Church-Turing thesis: a standalone construct

Alonzo Church proposed in 1936, in An unsolvable problem of elementary number theory, that the informal idea of an effectively calculable function, one a person could work out by a finite, rote procedure, coincides exactly with the class of functions his lambda-calculus, equivalently the general recursive functions, can express. In the same year Alan Turing reached the same boundary from a different direction in On computable numbers, with an application to the Entscheidungsproblem, defining computability through an idealised machine, now called a Turing machine, that reads and writes symbols on a tape by fixed rules, and it was then shown that the lambda-calculus, the recursive functions, and the Turing machine all pick out the very same set of functions. Stephen Kleene later collected these results and named the claim, calling it Church's thesis and Turing's thesis, so that today the joined statement is known as the Church-Turing thesis: whatever can be computed by any effective procedure can be computed by a Turing machine. Because the thesis ties an intuitive idea of what it means to compute to several precisely defined models that all agree, it fixes the outer limit of what algorithms can do and underlies the proofs that some problems, such as the halting problem, admit no algorithm at all. It is not a theorem with a proof but a claim about the correspondence between an intuitive concept and a formal one, and it is supported by the convergence of every model of computation proposed since.[1][2][3]

Unit

A foundational thesis identifying the class of effectively calculable functions with the Turing-computable functions

Recovery means

Not applicable

Measured by

Supported by the demonstrated equivalence of independent formal models of computation (Turing machines, lambda-calculus, general recursive functions) rather than by empirical measurement or formal proof