Research regarding algorithm generation/discovery/heuristics

Say I have a specification of preconditions and postconditions for a function. Is there a field of computer science that studies the automated generation of functions that satisfy those specifications?

For example:
Preconditions:

• I is a list

• Q is a binary relation specifying a total order on the

elements in I

Postcondition:

• O is a list

• There exists a bimap B (and its complement B') such that

• O[B[j]] = I[j], and

• O[j] = I[B'[j]],

• for every j, 0

• For every x, 0

The set of functions that satisfy this (I hope unambiguous) specification are the sorting algorithms. So, how do we get a computer to take this specification, and give us a sorting algorithm?

The phrase to look for is "program synthesis". There's lots of literature in the programming literature on this topic; I suggest using Google Scholar to search through the literature and find relevant publications.

These days one hot approach is using "program sketching". In program sketching, the programmer specifies a template for the code: partial code, with some holes left blank. The tool then automatically tries to fill in those holes in a way that is consistent with the preconditions/postconditions, or is consistent with some provided test cases. There's lot of literature on this topic. For an introduction to this line of work, I'll suggest the following tutorial:

The Sketching Approach to Program Synthesis. Armando Solar-Lezama. Tutorial at PLDI 2012.

StackExchange Computer Science Q#41318, answer score: 2