Research and Advances

Sequential formula translation

The syntax of an algorithmic language such as ALGOL is conveniently described as a sequence of states indicated by an element called cellar. Transitions are controlled by admissible state-symbol pairs which may be represented by a transition matrix. This description of syntax furnishes at the same time an extremely simple rule for translating into machine programs statements in the algorithmic language. Sequential treatment, however, is not feasible in the case of certain optimizing processes such as recursive address calculation.

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Research and Advances

Positivity and norms

Following some lines of joint work with A.S. Householder, the character and use of algebraic methods in the theory of norms is demonstrated. New results concerning norms with values in an Archimedian vector lattice (not necessarily being totally ordered) are given, in particular for the generalization of order unit norms, L-norms and M-norms. An example of application to operator norms is given concerning contraction properties of positive operators.
Research and Advances

The “Plankalkül” of Konrad Zuse: a forerunner of today's programming languages

Plankalkül was an attempt by Konrad Zuse in the 1940's to devise a notational and conceptual system for writing what today is termed a program. Although this early approach to a programming language did not lead to practical use, the plan is described here because it contains features that are standard in today's programming languages. The investigation is of historical interest; also, it may provide insights that would lead to advancements in the state of the art. Using modern programming terminology, the Plankalkül is presented to the extent it has been possible to reconstruct it from the published literature.

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