A Programming Language. by Kenneth E. Iverson

By Kenneth E. Iverson

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Birkhoff and MacLane, (1941)] because (1) the direction of the transformation (from a to c) is unequivocally indicated, and (2) the notation directly indicates a straightforward and efficient method for actual execu­ tion, namely, indirect addressing. 17 MapjJing and jJermutations 33 Consequently, if p, q, ... , t are vectors, each contained in b, then each can be represented jointly by the vector b and a mapping vector. , are texts, the total storage required for b and the mapping vectors might be considerably less than for the entire set of texts.

The index i = b l h, 2. the index k such that ale 3. the element ale. I2a. The ranking is performed (steps 1-3) by scanning the set b in order and comparing each element with the argument b. The second phase is a permutation of the integers 1,2, ... , v(b), which may be described by a permutation vector j, such that Ii = k. The selection of ji (step 4) then defines k, which, in turn, determines the selection of ale on step 5. 2. If b = (apple, booty, dust, eye, night), a = (Apfel, Auge, Beute, Nacht, Staub) are, respectively, a set of English words and a set of German correspondents (both in alphabetical order), and if the function required is the n1apping of a given English word b into its German equivalent a according to the dictionary corre­ spondences: English: apple booty dust eye night German: thenj = Apfel (1,3,5,2,4).

Exanlples of literals are the integers, the characters of the various alphabets, punctua­ tion nlarks, and ITIiscellaneous syITIbols such as S and ~~. 4 are 0, 1, and 2. It is important to distinguish clearly between general synlbols and literals. In ordinary algebra this presents little difficulty, since the only literals occurring are the integers and the decinlal point, and each general sylnbol employed includes an alphabetic character. 3 The language appear. Moreover, in a computer program, numeric symbols (register addresses) are used to represent the variables.

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