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APL Exercises 0
Beginnings
⎕io←0 throughout.
0.0 Outer Product (Function Table)
0.0.1 Boolean Functions
Predict the result of each expression before evaluating it.
| ∘.^ ⍨ 0 1 |
| ∘.∨ ⍨ 0 1 |
| ∘.⌊ ⍨ 0 1 |
| ∘.⌈ ⍨ 0 1 |
| ∘.= ⍨ 0 1 |
| ∘.≠ ⍨ 0 1 |
| ∘.< ⍨ 0 1 |
| ∘.≤ ⍨ 0 1 |
| ∘.≥ ⍨ 0 1 |
| ∘.> ⍨ 0 1 |
| ∘.⍲ ⍨ 0 1 |
| ∘.⍱ ⍨ 0 1 |
| |
| ∘.= ⍨ ⍳11 |
| ∘.≠ ⍨ ⍳11 |
| ∘.< ⍨ ⍳11 |
| ∘.≤ ⍨ ⍳11 |
| ∘.≥ ⍨ ⍳11 |
| ∘.> ⍨ ⍳11 |
| • | Which of the function tables are symmetric? (t≡⍉t) |
| • | What can you say about the functions whose tables are symmetric? |
| • | If f is a boolean function (with 0-1 arguments and results), ∘.f⍨0 1
is its truth table and the ravel of that is its intrinsic vector.
For f with valence n there are 2*2*n possible intrinsic vectors.
Find an APL function for each of the following intrinsic vectors:
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
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0.0.2 Arithmetic Functions
Predict the result of each expression before evaluating it.
| ∘.+ ⍨ ⍳11 |
| ∘.- ⍨ ⍳11 |
| ∘.× ⍨ ⍳11 |
| ∘.÷ ⍨ ⍳11 |
| ∘.⌊ ⍨ ⍳11 |
| ∘.⌈ ⍨ ⍳11 |
| ∘.| ⍨ ⍳11 |
| ∘.∧ ⍨ ⍳11 |
| ∘.∨ ⍨ ⍳11 |
| ∘.! ⍨ ⍳11 |
| ∘.* ⍨ ⍳11 |
| ∘.⍟ ⍨ 1+⍳11 |
| • | Which of the function tables are symmetric? |
| • | Why is it ∘.⍟ ⍨ 1+⍳11 and not ∘.⍟ ⍨ ⍳11 ? |
| • | If t←x∘.f y , what is the shape of t ?
| | • | If x and y are vectors and t←x∘.f y ,
how is t[i;j] computed? |
0.1 Reduction
0.1.1 Boolean Functions
Predict the result of each expression before evaluating it.
odometer←{⍉⍵⊤⍳×/⍵}
b←odometer 5⍴2
| ∧/b |
| ∨/b |
| ⌊/b |
| ⌈/b |
| =/b |
| ≠/b |
|
| ≤/b |
| ≥/b |
| >/b |
| ⍲/b |
| ⍱/b |
0.1.2 Arithmetic Functions
Predict the result of each expression before evaluating it.
x←1+?7⍴20
| +/x |
| -/x |
| ×/x |
| ÷/x |
| ⌊/x |
| ⌈/x |
| |/x |
| ∧/x |
| ∨/x |
| !/x |
| */x |
| ⍟/x |
0.1.3 Model
| • | Write a d-operator Reduce
such that (f/v)≡f Reduce v for vector v .
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0.2 Scan
0.2.1 Boolean Functions
Predict the result of each expression before evaluating it.
b←odometer 5⍴2
| ∧\b |
| ∨\b |
| ⌊\b |
| ⌈\b |
| =\b |
| ≠\b |
| <\b |
| ≤\b |
| ≥\b |
| >\b |
| ⍲\b |
| ⍱\b |
| • | Describe in words what each
of the above scans does on a boolean vector b .
For example, ∧\b is “all 1s until the first 0; 0 thereafter”. |
0.2.2 Arithmetic Functions
Predict the result of each expression before evaluating it.
x←1+?7⍴20
| +\x |
| -\x |
| ×\x |
| ÷\x |
| ⌊\x |
| ⌈\x |
| |\x |
| ∧\x |
| ∨\x |
| !\x |
| *\x |
| ⍟\x |
0.2.3 Model
| • | Write a d-operator Scan
such that (f\v)≡f Scan v for vector v . |
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