, of the difference between them:.

To understand what an algorithm is, it might help to start with something that is not an algorithm. When you learned to multiply single-digit numbers, you probably memorized the multiplication table. In effect, you memorized specific solutions. That kind of knowledge is not algorithmic. This trick is a general solution for multiplying any single-digit number by 9. Similarly, the techniques you learned for addition with carrying, subtraction with borrowing, and long division are all algorithms.

One of the characteristics of algorithms is that they do not require any intelligence to carry out. They are mechanical processes where each step follows from the last according to a simple set of rules.

Executing algorithms is boring, but designing them is interesting, intellectually challenging, and a central part of computer science. Some of the things that people do naturally, without difficulty or conscious thought, are the hardest to express algorithmically. Understanding natural language is a good example. We all do it, but so far no one has been able to explain how we do it, at least not in the form of an algorithm. As you start writing bigger programs, you might find yourself spending more time debugging.

More code means more chances to make an error and more places for bugs to hide. For example, if there are lines in your program and you check them one at a time, it would take steps. Instead, try to break the problem in half.

Look at the middle of the program, or near it, for an intermediate value you can check. Add a print statement or something else that has a verifiable effect and run the program. If the mid-point check is incorrect, there must be a problem in the first half of the program. If it is correct, the problem is in the second half. Every time you perform a check like this, you halve the number of lines you have to search. After six steps which is fewer than , you would be down to one or two lines of code, at least in theory.

Instead, think about places in the program where there might be errors and places where it is easy to put a check. Then choose a spot where you think the chances are about the same that the bug is before or after the check. Copy the loop from Square Roots and encapsulate it in a function called mysqrt that takes a as a parameter, chooses a reasonable value of x , and returns an estimate of the square root of a. The first column is a number, a ; the second column is the square root of a computed with mysqrt ; the third column is the square root computed by sqrt ; the fourth column is the absolute value of the difference between the two estimates.

The built-in function Meta. This expression can be evaluated in Julia with the function Core. Write a function called evalloop that iteratively prompts the user, takes the resulting input and evaluates it using eval , and prints the result. It should continue until the user enters done , and then return the value of the last expression it evaluated.

Strings are not like integers, floats, and booleans. A string is a sequence , which means it is an ordered collection of other values. The Unicode standard tackles the complexities of what exactly a character is, and is generally accepted as the definitive standard addressing this problem. It provides a unique number for every character on a world-wide scale. A string is a sequence of characters. You can access the characters one at a time with the bracket operator:. The second statement selects character number 1 from fruit and assigns it to letter.

The expression in brackets is called an index. The index indicates which character in the sequence you want hence the name. All indexing in Julia is 1-based—the first element of any integer-indexed object is found at index 1 and the last element at index end :. Strings are encoded using the UTF-8 encoding. UTF-8 is a variable-width encoding, meaning that not all characters are encoded in the same number of bytes. Because an emoji is encoded in 4 bytes and string indexing is byte based, the 5th element of fruits is a SPACE.

This means also that not every byte index into a UTF-8 string is necessarily a valid index for a character. If you index into a string at such an invalid byte index, an error is thrown:. A lot of computations involve processing a string one character at a time. Often they start at the beginning, select each character in turn, do something to it, and continue until the end.

This pattern of processing is called a traversal. One way to write a traversal is with a while loop:. This loop traverses the string and displays each letter on a line by itself. The function firstindex returns the first valid byte index. The keyword global before index indicates that we want to reassign the variable index defined in Main see Global Variables. Write a function that takes a string as an argument and displays the letters backward, one per line.

Each time through the loop, the next character in the string is assigned to the variable letter. The loop continues until no characters are left. The following example shows how to use concatenation string multiplication and a for loop to generate an abecedarian series that is, in alphabetical order.

This loop outputs these names in order:. A segment of a string is called a slice. Selecting a slice is similar to selecting a character:. The operator [n:m] returns the part of the string from the n -th byte to the m -th byte. So the same caution is needed as for simple indexing. If the first index is greater than the second the result is an empty string , represented by two quotation marks:. An empty string contains no characters and has length 0, but other than that, it is the same as any other string.

It is tempting to use the [] operator on the left side of an assignment, with the intention of changing a character in a string. The best you can do is create a new string that is a variation on the original:.

This example concatenates a new first letter onto a slice of greeting. It has no effect on the original string. Constructing strings using concatenation can become a bit cumbersome. Thus, you can interpolate any expression into a string using parentheses:. In a sense, find is the inverse of the [] operator. Instead of taking an index and extracting the corresponding character, it takes a character and finds the index where that character appears.

If the character is not found, the function returns This is the first example we have seen of a return statement inside a loop. This pattern of computation—traversing a sequence and returning when we find what we are looking for—is called a search. Modify find so that it has a third parameter, the index in word where it should start looking. This program demonstrates another pattern of computation called a counter. The variable counter is initialized to 0 and then incremented each time an a is found.

Encapsulate this code in a function named count , and generalize it so that it accepts the string and the letter as arguments. Then rewrite the function so that instead of traversing the string, it uses the three-parameter version of find from the previous section. Julia provides functions that perform a variety of useful operations on strings. For example, the function uppercase takes a string and returns a new string with all uppercase letters.

As it turns out, there is a function named findfirst that is remarkably similar to the function find we wrote:. Actually, the findfirst function is more general than our function; it can find substrings, not just characters:. By default, findfirst starts at the beginning of the string, but the function findnext takes a third argument, the index where it should start:.

With well-chosen variable names, Julia sometimes reads like English. Julia does not handle uppercase and lowercase letters the same way people do.

All the uppercase letters come before all the lowercase letters, so:. A common way to address this problem is to convert strings to a standard format, such as all lowercase, before performing the comparison. When you use indices to traverse the values in a sequence, it is tricky to get the beginning and end of the traversal right.

Here is a function that is supposed to compare two words and return true if one of the words is the reverse of the other, but it contains two errors:. The first if statement checks whether the words are the same length.

If not, we can return false immediately. Otherwise, for the rest of the function, we can assume that the words are the same length. This is an example of the guardian pattern. If we get through the whole loop and all the letters match, we return true. The function lastindex returns the last valid byte index of a string and prevind the previous valid index of a character. If we test this function with the words “pots” and “stop”, we expect the return value true , but we get false :.

The first time through the loop, the value of j is 3, which has to be 4. This time a BoundsError has been thrown. The value of i is 5, which is out a range for the string “pots”.

Run the program on paper, changing the values of i and j during each iteration. Find and fix the second error in this function. An integer value used to select an item in a sequence, such as a character in a string.

In Julia indices start from 1. A variable width character encoding capable of encoding all valid code points in Unicode using one to four 8-bit bytes. The process of evaluating a string containing one or more placeholders, yielding a result in which the placeholders are replaced with their corresponding values. You might want to experiment with some of them to make sure you understand how they work. The documentation uses a syntax that might be confusing. For example, in search string::AbstractString, chars::Chars, [start::Integer] , the brackets indicate optional arguments.

So string and chars are required, but start is optional. There is a built-in function called count that is similar to the function in Looping and Counting. A string slice can take a third index. A step size of 2 means every other character; 3 means every third, etc. A step size of -1 goes through the word backwards, so the slice [end] generates a reversed string.

Use this idiom to write a one-line version of ispalindrome from Exercise The following functions are all intended to check whether a string contains any lowercase letters, but at least some of them are wrong.

For each function, describe what the function actually does assuming that the parameter is a string. To rotate a word, rotate each letter by the same amount.

For example, “cheer” rotated by 7 is “jolly” and “melon” rotated by is “cubed”. Write a function called rotateword that takes a string and an integer as parameters, and returns a new string that contains the letters from the original string rotated by the given amount. You might want to use the built-in function Int , which converts a character to a numeric code, and Char , which converts numeric codes to characters. Letters of the alphabet are encoded in alphabetical order, so for example:.

Because c is the third letter of the alphabet. But beware: the numeric codes for uppercase letters are different. Potentially offensive jokes on the Internet are sometimes encoded in ROT13, which is a Caesar cypher with rotation If you are not easily offended, find and decode some of them. This chapter presents the second case study, which involves solving word puzzles by searching for words that have certain properties.

And I will present another program development plan: reduction to a previously solved problem. For the exercises in this chapter we need a list of English words. It is a list of official crosswords; that is, words that are considered valid in crossword puzzles and other word games.

In the Moby collection, the filename is of. This file is in plain text, so you can open it with a text editor, but you can also read it from Julia. The built-in function open takes the name of the file as a parameter and returns a file stream you can use to read the file. Julia provides several function for reading, including readline , which reads characters from the file until it gets to a NEWLINE and returns the result as a string:.

The file stream keeps track of where it is in the file, so if you call readline again, you get the next word:. You can also use a file as part of a for loop. This program reads words. Write a program that reads words. In Ernest Vincent Wright published a 50, word novel called Gadsby that does not contain the letter e. In fact, it is difficult to construct a solitary thought without using that most common symbol.

It is slow going at first, but with caution and hours of training you can gradually gain facility. Modify your program from the previous section to print only the words that have no e and compute the percentage of the words in the list that have no e. Can you find a combination of 5 forbidden letters that excludes the smallest number of words? Write a function named usesonly that takes a word and a string of letters, and that returns true if the word contains only letters in the list. Can you make a sentence using only the letters acefhlo?

Other than “Hoe alfalfa? Write a function named usesall that takes a word and a string of required letters, and that returns true if the word uses all the required letters at least once.

How many words are there that use all the vowels aeiou? How about aeiouy? Write a function called isabecedarian that returns true if the letters in a word appear in alphabetical order double letters are ok.

How many abecedarian words are there? All of the exercises in the previous section have something in common; they can be solved with the search pattern. The simplest example is:. The for loop traverses the characters in word.

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In January I adobe suite collection keygen xforce free download the preparation of a programming course targeting students without programming experience. I wanted to use Julia, but I found that there existed no book with the purpose of learning to program with Julia as the first programming language.

I knew the book Think Python by Allen Downey, which contains all the key ingredients to learn to program properly. However, this book was based on the Python programming language. My first draft book collector def free the course notes was a melting pot of all kinds of reference works, but the longer I worked on it, the more the content started to resemble the chapters of Think Python.

Soon, the idea of developing my course notes as a port of продолжить book to Julia came to fruition. All the material was available as Jupyter notebooks in vook GitHub repository. After I posted a message on the Julia Discourse site about the progress of my course, the feedback was overwhelming.

A book about basic programming concepts with Julia as the first programming language was apparently a missing link in the Julia universe. It was a fred ride. In August Julia v1. Both the toolchain and the example code had to be made Julia v1. I hope you enjoy working with this book, and that it helps you learn to program and think like a computer scientist, at least a little bit.

It is a free and open frre programming language. Choosing a programming language is book collector def free subjective. For me, the following characteristics of Julia are decisive:. Julia uses multiple dispatch, which allows the programmer to choose from different programming patterns adapted to the application.

Julia is an optionally typed programming language whose user-defined data types make the code clearer and more robust. Julia is a unique programming language because it solves the so-called “two languages problem. This does not mean it happens automatically. It is the responsibility of the programmer to optimize the code that forms a bottleneck, but this can done in Julia itself.

Used for program listings, as well as within paragraphs to refer to program elements such as variable or book collector def free names, databases, data types, environment variables, statements, and keywords.

If you are not familiar with Git, it is a version control system that allows you to keep track of the files that make up a project. A convenience package is provided that can be directly added to Julia. Both the REPL and a notebook interface are available. If you want to have Julia locally installed on your computer, you can download JuliaPro for free from Julia Computing. It consists of a recent Collectr version, the Juno interactive collfctor environment based on Atom, and a number of preinstalled Julia packages.

To a local install, you can also add the IJulia package and run a Jupyter notebook on your computer. I really want to thank Allen for ccollector Think Python and allowing me to port his book to Julia. Your enthusiasm is contagious! I would also like to thank the technical reviewers for this book, who made many helpful suggestions: Tim Besard, Bart Janssens, and David P. You forced me to do things book collector def free and make this book as original as possible. Thanks to all the students who worked with an early version of this book and all the contributors listed below who sent in corrections and suggestions.

If you book collector def free a suggestion or correction, please send email to ben. If I make a change based on your feedback, I will add you to the contributor list unless you ask to be omitted. Let me know what version of the book you are working with, and what format. If you include at least part of the sentence the error appears in, book collector def free will make it easy for me to search. Page and section numbers book collector def free fine, too, but not quite as easy to work with.

Scott Jones pointed out the name change book collector def free Void to Nothingand this started the migration to Julia v1. Free autodesk crack keygen autocad 2019 book collector def free of this book is to teach you to think like a computer scientist. This way of thinking combines some of the best подробнее на этой странице of mathematics, engineering, and natural science.

Like mathematicians, computer scientists use formal languages to denote ideas нажмите для продолжения computations. Like engineers, they design things, assembling components into systems and evaluating trade-offs among alternatives.

Like scientists, they observe the behavior of complex systems, book collector def free hypotheses, and test predictions. The single most important skill for a computer scientist is problem solving.

Problem solving means the ability to dollector problems, think creatively about solutions, and express a solution clearly and нажмите чтобы узнать больше. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills. On one level, you will be learning to program, a useful skill by itself. On another level, you will use programming as a means to an end.

As we go along, that end will become clearer. A program is a sequence of instructions that specifies how to perform a computation. The computation might be something mathematical, such as solving a system of equations or finding the roots of a polynomial, but it can also book collector def free a symbolic computation, such as searching for and replacing text in a document, or something graphical, like processing collecyor image or playing a video.

The details look bopk in different languages, but a few basic instructions appear in just about every language:.

So you can think of programming as the process of breaking a large, complex task into smaller and smaller subtasks until the subtasks are simple enough to be performed with one of these basic instructions.

One of the challenges of getting started with Julia is that you might have to install it and related software посетить страницу your computer. If you are familiar with your operating system, and especially collrctor you are comfortable with the command-line interface, you will have no trouble installing Julia.

But for beginners, it can be painful to learn about system administration and programming at the same time. To avoid that problem, I recommend that you start out running Julia in a browser. In the browser, you can run Julia on JuliaBox.

No installation is required—just point your browser there, log in, and start computing see JuliaBox. When it starts, you should see output like this:. The first lines contain information about the REPL, so it might book collector def free different for you.

But you should check that book collector def free version number is at least 1. The last line is a prompt that indicates that the REPL is ready for you to enter code. It displays a result on the screen. Book collector def free parentheses indicate that println is a function. Julia provides operatorswhich are по этому адресу that represent computations like addition and multiplication. You might wonder why the result is A value is one of the basic things a program works with, like a letter or a number.

Some values we have seen so far are 2 These values belong to different types : 2 is an integer Integers belong to the type Int64strings belong to Stringand floating-point numbers belong to Boook What about values like “2” and ” They look like numbers, but they are in quotation marks like strings.

These are strings too:. When you type a large integer, you might be tempted to use commas between groups of digits, as in 1, This is not a legal integer in Julia, but it is legal:. Julia parses 1, as a comma-separated sequence of integers. Natural languages are the languages people book collector def free, such as English, Spanish, and French. They were not designed by book collector def free although people try to impose some order on them frree they evolved naturally.

Formal colletor book collector def free languages that are designed by people for specific applications. For example, the notation that mathematicians use is a formal language that is particularly good at denoting relationships among numbers and symbols. Chemists use a formal language to represent the chemical structure of molecules.

And most importantly, programming languages are formal languages that have been designed to express computations. Dec languages tend to have strict syntax rules that govern the structure of statements. Syntax rules узнать больше здесь in two flavors, pertaining to book collector def free and structure. Tokens are the basic elements of the language, such as words, numbers, and chemical elements. The second type of syntax rule pertains to the way tokens are combined.

Similarly, in a chemical formula the subscript comes after the element book collector def free, not before. This sentence all valid tokens has, but invalid structure with. When you read a sentence in English or a statement in a formal language, minecraft windows shaders mod free download have to figure out the structure book collector def free in a natural language you do this subconsciously.

This process is called parsing. Although formal and natural languages have many features in common—tokens, structure, and syntax—there are some differences:. Natural languages are full of ambiguity, which people deal with by using contextual clues and other information.

Formal languages are designed to http://replace.me/13302.txt nearly or completely unambiguous, which means that any statement has exactly one meaning, regardless of context. In order to make fref for ambiguity and reduce misunderstandings, co,lector languages employ lots of redundancy. As a result, they are often verbose. Formal languages are less redundant and more concise. Natural languages are full of idiom and metaphor.

Def Leppard are an English rock band formed in in Sheffield. Sincethe band has consisted of Joe Elliott lead vocalsRick Savage bass, backing vocalsRick Allen drums, backing vocalsPhil Collen guitars, backing vocalsand Vivian Campbell guitars, backing vocals. They established themselves as part of the new wave of British heavy metal movement of the early s. The band’s greatest commercial success came between the early book collector def free and the early s.

Their second album, ‘s High ‘n’ Drywas produced by Mutt Langewho helped them begin to define their melodic hard rock style, and the album’s most popular track ” Bringin’ On the Heartbreak ” became one of the first rock videos played on MTV inbut the album only reached the Top 30 and 40 in the UK and US.

Reaching No. It also went to No. Hysteria book collector def free four Top 10 hits in New Zealand. Their next studio album, Adrenalize their first following the death of guitarist Steve Windows 10 recovery free downloadreached No.

It contained several hits, including the US Rock Tracks chart-topper, ” Let’s Get Rocked “, which became their biggest hit in several countries, including No.

Adrenalize went on to sell over 8 million copies worldwide. Their greatest hits album Vault http://replace.me/28286.txt, released infeatured the UK No.

Beginning with SlangDef Leppard released five albums between and book collector def free, with most usually reaching the Top 15 in several countries, including the UK, US and Canada. Their self-titled album was released in and reached the Top 10 in several посмотреть больше. As one of the world’s best-selling music artistsDef Leppard have sold more than million records worldwide, [2] and have two albums with RIAA diamond certification : Pyromania and Hysteria, [3] making them one of only five rock bands with two original studio albums selling more than 10 million copies in the US.

The band originally consisted of Willis on guitar, Savage on bass guitar after briefly playing guitar, and Kenning on drums. Only 18 at the time, Joe Elliott tried out for the band as a guitarist привожу ссылку a chance meeting with Willis after missing a bus in November The band’s initial rehearsals took place book collector def free Portland Worksand their first gig was in the dining hall in A Block in Westfield School in MosboroughSheffield.

Elliott proposed the name “Deaf Leopard” which was originally a band name he thought of while designing band posters in art class. According to Elliott, he successfully auditioned for the band by playing Lynyrd Skynyrd ‘s ” Free Bird ” in its entirety. He was replaced for those sessions by Frank Noon.

By the end of the month, Rick Allenthen only 15 years old, had joined the band as its full-time drummer. Throughoutthe band developed a loyal following among British hard rock and heavy metal fans and were considered among the leaders of the new wave of British heavy metal movement.

Mensch, who admitted that he had had his eye on the band, became their manager. This incident was partially blamed on a cover story in Sounds music newspaper by the journalist Geoff Barton titled, “Has the Leppard changed its spots?

In a documentary on the band recorded for BBC 2Book collector def free recalls feelings of guilt over the story and having a “stand-up row” with the band’s manager, Mensch, backstage at the show. Lange’s meticulous approach in the studio helped them begin to define their sound. Despite the album’s unimpressive sales figures it only peaked at number 26 in the UK and 38 in the USthe band’s video for ” Bringin’ On the Heartbreak ” became one of the first metal videos played on MTV inbringing the band increased visibility in the US.

The band opened for Ozzy Osbourne and Blackfoot. On 11 JulyPete Willis was fired due нажмите для продолжения excessive по ссылке consumption on the job and was replaced by Phil Collen of Girl the next day.

This personnel change took place during the recording of their third album, Pyromaniawhich was released on 20 January and also produced by Lange. The cover artwork depicted a cartoon image of a huge flame emerging from the top floor of a skyscraper, with a bullseye aimed at the flame. Fuelled by “Photograph”, “Rock of Ages”, and the third single ” Foolin’ “, Pyromania went on to sell six million copies in more thancopies every week in that year and was held from the top of the US charts only by Michael Jackson’s Thriller.

Following book collector def free breakthrough, the band moved to Dublin in February for tax purposes to begin writing the follow-up to Pyromania.

Mutt Lange initially joined in on the songwriting sessions but then suddenly declined to return as producer due to exhaustion. However, Steinman worked only briefly with the band, and the recording work book collector def free not released.

On the afternoon of 31 Decemberdrummer Rick Allen was involved in a car accident, with his then-girlfriend Miriam Barendsen, on the A57 road in the countryside a few miles west book collector def free Sheffield.

Doctors initially reattached the arm, but it was later amputated due to an infection. Despite the severity of the accident, Rick Allen was committed to continuing his role as Def Leppard’s drummer and realised that he could use his legs to do some of the drumming work previously done with his arms. Allen was placed in a separate studio to practice his new drums.

After a few months, Allen gathered the band together and performed the intro to the Led Zeppelin version of ” When the Levee Breaks ” to showcase his progress to the band. Joe Elliott reports this as being a “very emotional moment. When Rich turned up late for a gig, he and the band realised Allen could drum alone. Allen’s comeback was sealed at the Monsters of Rock festival in England, with an emotionally charged ovation after his introduction by Joe Elliott.

After over three years of recording, Def Leppard’s fourth album, Hysteriawas released on 3 August One of the first singles from the album, ” Animal “, became the book collector def free first Top 10 hit in the UK, reaching No. Hysteria topped the UK Album Charts меня audirvana dlna server free Вами its first week of release, and has since spent weeks on the chart.

The song hit No. In Januarythe band scored another US Top 5 hit with ” Armageddon It “, and by spring of the final single ” Rocket ” was in the Top 15 in the US [42] and several other countries.

Wanting to give fans book collector def free new after the massive radio and video airplay for not only the seven singles but also the album tracks that radio DJs were playing off the album, the band performed “Tear It Down”, a Hysteria B-side at the MTV Video Music Awards.

It remained on the charts for http://replace.me/29974.txt years and has sold over 25 million copies book collector def free. This concept proved wildly popular with fans as seen in the videos for “Pour Some Sugar on Me” and “Armageddon It” and was used again for the Adrenalize tour.

Following Hysteriathe band quickly set out to work on their fifth album, hoping to avoid another lengthy instalar microsoft word 2016 gratis free download. Steve Clark ‘s alcoholism worsened to the point that he was constantly in and out of rehab. Recording sessions suffered from this distraction, and in mid, Clark was granted a book collector def free leave of absence from the band.

Clark died from a mix of prescription drugs and alcohol on 8 Januaryin his London home. Def Leppard’s fifth album, Adrenalizewas finally released on 31 March The album simultaneously entered at number one on both the UK and US album charts, staying number one on the latter for five weeks, while also reaching the summit on the Canadian and Australian charts and hitting No.

In sony vegas pro 13 keygen crack free period between late and earlyauditions for book collector def free guitarist commenced. Ultimately, the band chose Vivian Campbell informerly of Dio and Whitesnake. Amidst the increasing popularity of alternative rock, the band decided to balance their original image as rebellious rock stars with a slightly friendlier energy, combining heavy metal with melodies and hooks more book collector def free of pop music.

A collection of B-sides and unreleased tracks recorded between book collector def freecalled Retro Activewas released in Octoberpreceded by the success of the посетить страницу ballad ” Two Steps Behind ” from the Arnold Schwarzenegger film Last Action Hero.

InDef Leppard issued their first greatest hits collection, Vault: Def Leppard Greatest Hits —which reached number 3 in the UK, Top 10 in several other countries, and eventually sold over 5 million copies in the US. The band rehearsed and played the songs together in the studio instead of recording parts separately, resulting in a much more live-sounding album.

VH1 revived the band’s fortunes in the US in by featuring them on one of the first episodes of Behind the Music. Re-runs of the episode yielded some of the series’ highest ratings and brought the band’s music back into the public consciousness following years of burial by the microsoft office professional plus 2013 end of support free download rock climate.

The episode was even parodied on Saturday Night Live. In an effort to capitalise on this new momentum, Def Leppard returned to its classic sound with the album Euphoria. Euphoria peaked at No. The docudrama covered the band’s http://replace.me/17483.txt between throughrecounting the trials and triumphs of Rick Allen and Steve Clark. Def Leppard’s eighth book collector def free, Xsaw the band’s musical direction moving more towards pop and further away from the band’s hard rock roots.

X ultimately became the band’s least book collector def free release, peaking at No. An expanded book collector def free updated best-of collection, Best Ofwas released internationally in October Def Leppard book collector def free at the Live 8 show in Philadelphia and toured in the summer with Bryan Adams. It debuted at No. Soon afterwards, they embarked on a US tour with Journey. That October, Hysteria was re-released in a two-disc deluxe edition format, which combined the original remastered album with B-sides, remixes, and bonus tracks from single releases.

On 25 AprilDef Leppard released their first album of new studio material in six years, Songs from the Sparkle Lounge. The book collector def free debuted book collector def free No. They also played several European rock festivals. The band then returned to Europe before coming back for a second leg of the UK tour in June. Again they were joined by Whitesnake; however, hard rock band Thunder supported at some of these shows.

Black Stone Cherry continued to support most of the dates, including some of the Thunder ones. The extension saw them visit Japan, Australia and New Zealand. Whitesnake continued to support Def Leppard book collector def free their Indian and Japanese dates. The band cited, “unforeseen personal matters”, as the reason for the cancellations. Not at all. We often joke, what else would we do?

You just can’t imagine doing anything else. After taking a year off from touring inthe band announced on 22 February that they would be releasing their first live album in the summer. The residency, referred to as Viva!

Hysteria, featured a two-part show, book collector def free the first half featuring Def Больше на странице opening for themselves, under the alias “Ded Flatbird”, jokingly called the best Def Leppard cover band in the worldwhen they played songs they very rarely play live, going all the way back to “Good Morning Freedom”, a B-side from the single “Hello America” released in Februaryan era usually left untouched by the band.

The opening set varied each night, from playing the best hits from albums like On Through the NightSlangand Euphoriato being the entire first half of High ‘n’ Dry. The second half, and “main event” was Def Leppard, as themselves playing their best-selling album, Hysteriafrom start to finish.

A live album, also titled Viva! Hysteria was released on 22 October This was the first time the band had played an album book collector def free from start to finish. On 11 Februarythe band released a remastered deluxe edition of their album Slang after much delay. The album, still coveted by many loyal fans of the band, now features 30 tracks including demos, B-sides, and unreleased material.

The album was produced by Tom Allom. It charted at No. Other tracks are re-recorded versions of early demos, some of which later appeared on the box set The Early Years 79— However, the version of “Wasted” that appears on the single is a different recording from that of the LP, as is its B-side, “Hello America”. Joe Elliott had done the spoken portion in earlier live performances and demo recordings that showed up on some early bootlegs.

From Wikipedia, the free encyclopedia. Def Leppard. Startling Studios Ascot, Berkshire. Side one No. Title Writer s Solos Length 1. Clark Elliott Savage Willis. Side two No. Title Writer s Solos Length 7. Official Charts Company. Retrieved 13 August Retrieved 30 April Rolling Stone. Retrieved 23 March Recording Industry Association of America. Retrieved 14 August All Media Network. ISBN Encyclopedia of Popular Music.

Retrieved 4 August Australian Chart Book — illustrated ed. St Ives, N. UK Albums Chart. Retrieved 2 April Retrieved 16 February Music Canada. Live from Detroit. The Def Leppard E. The Lost Session. Till You Drop “. Authority control MusicBrainz release group. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Heavy metal. Colonel Tom Allom. On Through the Night High ‘n’ Dry Collector’s Guide to Heavy Metal.

Clark Elliott Andrew Smith. MusicBrainz release group.

The Definitive Voice of Entertainment News Subscribe for full access to The Hollywood Reporter. See My Options Sign Up. This is a book that swoons and a book that stinks. It is a book that you must read if you are a writer, as a reminder that every sense can be used enslave a reader. It calls itself the story of a murderer, but the journey as to why and how he kills is so evocative and sensual that it is quite different from any murderous tale you’ve read. Land Record Book; Schedule of In Lots; Annexations; Military Discharge (DD) Veteran Grave Registration; Atlases – Historic; Zoning Resolutions; Registered Land Certificate Search; Monthly Activity Reports; Historical Records; Search Real estate records. Home Search Records Geographical Indexes prior SUBDIVISION INDEXES. Praise for Diana Gabaldon’s Outlander novels “Marvelous and fantastic adventures, romance, sex perfect escape reading.” — San Francisco Chronicle, on Outlander “History comes deliciously alive on the page.” —New York Daily News, on Outlander “Gabaldon is a born storyteller The pages practically turn themselves.” — The Arizona Republic, on Dragonfly .

Official Charts Company. Retrieved 13 August Retrieved 30 April Rolling Stone. Retrieved 23 March Recording Industry Association of America. Retrieved 14 August All Media Network. ISBN Encyclopedia of Popular Music. Retrieved 4 August Australian Chart Book — illustrated ed. St Ives, N. UK Albums Chart. Retrieved 2 April Retrieved 16 February Music Canada.

Official Charts Company. Retrieved 13 August Oxford Music Online. Oxford University Press. Hachette UK. Retrieved 29 April Retrieved 27 March Retrieved 28 May Ultimate Classic Rock. Cover Story. Retrieved 20 February Archived from the original on 11 September Retrieved 17 November Omnibus Press. Retrieved 5 August Spin magazine. February The Tombstone Tourist: Musicians. Retrieved 30 March The Rough Guide to Rock. ProQuest Retrieved 4 February Retrieved 15 December Archived from the original on 12 October Retrieved 23 October Guitar Center’s Hollywood Rockwalk.

Def Leppard Official Website. Retrieved 10 June Retrieved 16 March Retrieved 29 May Retrieved 19 March Tuscaloosa News. Guitar World. Archived from the original on 4 October Retrieved 15 April Retrieved 9 October Archived from the original on 21 January Retrieved 14 September Retrieved 13 February Retrieved 21 October Archived from the original on 27 September Retrieved 30 April That Metal Show. Season 3. Episode 5. Archived from the original on 26 May Retrieved 2 October Archived from the original on 31 May Archived from the original on 31 March Yorkshire Post.

Retrieved 4 November Retrieved 2 April Retrieved 22 April The New York Times. Archived from the original on 23 June U Discover Music. Retrieved 2 February Brave Words. Metal Head Zone. Retrieved 20 January Please enter a valid email address. Please select a newsletter. Sign up. Firaxis delays Marvel’s Midnight Suns, maybe until Khalid , People spent much less time watching gaming streams this spring, report says By K. Holt , Bonifacic ,

Sign up. Firaxis delays Marvel’s Midnight Suns, maybe until Khalid , People spent much less time watching gaming streams this spring, report says By K. Holt , Bonifacic , People spent much less time watching gaming streams this spring, report says Facebook Gaming saw a far bigger decline than Twitch and YouTube Gaming, according to Streamlabs and Stream Hatchet.

We have two newsletters, why not sign up for both? Retrieved 27 September Hysteria with Def Leppard’s Joe Elliott”.

Sheffield Star. Archived from the original on 21 December Retrieved 20 December Retrieved 1 March Retrieved 8 January Rock on the Net. Retrieved 22 July Retrieved 25 November Planet Rock. Retrieved 13 December Music Sales Group.

Rolling Stone. Archived from the original on 29 October Turnaround, ISBN Jeffrey Def Leppard: Arena Rock Band. Steve Clark Biography Allmusic. The Billboard book of number one hits 4th ed. New York: Billboard Books. ISBN The Guardian. Retrieved 7 October The N. Iron Pages Books 3 ed. Berlin, Germany: I. Retrieved 17 April Official Charts Company. Retrieved 13 August Oxford Music Online. Oxford University Press. Hachette UK. Retrieved 29 April Retrieved 27 March Retrieved 28 May Ultimate Classic Rock.

Cover Story. Retrieved 20 February Archived from the original on 11 September Retrieved 17 November Omnibus Press. Retrieved 5 August Spin magazine. February The Tombstone Tourist: Musicians.

Retrieved 30 March The Rough Guide to Rock. ProQuest Retrieved 4 February Retrieved 15 December Archived from the original on 12 October Retrieved 23 October Guitar Center’s Hollywood Rockwalk. Retrieved 23 December Retrieved 28 March Retrieved 27 April Archived from the original on 18 December Archived from the original on 14 December Retrieved 3 February Retrieved 3 May Archived from the original on 23 February Retrieved 23 February Archived from the original on 5 March Retrieved 7 March Archived from the original on 24 August Retrieved 13 July Archived from the original on 20 March Triple M.

Retrieved 5 June Retrieved 27 June Retrieved 15 November Virgin media, 10 June Retrieved 3 September Archived from the original on 12 February Retrieved 12 February Grand Forks Herald. Retrieved 28 August Big, Winger Singers Step In”. Retrieved 30 March — via Twitter. Live from Detroit”. Retrieved 3 June Retrieved 19 January Retrieved 25 October Retrieved 14 December Retrieved 18 December Def Leppard.

Def Leppard Official Website. Retrieved 10 June Retrieved 16 March Retrieved 29 May Retrieved 19 March Tuscaloosa News. These notes are called comments , and they start with the symbol:. In this case, the comment appears on a line by itself. You can also put comments at the end of a line:. Everything from the to the end of the line is ignored—it has no effect on the execution of the program.

Comments are most useful when they document non-obvious features of the code. It is reasonable to assume that the reader can figure out what the code does; it is more useful to explain why.

Good variable names can reduce the need for comments, but long names can make complex expressions hard to read, so there is a tradeoff. Three kinds of errors can occur in a program: syntax errors, runtime errors, and semantic errors. It is useful to distinguish between them in order to track them down more quickly. If there is a syntax error anywhere in your program, Julia displays an error message and quits, and you will not be able to run the program.

During the first few weeks of your programming career, you might spend a lot of time tracking down syntax errors. As you gain experience, you will make fewer errors and find them faster.

The second type of error is a runtime error, so called because the error does not appear until after the program has started running. These errors are also called exceptions because they usually indicate that something exceptional and bad has happened. Runtime errors are rare in the simple programs you will see in the first few chapters, so it might be a while before you encounter one.

If there is a semantic error in your program, it will run without generating error messages, but it will not do the right thing. It will do something else. Specifically, it will do what you told it to do. Identifying semantic errors can be tricky because it requires you to work backward by looking at the output of the program and trying to figure out what it is doing.

A reserved word that is used to parse a program; you cannot use keywords like if , function , and while as variable names. A section of code that represents a command or action. So far, the statements we have seen are assignments and print statements. Rules governing the order in which expressions involving multiple mathematical operators and operands are evaluated.

Information in a program that is meant for other programmers or anyone reading the source code and has no effect on the execution of the program. Repeating my advice from the previous chapter, whenever you learn a new feature, you should try it out in interactive mode and make errors on purpose to see what goes wrong.

In some languages every statement ends with a semi-colon, ;. What happens if you put a semi-colon at the end of a Julia statement? In math notation you can multiply x and y like this: x y.

What happens if you try that in Julia? What about 5x? What is the volume of a sphere with radius 5? What is the total wholesale cost for 60 copies? If I leave my house at am and run 1 mile at an easy pace per mile , then 3 miles at tempo per mile and 1 mile at easy pace again, what time do I get home for breakfast? In the context of programming, a function is a named sequence of statements that performs a computation. When you define a function, you specify the name and the sequence of statements.

The name of the function is println. The expression in parentheses is called the argument of the function. The result is also called the return value. Julia provides functions that convert values from one type to another. The parse function takes a string and converts it to any number type, if it can, or complains otherwise:. This second example finds the sine of radians.

The name of the variable is a hint that sin and the other trigonometric functions cos , tan , etc. If you know trigonometry, you can check the previous result by comparing it to the square root of two divided by two:. So far, we have looked at the elements of a program—variables, expressions, and statements—in isolation, without talking about how to combine them. One of the most useful features of programming languages is their ability to take small building blocks and compose them.

For example, the argument of a function can be any kind of expression, including arithmetic operators:. Almost anywhere you can put a value, you can put an arbitrary expression, with one exception: the left side of an assignment statement has to be a variable name.

Any other expression on the left side is a syntax error we will see exceptions to this rule later. So far, we have only been using the functions that come with Julia, but it is also possible to add new functions. A function definition specifies the name of a new function and the sequence of statements that run when the function is called.

Here is an example:. The name of the function is printlyrics. The first line of the function definition is called the header ; the rest is called the body. The body is terminated with the keyword end and it can contain any number of statements. For readability the body of the function should be indented. Once you have defined a function, you can use it inside another function. For example, to repeat the previous refrain, we could write a function called repeatlyrics :.

Pulling together the code fragments from the previous section, the whole program looks like this:. This program contains two function definitions: printlyrics and repeatlyrics. Function definitions get executed just like other statements, but the effect is to create function objects.

The statements inside the function do not run until the function is called, and the function definition generates no output. As you might expect, you have to create a function before you can run it. In other words, the function definition has to run before the function gets called. Move the last line of this program to the top, so the function call appears before the definitions. Run the program and see what error message you get. Now move the function call back to the bottom and move the definition of printlyrics after the definition of repeatlyrics.

What happens when you run this program? To ensure that a function is defined before its first use, you have to know the order statements run in, which is called the flow of execution.

Execution always begins at the first statement of the program. Statements are run one at a time, in order from top to bottom. A function call is like a detour in the flow of execution. Instead of going to the next statement, the flow jumps to the body of the function, runs the statements there, and then comes back to pick up where it left off. That sounds simple enough, until you remember that one function can call another. While in the middle of one function, the program might have to run the statements in another function.

Then, while running that new function, the program might have to run yet another function! Fortunately, Julia is good at keeping track of where it is, so each time a function completes, the program picks up where it left off in the function that called it. When it gets to the end of the program, it terminates. Sometimes it makes more sense if you follow the flow of execution. Some of the functions we have seen require arguments. For example, when you call sin you pass a number as an argument.

Some functions take more than one argument: parse takes two, a number type and a string. Inside the function, the arguments are assigned to variables called parameters. Here is a definition for a function that takes an argument:. This function assigns the argument to a parameter named bruce. When the function is called, it prints the value of the parameter whatever it is twice.

The same rules of composition that apply to built-in functions also apply to programmer-defined functions, so we can use any kind of expression as an argument for printtwice :. The name of the variable we pass as an argument michael has nothing to do with the name of the parameter bruce. When you create a variable inside a function, it is local , which means that it only exists inside the function. This function takes two arguments, concatenates them, and prints the result twice. Here is an example that uses it:.

When cattwice terminates, the variable concat is destroyed. If we try to print it, we get an exception:. Parameters are also local. For example, outside printtwice , there is no such thing as bruce. To keep track of which variables can be used where, it is sometimes useful to draw a stack diagram. Like state diagrams, stack diagrams show the value of each variable, but they also show the function each variable belongs to.

Each function is represented by a frame. A frame is a box with the name of a function beside it and the parameters and variables of the function inside it. The stack diagram for the previous example is shown in Stack diagram. The frames are arranged in a stack that indicates which function called which, and so on. In this example, printtwice was called by cattwice , and cattwice was called by Main , which is a special name for the topmost frame.

When you create a variable outside of any function, it belongs to Main. Each parameter refers to the same value as its corresponding argument. So, part1 has the same value as line1 , part2 has the same value as line2 , and bruce has the same value as concat. If an error occurs during a function call, Julia prints the name of the function, the name of the function that called it, and the name of the function that called that , all the way back to Main.

For example, if you try to access concat from within printtwice , you get a UndefVarError :. This list of functions is called a stacktrace. It tells you what program file the error occurred in, and what line, and what functions were executing at the time. It also shows the line of code that caused the error.

The order of the functions in the stacktrace is the inverse of the order of the frames in the stack diagram. The function that is currently running is at the top. Some of the functions we have used, such as the math functions, return results; for lack of a better name, I call them fruitful functions.

They are called void functions. When you call a fruitful function, you almost always want to do something with the result; for example, you might assign it to a variable or use it as part of an expression:. But in a script, if you call a fruitful function all by itself, the return value is lost forever! If you assign the result to a variable, you get a special value called nothing. To print the value nothing , you have to use the function show which is like print but can handle the value nothing.

The value nothing is not the same as the string “nothing”. It is a special value that has its own type:. The functions we have written so far are all void. We will start writing fruitful functions in a few chapters. It may not be clear why it is worth the trouble to divide a program into functions.

There are several reasons:. Creating a new function gives you an opportunity to name a group of statements, which makes your program easier to read and debug. Functions can make a program smaller by eliminating repetitive code. Later, if you make a change, you only have to make it in one place. Dividing a long program into functions allows you to debug the parts one at a time and then assemble them into a working whole.

Well-designed functions are often useful for many programs. Once you write and debug one, you can reuse it. One of the most important skills you will acquire is debugging. Although it can be frustrating, debugging is one of the most intellectually rich, challenging, and interesting parts of programming. In some ways debugging is like detective work. You are confronted with clues and you have to infer the processes and events that led to the results you see. Debugging is also like an experimental science.

Once you have an idea about what is going wrong, you modify your program and try again. If your hypothesis was correct, you can predict the result of the modification, and you take a step closer to a working program.

If your hypothesis was wrong, you have to come up with a new one. As Sherlock Holmes pointed out,. When you have eliminated the impossible, whatever remains, however improbable, must be the truth. For some people, programming and debugging are the same thing. That is, programming is the process of gradually debugging a program until it does what you want. The idea is that you should start with a working program and make small modifications, debugging them as you go.

For example, Linux is an operating system that contains millions of lines of code, but it started out as a simple program Linus Torvalds used to explore the Intel chip. This later evolved to Linux. A named sequence of statements that performs some useful operation.

Functions may or may not take arguments and may or may not produce a result. A statement that creates a new function, specifying its name, parameters, and the statements it contains.

A value created by a function definition. The name of the function is a variable that refers to a function object. A statement that runs a function. It consists of the function name followed by an argument list in parentheses. A value provided to a function when the function is called. This value is assigned to the corresponding parameter in the function.

The result of a function. If a function call is used as an expression, the return value is the value of the expression. Using an expression as part of a larger expression, or a statement as part of a larger statement. A graphical representation of a stack of functions, their variables, and the values they refer to.

A box in a stack diagram that represents a function call. It contains the local variables and parameters of the function. These exercises should be done using only the statements and other features we have learned so far. Write a function named rightjustify that takes a string named s as a parameter and prints the string with enough leading spaces so that the last letter of the string is in column 70 of the display.

Use string concatenation and repetition. Also, Julia provides a built-in function called length that returns the length of a string, so the value of length “monty” is 5. A function object is a value you can assign to a variable or pass as an argument.

For example, dotwice is a function that takes a function object as an argument and calls it twice:. Modify dotwice so that it takes two arguments, a function object and a value, and calls the function twice, passing the value as an argument. Use the modified version of dotwice to call printtwice twice, passing “spam” as an argument.

Define a new function called dofour that takes a function object and a value and calls the function four times, passing the value as a parameter.

There should be only two statements in the body of this function, not four. The output from the next print statement would begin on the next line. This chapter presents a case study that demonstrates a process for designing functions that work together. It introduces turtle graphics, a way to create programmatic drawings. Turtle graphics are not included in the Standard Library, so the ThinkJulia module has to be added to your Julia setup.

The examples in this chapter can be executed in a graphical notebook on JuliaBox, which combines code, formatted text, math, and multimedia in a single document see JuliaBox. A module is a file that contains a collection of related functions. Julia provides some modules in its Standard Library.

Before we can use the functions in a module, we have to import it with an using statement:. The ThinkJulia module provides a function called Turtle that creates a Luxor.

Once you create a turtle, you can call a function to move it around a drawing. For example, to move the turtle forward:. The svg keyword runs a macro that draws a SVG picture. Macros are an important but advanced feature of Julia. The arguments of forward are the turtle and a distance in pixels, so the actual size depends on your display. Another function you can call with a turtle as argument is turn for turning. The second argument for turn is an angle in degrees. Also, each turtle is holding a pen, which is either down or up; if the pen is down, the turtle leaves a trail when it moves.

Moving the turtle forward shows the trail left behind by the turtle. This is the simplest use of the for statement; we will see more later. But that should be enough to let you rewrite your square-drawing program. The syntax of a for statement is similar to a function definition. It has a header and a body that ends with the keyword end. The body can contain any number of statements. A for statement is also called a loop because the flow of execution runs through the body and then loops back to the top.

In this case, it runs the body four times. This version is actually a little different from the previous square-drawing code because it makes another turn after drawing the last side of the square. The extra turn takes more time, but it simplifies the code if we do the same thing every time through the loop. This version also has the effect of leaving the turtle back in the starting position, facing in the starting direction.

The following is a series of exercises using turtles. They are meant to be fun, but they have a point, too. While you are working on them, think about what the point is. Write a function called square that takes a parameter named t , which is a turtle.

It should use the turtle to draw a square. Write a function call that passes t as an argument to square , and then run the macro again. Add another parameter, named len , to square. Modify the body so length of the sides is len , and then modify the function call to provide a second argument.

Run the macro again. Test with a range of values for len. Make a copy of square and change the name to polygon. Write a function called circle that takes a turtle, t , and radius, r , as parameters and that draws an approximate circle by calling polygon with an appropriate length and number of sides. Test your function with a range of values of r. Make a more general version of circle called arc that takes an additional parameter angle , which determines what fraction of a circle to draw.

The first exercise asks you to put your square-drawing code into a function definition and then call the function, passing the turtle as a parameter. Here is a solution:. The innermost statements, forward and turn are indented twice to show that they are inside the for loop, which is inside the function definition. Wrapping a piece of code up in a function is called encapsulation. One of the benefits of encapsulation is that it attaches a name to the code, which serves as a kind of documentation.

Another advantage is that if you re-use the code, it is more concise to call a function twice than to copy and paste the body! Adding a parameter to a function is called generalization because it makes the function more general: in the previous version, the square is always the same size; in this version it can be any size.

The next step is also a generalization. Instead of drawing squares, polygon draws regular polygons with any number of sides.

The next step is to write circle , which takes a radius, r , as a parameter. Here is a simple solution that uses polygon to draw a sided polygon:. Thus, polygon draws a sided polygon that approximates a circle with radius r. One limitation of this solution is that n is a constant, which means that for very big circles, the line segments are too long, and for small circles, we waste time drawing very small segments.

One solution would be to generalize the function by taking n as a parameter. This would give the user whoever calls circle more control, but the interface would be less clean. The interface of a function is a summary of how it is used: what are the parameters? What does the function do? And what is the return value? In this example, r belongs in the interface because it specifies the circle to be drawn. Rather than clutter up the interface, it is better to choose an appropriate value of n depending on circumference :.

The steps of this process are:. Once you get the program working, identify a coherent piece of it, encapsulate the piece in a function and give it a name. Repeat steps 1—3 until you have a set of working functions. Copy and paste working code to avoid retyping and re-debugging. Look for opportunities to improve the program by refactoring. For example, if you have similar code in several places, consider factoring it into an appropriately general function. This approach lets you design as you go along.

Documentation can be accessed in the REPL or in a notebook by typing? Docstrings are often triple-quoted strings, also known as multiline strings because the triple quotes allow the string to span more than one line. A docstring contains the essential information someone would need to use this function. It explains concisely what the function does without getting into the details of how it does it.

It explains what effect each parameter has on the behavior of the function and what type each parameter should be if it is not obvious. Writing this kind of documentation is an important part of interface design.

A well-designed interface should be simple to explain; if you have a hard time explaining one of your functions, maybe the interface could be improved. An interface is like a contract between a function and a caller.

Conversely, conditions at the end of the function are postconditions. Postconditions include the intended effect of the function like drawing line segments and any side effects like moving the turtle or making other changes.

Preconditions are the responsibility of the caller. If the caller violates a properly documented! If the preconditions are satisfied and the postconditions are not, the bug is in the function. If your pre- and postconditions are clear, they can help with debugging.

The process of replacing something unnecessarily specific like a number with something appropriately general like a variable or parameter. A description of how to use a function, including the name and descriptions of the arguments and return value. The process of modifying a working program to improve function interfaces and other qualities of the code. You can do the arithmetic by hand or add print statements to the code. The version of arc in Refactoring is not very accurate because the linear approximation of the circle is always outside the true circle.

As a result, the turtle ends up a few pixels away from the correct destination. My solution shows a way to reduce the effect of this error. Read the code and see if it makes sense to you. If you draw a diagram, you might see how it works. Write an appropriately general set of functions that can draw flowers as in Turtle flowers. Write an appropriately general set of functions that can draw shapes as in Turtle pies.

The letters of the alphabet can be constructed from a moderate number of basic elements, like vertical and horizontal lines and a few curves.

Design an alphabet that can be drawn with a minimal number of basic elements and then write functions that draw the letters.

The main topic of this chapter is the if statement, which executes different code depending on the state of the program. But first I want to introduce two new operators: floor division and modulus.

For example, suppose the run time of a movie is minutes. You might want to know how long that is in hours. Conventional division returns a floating-point number:. Floor division returns the integer number of hours, rounding down:.

The modulus operator is more useful than it seems. Also, you can extract the right-most digit or digits from a number.

A boolean expression is an expression that is either true or false. Although these operations are probably familiar to you, the Julia symbols are different from the mathematical symbols.

The semantics meaning of these operators is similar to their meaning in English. Finally, the! In order to write useful programs, we almost always need the ability to check conditions and change the behavior of the program accordingly. Conditional statements give us this ability. The simplest form is the if statement:. The boolean expression after if is called the condition. If it is true, the indented statement runs. If not, nothing happens. Statements like this are called compound statements.

There is no limit on the number of statements that can appear in the body. The syntax looks like this:. If the remainder when x is divided by 2 is 0, then we know that x is even, and the program displays an appropriate message. If the condition is false, the second set of statements runs.

Since the condition must be true or false, exactly one of the alternatives will run. The alternatives are called branches , because they are branches in the flow of execution. Sometimes there are more than two possibilities and we need more than two branches. One way to express a computation like that is a chained conditional :. Again, exactly one branch will run. There is no limit on the number of elseif statements.

Each condition is checked in order. If the first is false, the next is checked, and so on. If one of them is true, the corresponding branch runs and the statement ends. Even if more than one condition is true, only the first true branch runs. One conditional can also be nested within another. We could have written the example in the previous section like this:. The outer conditional contains two branches. The first branch contains a simple statement. The second branch contains another if statement, which has two branches of its own.

Those two branches are both simple statements, although they could have been conditional statements as well. Although the non-compulsory indentation of the statements makes the structure apparent, nested conditionals become difficult to read very quickly. It is a good idea to avoid them when you can. Logical operators often provide a way to simplify nested conditional statements.

For example, we can rewrite the following code using a single conditional:. It is legal for one function to call another; it is also legal for a function to call itself. It may not be obvious why that is a good thing, but it turns out to be one of the most magical things a program can do. For example, look at the following function:. If n is 0 or negative, it outputs the word, “Blastoff!

A function that calls itself is recursive ; the process of executing it is called recursion. For simple examples like this, it is probably easier to use a for loop. But we will see examples later that are hard to write with a for loop and easy to write with recursion, so it is good to start early. In Stack Diagrams , we used a stack diagram to represent the state of a program during a function call. The same kind of diagram can help interpret a recursive function.

It does not make a recursive call, so there are no more frames.

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