Remark: This result can also be obtained as a consequence of a theorem of Ehrenfeucht and Mycielski which states that, if T + [logical not][alpha] is undecidable, then there is no recursive function
f such that [W.
To demonstrate the significance of the EP data model being both a data model and a language semantically equivalent to a class of total recursive functions
, the authors of the articles [27 and 23] suggested an objective view on easiness.
In order to be able to tackle effectively the problem of whether it is legitimate, in the light of Hilbert's finitism of the 1920s, to identify the finitist functions with the primitive recursive functions
, let us do some preparatory work and ask: Did Hilbert qua finitist mathematician believe in the existence of functions?
We describe recursive function
definitions in Section 2.
Note that the students were developing an informal understanding of recursive functions
1967]: Theory of Recursive Functions
and Effective Computability.
Kevin Xu, and his colleagues in the opening paper brief the conceptual differences between a "data model" and a "programming Language" and more specifically addressed the Enterprise-Participant model as a semantic equivalent to the class of total recursive functions
More usually, recursive functions
are simultaneously described and named by writing f ?
A machine independent theory of the complexity of recursive functions
Type inference for the Typerec construct would require solving equations over expressions involving primitive recursive functions
, which appears difficult or impossible.
There are many general methods for transforming recursive functions
to equivalent iterative programs (one method is often illustrated on a recursive factorial function).
The source language is the explicitly typed call-by-value lambda calculus with ML style polymorphism and recursive functions