In this problem, you're asked to enter a line of APL, including data given to APL symbols. This line will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described in the problem description.

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1: Existentialism

In APL text data must appear between single quotes. For example 'ABC' will give a result that looks like ABC.

In APL, yes/no questions are answered with 1 for yes and 0 for no.

The symbol ∊ is Exists In (and it looks like E too) because it reports whether letters of the text on its left exist in the text on its right. For example, 'APL' ∊ 'DYALOG' gives 1 0 1 because:

• 1: yes, 'A' exists in 'DYALOG'
• 0: no, 'P' does not exist in 'DYALOG'
• 1: yes, 'L' exists in 'DYALOG'

Note that what we’re looking for goes on the left of the ∊, and where we’re looking goes on its right.

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Write a single line of APL that uses ∊ to show that each of the letters in the English alphabet 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' (← click to copy) is found in the text 'THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG' (← click to copy). The result should be 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, that is, 26 1s.

In this problem, you’re asked to enter a single symbol that represents a comparison. The APL Challenge system will check that you entered the correct symbol.

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2: Comparing This to That

APL has six symbols that compare the data on their left the data on their on the right. Just like ∊ from Problem 1, they give 1 for yes and 0 for no when answering whether the statement is true.

The six comparisons are Smaller Than (<), Smaller Than Or Equal To (≤), Equal To (=), Bigger Than Or Equal To (≥), Bigger Than (>), and Not Equal To (≠).

You can check what each symbol will give in a line like 2 < 3 by using its name instead of its symbol. For example, we could say Is 2 Smaller Than 3? — yes, that's a true statement, so 2 < 3 will give 1 for yes.

APL can compare entire lists of numbers, rather than just single numbers. For example, 1 2 3 = 5 4 3 gives 0 0 1 because:

• 0: no, 1 is not equal to 5
• 0: no, 2 is not equal to 4
• 1: yes, 3 is equal to 3

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Which comparison symbol will give 0 1 0 1 0 with 3 5 4 8 6 on its left and 3 4 5 3 9 on its right?

In other words, which symbol would you place in the box ( ⎕ ) of the APL code 3 5 4 8 6 ⎕ 3 4 5 3 9 (← click to copy) so that the answer will be 0 1 0 1 0?

In this problem, you're asked to enter a line of APL, including data given to APL symbols. This line will be tested by the APL Challenge system to check that it gives the correct result and uses the methods described in the problem description.

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3: Picky Picky

The symbol ⊃ is called Pick because, when given a number (let’s call it n) on its left and a list on its right, it picks item number n from the list. For example, 2 ⊃ 'DYALOG' gives Y and 2 ⊃ 'DYALOG' 'APL' gives APL.

So far, we’ve only used text (in single quotes) and lists of numbers like 'DYALOG APL' and 3 1 4 1 5 9. Both of these are simple lists; one is a list of letters (we count space as a letter), the other is a list of numbers (the spaces between numbers don’t count). APL can also handle lists of lists, and so on. For example, 'DYALOG' 'APL' is a list of two texts, that is, a list of two lists of letters.

If we want additional levels of lists inside lists, we use round brackets to mark each list. For example, (1 2 3)(2 7 1 8) is a list of two lists of numbers, and ('KEN' 'IVERSON')('DYALOG' 'APL') is a list of lists of texts (with each text itself being a list of letters).

If we give Pick a list of numbers (rather than a single number) on the left (we’ll still call it n), then:

1. the first number from n picks the appropriate item from the list on the right of Pick
2. the second number from n picks the appropriate item from that list
3. and so on

For example, 2 1 ⊃ 'DYALOG' 'APL' will pick:

1. item 2 from 'DYALOG' 'APL', which is 'APL'
2. item 1 from 'APL', which is 'A'

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Write a line of APL using ⊃ that will pick the 'G' from ('KEN' 'IVERSON')('DYALOG' 'APL') (← click to copy).

In this problem, you are asked to write an APL expression (line of APL), including arguments (data given to APL symbols). This expression will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described in the problem description.

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4: Partition Condition

Partition ⊆ is a function (symbol) that cuts up text into parts: It takes a text as its right argument and a list of numbers as its left argument. The list of numbers has only 1s and 0s, and specifies how to cut the text into parts. Characters (letters and spaces) in the text corresponding to 0s are discarded; a new part is then started. For example, 0 0 1 1 0 1 1 1 1 0 0 1 1 1 ⊆ 'THIS PARTITION' gives:

┌──┬────┬───┐
│IS│PART│ION│
└──┴────┴───┘

We can show what’s going on like this:

0 0 1 1 0 1 1 1 1 0 0 1 1 1
t h i s   p a r t i t i o n

Remember the comparison functions from Problem 2? We used them with single numbers on both sides and with lists of numbers on both sides. However, they can also take a single number on the left and a list on the right. For example, 4 < 3 5 7 gives 0 1 1, because:

• 0: no, 4 is not less than 3
• 1: yes, 4 is less than 5
• 1: yes, 4 is less than 7

Furthermore, we only used the comparison functions with numbers, but two of them, = and ≠, work on characters too. For example, 'APL' = 'ABC' gives 1 0 0, because:

• 1: yes, A is equal to A
• 0: no, P is not equal to B
• 0: no, L is not equal to C

An APL function takes the answer of all the code to its right as its right argument. For example, 2×3+4 gives 14, rather than the 10 that you might expect. This is because the × takes the answer of 3+4 as its right argument. However, you can use round brackets to change the order in which things are calculated, limiting any right argument so it only goes as far as the nearest closing bracket …) on its right: (2×3)+4 gives 10.

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Using ⊆, one of the comparison functions, and round brackets, write an expression that will cut the text 'THE QUICK BROWN FOX' into words at the space characters (' '). The answer should be

┌───┬─────┬─────┬───┐
│THE│QUICK│BROWN│FOX│
└───┴─────┴─────┴───┘

(Hint: You will need to use the text 'THE QUICK BROWN FOX' twice, so don’t forget that you can click on it to copy it.)

In this problem, you’re asked to enter a single comparison function. The APL Challenge system will check that you entered the correct symbol.

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5: You Can Scan!

The APL symbols you’ve met so far take one data argument on each side. These symbols are called functions. APL also has operators which take a data argument on the right (just like functions), but on the left take a function instead of data. Each operator uses the given function with the given data in a specific way. Scan \ is such an operator. It takes a list on its right, and a function on its left. The function could be Plus (+) or Times (×), or any of the comparison functions you met in Problem 2.

Scan gives an answer of the same length as the given list:

1. The first item of the answer is the same as the first item in the list
2. The second item of the answer is calculated by putting the function between the first and second items of the list
3. The third item of the answer is calculated by putting the function between the first three items of the list
4. and so on

The first item of the answer is the same as the first item in the list. The second item of the answer is calculated by putting the function between the first and second items of the list. The third item of the answer is calculated by putting the function between the first three items of the list. And so on.

For example, +\ 1 9 2 0 1 2 1 7 gives 1 10 12 12 13 15 16 23, as follows:

1                              →   1
1 + 9                          →  10
1 + 9 + 2                      →  12
1 + 9 + 2 + 0                  →  12
1 + 9 + 2 + 0 + 1              →  13
1 + 9 + 2 + 0 + 1 + 2          →  15
1 + 9 + 2 + 0 + 1 + 2 + 1      →  16
1 + 9 + 2 + 0 + 1 + 2 + 1 + 7  →  23

and <\ 0 0 1 0 1 0 1 gives 0 0 1 0 0 0 0, as follows:

0                          →  0
0 < 0                      →  0
0 < 0 < 1                  →  1
0 < 0 < 1 < 0              →  0
0 < 0 < 1 < 0 < 1          →  0
0 < 0 < 1 < 0 < 1 < 0      →  0
0 < 0 < 1 < 0 < 1 < 0 < 1  →  0

Remember from the previous problem that, when an APL expression contains multiple functions, they are applied from right to left. So, 0 < 0 < 1, which is 0 < (0 < 1), which is 0 < (1), and so on.

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Which comparison function, when used with Scan and a right argument of 0 1 1 0 0 1 0 1 0 1 1 0, will give 0 1 0 0 0 1 1 0 0 1 0 0?

In other words, which symbol would you place in the box ( ⎕ ) of the APL code ⎕\ 0 1 1 0 0 1 0 1 0 1 1 0 (← click to copy) so the expression gives 0 1 0 0 0 1 1 0 0 1 0 0?

In this problem, you are asked to write an APL expression, including arguments. This expression will be tested by the APL Challenge system to check that it gives the correct answer and uses the methods described in the problem description.

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6: Leading Question

Every APL function you’ve met to far, has taken two arguments, but some functions only take one argument. For those, the single argument goes on the right. The Not function ~ is an example of such a function. It swaps 1s and 0s, turning each 1 (yes) in its right argument into a 0 (no) and each 0 (no) into a 1 (yes): ~ 1 1 0 1 0 0 1 gives 0 0 1 0 1 1 0.

In the last problem you learned about the Scan operator. The related Reduce operator / returns the last item of what would have been Scan’s result. For example, +/ 1 9 2 0 1 2 1 7 returns 23 (that is, 1+9+2+0+1+2+1+7).

You can use the And function ∧ to see whether both of two statements are true. This gives 1 (yes) if both its left and right arguments are 1 (yes); if any of its arguments are 0 (no), it gives 0 (no).

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Using Plus (+), Reduce (/), And (∧), Scan (\), Not (~), and Exists In (∊), write an APL expression that counts how many consonants (non-vowels) are at the beginning of the word 'SCHNITZELS' (← click to copy), before the first vowel (which is I).

(Use 'AEIOU' as your list of vowels.)

In this problem, you are asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

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7: You Have My Word

You can create your own function by putting an expression in curly brackets. Within this expression, if needed, ⍺ (alpha) refers to the argument to the left of { and ⍵ (omega) refers to the argument to the right of }. (This is because alpha and omega are the left-most and right-most letters of the Greek alphabet, respectively.) For example, a function that adds its arguments and then multiplies by two could be written {2×⍺+⍵}.

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Using Pick (⊃) and your answer for Problem 4, write a function that takes a number n as its left argument and a text that has words (with spaces between them) as its right argument, and gives word number n from the text. For example:

      1 {answer} 'THE QUICK BROWN FOX'
THE

      3 {answer} 'THE QUICK BROWN FOX'
BROWN

      5 {answer} '   EXTRA    SPACES DO NOT MATTER   '
MATTER

(The text will have at least n words.)

In this problem, you are asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

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8: Give Me a Break!

In Problem 4, you learnt how to cut text into parts based on the location of space characters. You will now take that a step further by cutting a text into parts based on the location of characters from a list. Remember from Problem 3 that a text is just a list of characters.

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Using Not (~), Exists In (∊) and Partition (⊆), write a function that takes a text on its right and a list of characters on its left and cuts the text at those characters. For example:

      ':- ,()' {answer} 'THREE-CHARACTER ANIMALS: CAT,DOG,ELK,EEL (AND BAT)'
┌─────┬─────────┬───────┬───┬───┬───┬───┬───┬───┐
│THREE│CHARACTER│ANIMALS│CAT│DOG│ELK│EEL│AND│BAT│
└─────┴─────────┴───────┴───┴───┴───┴───┴───┴───┘

      ':/.?=' {answer} 'HTTPS://WWW.BLOOFO.COM:8080?NAME=VALUE'
┌─────┬───┬──────┬───┬────┬────┬─────┐
│HTTPS│WWW│BLOOFO│COM│8080│NAME│VALUE│
└─────┴───┴──────┴───┴────┴────┴─────┘

In this problem, you are asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

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9: Turning up the Heat

Remember from Problem 7 that ⍺ refers to the left argument of your own function, but you also learnt in Problem 6 that not all functions need a left argument. Such functions do not need an ⍺. For example, a function to multiply its sole (right) argument by itself and then subtract one could be written {(⍵×⍵)-1}.

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Write a function that describes a temperature given in degrees Fahrenheit: If the temperature is below 32 (you don’t need to handle negative temperatures) it is 'FREEZING', while if it is 32 or higher, but below 50, it is merely 'COLD'. From 50 it becomes 'CHILLY', then from 70 it is 'PLEASANT', from 85 it is 'HOT' and at or above 95 it is 'HELLISH'. For example:

      {answer} 33
COLD

      {answer} 14
FREEZING

      {answer} 83
PLEASANT

In this problem, you are asked to enter your own APL function, without giving it any arguments. Your function will be checked by the APL Challenge system using several tests to see whether it is correct.

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10: Pick a Vowel

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Using the techniques you have learnt so far, write a function that takes a word as its right argument and gives the word’s first vowel as its answer. For example:

      {answer} 'SPHRAGISTIC'
A

      {answer} 'SEAL'
E

      {answer} 'ICONOGRAPH'
I

(The given word will have at least one vowel. Use 'AEIOU' as your list of vowels.)