This article expands on Curry's work on how to implement the problem of inverse interpolation on the ENIAC (1946) and his subsequent work on developing a theory of program composition (19481950). It is shown that Curry's hands-on experience with the ENIAC on the one side and his acquaintance with systems of formal logic on the other, were conductive to conceive a compact notation for program construction which in turn would be instrumental to a mechanical synthesis of programs. Since Curry's systematic programming technique pronounces a critique of the Goldstine-von Neumann style of coding, his calculus of program composition not only anticipates automatic programming but also proposes explicit hardware optimizations largely unperceived by computer history until Backus' famous ACM Turing Award lecture (1977). The cohesion of these findings asks for an integrative historiographical approach. An appendix gives, for the first time, a full description of Curry's arithmetic compiler.

%B Journal of Logic and Computation %G eng %R 10.1093/logcom/exs072 %0 Report %D 2012 %T A short history of small machines %A De Mol, Liesbeth %A Bullynck, Maarten %XOne of the most famous results of Alan M. Turing is the so-called universal Tur- ing machine (UTM). Its in uence on (theoretical) computer science can hardly be overestimated. The operations of this machine are of a most elementary na- ture but nonetheless considered to capture all the (human) processes that can be carried out in computing a number. This kind of elementary machine ts into a tradition of `*logical minimalism*' that looks for simplest sets of operations or axioms. It is part of the more general research programme into the foundations of mathematics and logic that was carried out in the beginning of the 20th cen- tury. In the 1940s and 1950s, however, this tradition was redened in the context of `computer science' when computer engineers, logicians and mathematicians re-considered the problem of small(est) and/or simple(st) machines in the con- text of actual engineering practices. This paper looks into this early history of research on small symbolic and physical machines and tie it to this older tradi- tion of logical minimalism. Focus will be on how the transition and translation of symbolic machines into real computers integrates minimalist philosophies as parts of more complex computer design strategies. This contextualizes Turing's machines at the turn from logic to machines.

A complete reconstruction of Lehmer's ENIAC set-up for computing the exponents of p modulo two is given. This program served as an early test program for the ENIAC (1946). The reconstruction illustrates the difficulties of early programmers to find a way between a man operated and a machine operated computation. These difficulties concern both the content level (the algorithm) and the formal level (the logic of sequencing operations).

%B Archive for Mathematical Logic %V 49 %P 123–146 %G eng %U http://dx.doi.org/10.1007/s00153-009-0169-8 %0 Conference Paper %B Logic and Theory of Algorithms %D 2008 %T A week-end off: the first extensive number-theoretical computation on the ENIAC %A De Mol, Liesbeth %A Bullynck, Maarten %E Beckmann, Arnold %E Dimitracopoulos, Costas %E Löwe, Benedikt %XThe first extensive number-theoretical computation run on the ENIAC, is reconstructed. The problem, computing the exponent of 2 modulo a prime, was set up on the ENIAC during a week-end in July 1946 by the number-theorist D.H. Lehmer, with help from his wife Emma and John Mauchly. Important aspects of the ENIAC's design are presented-and the reconstruction of the implementation of the problem on the ENIAC is discussed in its salient points.

%B Logic and Theory of Algorithms %I Springer Verlag %@ 978-3-540-69405-2 %G eng %R 10.1007/978-3-540-69407-6_19