By Timothy Budd

ISBN-10: 0387966439

ISBN-13: 9780387966434

Offers the result of an research into the problems raised by means of the improvement of a compiler for APL, a truly excessive point machine programming language. APL offers a host of novel difficulties for a compiler author: vulnerable variable typing, run time adjustments in variable form, and a number of primitive operations. throughout the integration of numerous lately built compiler building ideas, akin to facts movement research, and a unique and house effective call for pushed or lazy review method of code iteration, the writer has been in a position to produce a real compiler for the language whereas nonetheless keeping the felxibility and simplicity which are the hallmarks of APL.

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**Additional resources for An APL Compiler**

**Example text**

Prove the Horizontal Line Test for one-to-one functions. 11. Consider the set S from Activity 3. a. Give a direct proof that -12 is in S. h. Give an indirect proof that -50 is not in S. 12. Here is a brief mathematical argument: If n is a prime number then 2n - 1 is prime. However, 211 - 1 = 2047 = 23 * 89. Therefore 11 is not prime. a. Identify the propositions in this argument and assign variables to them. h. Write the argument in symbolic form. What kind of proof is this trying to be? c. Explain what is wrong with the argument.

D. Which natural numbers have exactly four divisors? 20. a. Write a func that accepts a pair of integers x and y and decides whether (x mod n) * (y mod n) = (x * y) mod n. Your func should return either true or false. Test your func on some pairs of values and explain the results. h. How could you modify this func to obtain one which always returns true? 21. Demonstrate that 2,3, -1, and -2 can each be formed by linear combinations of 3403 and 3503. Explain how any integer K could be formed. 22.

4. Suppose that we know that the three statements PI P 4 are all true. a. Is it true that PI -7 -7 P2, P2 -7 P3, P3 -7 P4? Why or why not? h. Use ISETL to produce a truth table showing PI, P2, P3, P4, PI -7 P4. Print a copy of your table and cross out any lines on which the statement PI -7 P2 is not true. Then cross out any lines on which P2 -7 P3 is not true or on which P3 -7 P4 is not true. Does the remaining portion of the table agree with your answer from part 4a? Tell how you know. c. How was the idea from this activity used in Activity 3?

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