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CHAPTER 11 MULTIPLE ASSIGNMENT
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Expanded version of this assignment:9 IA := ARRAY INTEGER [ IA[1], IA[2], IA[3], 0, IA[5] ] , IA := ARRAY INTEGER [ IA[1], 8, IA[3], IA[4], IA[5] ] ; The constituent assignments here both involve the same target variable: namely, the array variable IA. Of course, we would like the overall multiple assignment to be equivalent to the following: IA := ARRAY INTEGER [ IA[1], 8, IA[3], 0, IA[5] ] ; Again, we ll explain how this effect can be achieved in the next section. For a final example, we return to suppliers and parts. Suppose that for some (bizarre!) reason, relvar S is subject to the constraint that suppliers S2 and S3 must have total status 40. Then each of the following single assignments will fail (we use the UPDATE shorthand for convenience): UPDATE S WHERE S# = S# ('S2') ( STATUS := 15 ) ; UPDATE S WHERE S# = S# ('S3') ( STATUS := 25 ) ; But the following multiple assignment will succeed (again we use the UPDATE shorthand): UPDATE S WHERE S# = S# ('S2') ( STATUS := 15 ) , UPDATE S WHERE S# = S# ('S3') ( STATUS := 25 ) ; Again both of the constituent assignments involve the same target variable, here relvar S. (This time we leave the desired single-assignment equivalent as a somewhat nontrivial exercise for the reader.)
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Semantics
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The previous section should be sufficient to hint at some of the complications involved in getting the semantics of multiple assignment right; indeed, in The Third Manifesto, we got them wrong twice, as already mentioned. Partly because we believe that examining blind alleys can be instructive (and partly just for the record), we summarize our failed attempts here. Let multiple assignment MA consist of single assignments, in sequence, A1, A2, ..., An. Then: In The Third Manifesto, first edition, we simply defined MA to be equivalent to executing A1, A2, ..., An in sequence (except that no constraint checking was done until the end, of course). This definition didn t work because it meant (for example) that the assignment X := Y , Y := X ; would fail to interchange the values of X and Y (it would set X equal to Y but then leave Y unchanged).
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9. Note the implication here that an expression such as IA[4] on the left side of an assignment is a pseudovariable reference; logically, it is.
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CHAPTER 11 MULTIPLE ASSIGNMENT
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In the second edition, by contrast, we required all of the right sides to be evaluated first; then we required A1, A2, ..., An to be executed in parallel (followed by the constraint checking). This definition didn t work because it meant (for example) that the assignment X := Y , X := Z ; would have an unpredictable effect. And in the book Temporal Data and the Relational Model, by C. J. Date, Hugh Darwen, and Nikos A. Lorentzos (Morgan Kaufmann, 2003), we got the semantics wrong again ... To be specific, we required all of the right sides to be evaluated first, and then we required A1, A2, ..., An to be executed in sequence instead of in parallel (followed by the constraint checking as usual). This definition didn t work because it meant (for example) that the assignment THE_X ( P ) := 7.0 , THE_Y ( P ) := 5.0 ; would have no effect on THE_X(P), as explained in the previous section. Here then is our current last word (!) on the subject. Again, let MA be the multiple assignment A1 , A2 , ... , An ; Then the semantics of MA are defined by the following pseudocode (steps 1-4): 1. For i := 1 to n, expand any syntactic shorthands involved in Ai. After all such expansions, let MA take the form V1 := X1 , V2 := X2 , ... , Vz := Xz ; for some z n, where Vi is the name of some variable not defined in terms of any others and Xi is an expression of declared type the same as that of Vi. Here: a. Vi (i = 1, 2, ..., z) is the name of some declared variable (not a pseudovariable) that s not defined in terms of any others. Note: We say not defined in terms of any others in order to take care of assignment to views. Views are variables that are defined in terms of others; thus, assignments to views are replaced by assignments to the relevant view-defining expressions, and those assignments are then replaced by assignments to the relvars in terms of which the views are defined. This process is repeated until all of the assignments have base relvars as their targets. b. Xi (i = 1, 2, ..., z) is an expression whose declared type is the same as that of Vi. Note: The declared type of an operational expression is the declared type of the result of the outermost operator involved in that expression. 2. Let p and q (1 p < q z) be such that Vp and Vq are identical and there is no r (r < p or p < r < q) such that Vp and Vr are identical. Replace Aq in MA by an assignment of the form Vq := WITH Xp AS Vq : Xq and remove Ap from MA. Repeat this process until no such pair p and q remains. Let MA now consist of the sequence U1 := Y1 , U2 := Y2 , ... , Um := Ym ; where each Ui is some Vj (1 i j m z).
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