Recursive Functions (Stanford Encyclopedia of Philosophy)
Such a definition might at first appear circular in virtue of the fact that the value of fact(x) on the left hand side is defined in terms the same function on the righthand side. However a…
LPO Proofs in Two Educational Contexts
It turns out that there is no clear winner in both contexts, but the newly introduced so-called shuffled Fitch style is the most practical choice.
A functional proof pearl: inverting the Ackermann hierarchy
This work implements in Gallina a hierarchy of functions that calculate the upper inverses to the hyperoperation/Ackermann hierarchy and shows that these functions are consistent with the usual definition of the inverse Ackermann function α(n).
History of Informatics. From recursivity to the Turing universal machine and Horn clauses
- Computer Science
The article describes the contribution of Romanian scientists in several fields of scientific research, on the fundamentals of calculus theory, the fundamentals of cybernetics, the algebra theory of…
Computational Multiscale Modeling of Fluids and Solids
mathematical notation of set theory and functions on sets are helpful but not essential. This notation is introduced and explained in Part I of this book, particularly in Chap. 3. The same holds for…
Turing, Gödel and the “Bright Abyss”
- Computer Science
We consider the development of computability in the 1930s from what we have called the formalism free point of view. We employ a dual conceptual framework: confluence together with grounding.
Explication, Open-Texture, and Church’s Thesis
Advanced Control Flow
This chapter reviews basic control flow and then presents advanced control flow, which is not easily simulated using the basic control structures.
Two-dimensional modal logics with difference relations
The notion of products of propositional modal logics, introduced by Segerberg  and Shehtman , provides a conceptually appealing approach to combining modallogics.
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