Lambda the Ultimate

Imperative Functional Programs that Explain their Work
Wilmer Ricciotti, Jan Stolarek, Roly Perera, James Cheney
submitted on arXiv on 22 May 2017

Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work by Perera et al., where dynamic slicing was defined for pure higher-order functional programs as a Galois connection between lattices of partial inputs and partial outputs. We extend this approach to imperative functional programs that combine higher-order programming with references and exceptions. We present proofs of correctness and optimality of our approach and a proof-of-concept implementation and experimental evaluation.

Dynamic slicing answers the following question: if I only care about these specific part of the trace of my program execution, what are the only parts of the source program that I need to look at? For example, if the output of the program is a pair, can you show me that parts of the source that impacted the computation of the first component? If a part of the code is not involved in the trace, or not in the part of the trace that you care about, it is removed from the partial code returned by slicing.

What I like about this work is that there is a very nice algebraic characterization of what slicing is (the Galois connection), that guides you in how you implement your slicing algorithm, and also serves as a specification to convince yourself that it is correct -- and "optimal", it actually removes all the program parts that are irrelevant. This characterization already existed in previous work (Functional Programs that Explain Their Work, Roly Perera, Umut Acar, James cheney, Paul Blain Levy, 2012), but it was done in a purely functional setting. It wasn't clear (to me) whether the nice formulation was restricted to this nice language, or whether the technique itself would scale to a less structured language. This paper extends it to effectful ML (mutable references and exceptions), and there it is much easier to see that it remains elegant and yet can scale to typical effectful programming languages.

The key to the algebraic characterization is to recognize two order structures, one on source program fragment, and the other on traces. Program fragments are programs with hole, and a fragment is smaller than another if it has more holes. You can think of the hole as "I don't know -- or I don't care -- what the program does in this part", so the order is "being more or less defined". Traces are also partial traces with holes, where the holes means "I don't know -- or I don't care -- what happens in this part of the trace". The double "don't know" and "don't care" nature of the ordering is essential: the Galois connection specifies a slicer (that goes from the part of a trace you care about to the parts of a program you should care about) by relating it to an evaluator (that goes from the part of the program you know about to the parts of the trace you can know about). This specification is simple because we are all familiar with what evaluators are.