Questioning a Dogma of Algorithmic Thinking in Our Time

The container notation and other results from \(\lambda \) -philosophy obtained in the previous chapters and in this one are put together to dispute a widely accepted dogma of our time, one concerning the philosophy of computer science. More specifically, the basic operations of the Turing machine model are of two kinds: printing actions and motion actions. In contrast, the \(\lambda \) -calculus under the interpretation offered by the container notation ( \(=\) the \(\lambda \) -CN-calculus) is based on a single active operation (substitution) and a no-operation. Then, the latter is simpler than the former. Furthermore, the \(\lambda \) -CN-calculus is based on Spelke’s principle of solidity and other results from cognitive science which refer to a very basic stage of cognitive development. So, the \(\lambda \) -CN-calculus is at least as intuitive and natural (concerning effectiveness) as the Turing machine model (or even more so due to the container notation). Consequently, the extended belief (often assumed dogmatically by educators and researchers) that Turing’s approach is more convincing or more important than Church’s approach is clearly untenable (except for the construction of computer hardware). Therefore, the widespread preference for Turing machines and the neglect of the \(\lambda \) -calculus for both teaching and research tasks is today unacceptable and unjustifiable.