Program synthesis comprises a range of technologies for the automatic generation of executable computer programs from high-level specifications of their behaviour. In contrast to compilation, the specifications are usually non-algorithmic.
The idea originated in the 60s with the aim of using techniques
from artificial intelligence to build an automatic programmer,
exploiting deep connections between mathematics and the theory of programming.
Lack of early success meant that the mathematical approach soon fell out of favour, along with enthusiasm for AI, in general. Although some researchers still
work on formal approaches, more success has been obtained by combining pure deductive techniques with powerful heuristics, and limiting their application to specific domains.
Some feel that the concept of automated program generation often results in poor "factoring" of information. Known redundancy should be factored out, not introduced, it is said. However, sometimes specific programming languages are limited such that one has to introduce repetition of a concept or pattern in order to keep using the same language. Here is a simplified illustration of factoring:
Poor Factoring:
x = a + a + a + a + a
Good Factoring:
x = a * 5 (where the asterisk is "times")
Program generation tends to focus on automating the repetition seen in the first example, when a better approach is perhaps to find a higher-order abstraction, which is multiplication in this case. Other examples include putting parameters into a file or database instead of inside application code.