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4 Write a do clause that constructs the transpose (rows and columns interchanged) of a 4 x 4 array. The greatest weakness of the program is that it gets stuck in any dead end, whereas one may find a way out by retracing one's steps and taking an alternative route. As one retreats from a dead end the squares should be marked so that they are not revisited. To do this backtracking, we could keep a list of the squares as they are visited, but it is sufficient to know the previous square by storing the direction of each move.

2' has the same effect. The standard arithmetic operators apply to complex numbers, and in suitable contexts real numbers will be widened to complex, just as integers are widened to reals. In addition, the operator 'conj' gives the complex conjugate, and 'arg' the principal argument. 4 by also printing any complex roots. CALENDARS: PROCEDURES 45 We extend the BNF to include mode declarations ( identity decl ) : := mode ( modename ) = (type ) (,( modename ) = ( type ))* (mode name ) : := (new keyword) where the latter is an identifier in boldface type (or underlined) that is not already in use.

Unlike proc variables, op symbols cannot be declared separately from the routines defining them. They only occur in identity declarations of the form (identity decl) : := op ( opsymbol) = (non-void routine) The ( opsymbol ) allowed depends on the implementation, but unused characters like £ can always be used, and the standard operators can be re-defined or extended to different types. An example used in chapter 3 is the concatenation of a string and a character, for example, "BAT" + "H" gives "BATH".

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