[RossBencina]

Interesting. Are there more examples somewhere? I'm curious about cases where multiple examples are required. The associativity "example" corresponds directly to the rewrite rule definition, so it doesn't really illuminate the distinction between specifying a rewrite rule and inferring a rule from multiple examples.

[heavymemory]

Right, associativity is the simplest case because the structure is visible directly in one example.

The system needs multiple examples when there is more than one varying part and a single example is ambiguous. A simple example is wrapping a function call. With:

    doThing(x) → log(doThing(x))
    process(y) → log(process(y))

the system learns that: the function name varies the argument varies he outer log(…) is constant

From that it infers the general rule and applies it to new inputs. A single example would not be enough to disambiguate that pattern.