Canonical software development examples emphasizing "proving safety/usefulness before running" over the "tool" software development approach are cryptographic libraries and NASA space shuttle navigation.

At the time of writing this comment, there was recent furor over software called CryptoCat that didn't provide enough warnings that it was not properly vetted by cryptographers and thus should have been assumed to be inherently insecure. Conventional wisdom and repeated warnings from the security community state that cryptography is extremely difficult to do properly and attempting to create your own may result in catastrophic results. A similar thought and development process goes into space shuttle code.

It seems that the FAI approach to "proving safety/usefulness" is more similar to the way cryptographic algorithms are developed than the (seemingly) much faster "tool" approach, which is more akin to web development where the stakes aren't quite as high.

EDIT: I believe the "prove" approach still allows one to run snippets of code in isolation, but tends to shy away from running everything end-to-end until significant effort has gone into individual component testing.