The programming language Pascal has a construct repeatuntil for a logical post-test loop. The syntax is given by the following (somewhat simplified) grammar:

| id = + | * | () | id | int-literal | ; repeat until (id relop id)

1. This problem deals with the operational semantics for this construct.

You may assume that the attribute grammar for the operational semantics of assignment statements and expressions are the same as those in the slides, and the operational semantics for statement lists is as follows:

{.code .code}

[2] ; {.code = [2].code || .code}

a. Write an attribute grammar for the intermediate code for repeat loops. You may assume, if needed, that there is a function negate(relop) that returns the opposite of the given relational operations lexeme (for example, negate(<) is >=).

b. Show the decorated parse tree and the intermediate code generated by your grammar for the following source code. a = 0; b = 10; c = 150; repeat a = a + 3; b = b*a until (b > c)

2. This problem deals with the denotational semantics for the same construct. You may assume that the denotational semantics for decimal numbers, expressions, assignment statements, and statement lists are as given in the textbook and slides.

a. Write the denotational-semantics definition for the function

Mr(,s), where s is the initial state before the loop begins execution.

(HINT: Unlike a logical pre-test loop, a logical post-test loop executes the statement list at least once. What is the effect of this on the state when the first logical test is performed?)

b. Use your denotational semantics to compute

Mr(repeat a = a+3; b = b*a until (b > c), {,,})