In theoretical computer science, correctness of an algorithm is asserted when it is said that the algorithm is correct with respect to a specification. Functional correctness refers to the input-output behaviour of the algorithm (i.e., for each input it produces the correct output). See also program verification.
A distinction is made between total correctness, where it is additionally required that the algorithm terminates, and partial correctness, which simply requires that if an answer is returned it will be correct. Since there is no general solution to the halting problem, a total correctness assertion may lie much deeper.
For example if we are successively searching though integers 1, 2, 3, ... to see if we can find an example of some phenomenon — say an odd perfect number — it is quite easy to write a partially correct program (use integer factorization to check n as perfect or not). But to say this program is totally correct would be to assert something currently not known in number theory.
A proof would have to be a mathematical proof, assuming both the algorithm and specification are given formally. In particular it is not expected to be a correctness assertion for a given program implementing the algorithm on a given machine. That would involve such considerations as limitations on memory.
A deep result in proof theory, the Curry-Howard correspondence, states that a proof of functional correctness in constructive logic corresponds to a certain program in the lambda calculus. Converting a proof in this way is called program extraction.
The Corrections is a novel of social criticism by American author Jonathan Franzen.
Chip, the middle child, is a politically correct university lecturer whose unfortunate predilection for attractive young girls lands him in a world of self-loathing and financial difficulty, and, eventually, Lithuania.
Denise, the youngest of the family, is successful in her career as a chef, but unsuccessful in fulfilling her mother's requests of finding a nice young Midwestern man to marry, not least as she begins to question her sexuality.
Franzen, a native of the Chicago suburb of Western Springs, said Monday he had sent an e-mail to the television talk show host asking her forgiveness, but had not received a reply.
Winfrey's choice of The Corrections for her club was announced Sept. 24 and Franzen had been expected to appear on her show in the next few weeks.
The Corrections, the story of an alienated Midwestern family, was a best seller before the Oprah selection and more than 500,000 copies are in print.
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