Great Ideas in Computer Science

Karel the Robot (continued)

a)    test reversal:

    IF <test>
        THEN <instr-1>
        ELSE <instr-2>

    is equivalent to

    IF <opposite test>
        THEN <instr-2>
        ELSE <instr-1>

    e.g.,    IF next-to-a-beeper
                THEN pickbeeper
                ELSE move

                is equiv to

                IF not-next-to-a-beeper
                    THEN move
                    ELSE pickbeeper

    e.g., the awkard program:

            IF next-to-a-beeper
                THEN <do next instr>
                ELSE move

            is equiv to

            IF not-next-to-a-beeper
                THEN move

            (don't need ELSE !)

b) bottom factoring:

    IF facing-north
        THEN
            BEGIN
                move;
                turnleft
            END
        ELSE
            BEGIN
                putbeeper;
                turnleft
            END

    which has a common instruction (turnleft) that can
    be "factored out"

        - cf. (2*3) + (4*3), which = 6+12 = 18
                = (2+4)*3, which = 6*3 = 18

    & is equiv to:

    IF facing-north
        THEN move
        ELSE putbeeper;
    turnleft

c) top factoring:

    IF <test>
        THEN
            BEGIN
                <instr-1>;
                <instr-2>
            END
        ELSE
            BEGIN
                <instr-1>;
                <instr-3>
            END

    is equiv to

    <instr-1>;
    IF <test>
        THEN <instr-2>
        ELSE <instr-3>

d)    redundant-test factoring:

    IF <test-1>
        THEN
            BEGIN
                <instr-1>;
                IF <test-1>
                    THEN <instr-2>
            END

    is equiv to

    IF <test-1>
        THEN
            BEGIN
                <instr-1>;
                <instr-2>
            END

Warning:  Only works if <instr-1> doesn't change
                the condition of <test>

B.  Dangling Else

IF facing-north
    THEN IF front-is-clear
                THEN move
                ELSE turnleft

vs.

IF facing-north
    THEN IF front-is-clear
                THEN move
    ELSE turnleft

There are 2 different intents here, but only 1 instr.
Therefore, to get the intent of the 2nd, do:

    IF facing-north
        THEN
            BEGIN
                IF front-is-clear
                    THEN move
            END
        ELSE turnleft