  Modern software relies on libraries and uses them via application programming
interfaces (APIs). Correct API usage as well as many software engineering tasks
are enabled when APIs have formal specifications. In this work, we analyze the
implementation of each method in an API to infer a formal postcondition.
Conventional wisdom is that, if one has preconditions, then one can use the
strongest postcondition predicate transformer (SP) to infer postconditions.
However, SP yields postconditions that are exponentially large, which makes
them difficult to use, either by humans or by tools. Our key idea is an
algorithm that converts such exponentially large specifications into a form
that is more concise and thus more usable. This is done by leveraging the
structure of the specifications that result from the use of SP. We applied our
technique to infer postconditions for over 2,300 methods in seven popular Java
libraries. Our technique was able to infer specifications for 75.7% of these
methods, each of which was verified using an Extended Static Checker. We also
found that 84.6% of resulting specifications were less than 1/4 page (20 lines)
in length. Our technique was able to reduce the length of SMT proofs needed for
verifying implementations by 76.7% and reduced prover execution time by 26.7%.
