My Haskell Program does not fail. Proof?
Proving correctness of programs and ensuring they are bug-free has always been a challenging problem.
Mostly we have relied on manual testing to check the correctness of programs.
Strong static type systems help us to write bug free programs from the start but many interesting cases can miss out.
Many tools such as QuickCheck, Liquid Haskell have been developed to address this issue.
In this talk, we will presenting a different approach, Bounded Model Checking (BMC), which has been very successful in proving correctness of imperative programs by means of tools such as CBMC.
We will explain how BMC works at high level, how we have adopted it for Haskell and our success with the same.
We will also present how you can use it to prove correctness of your Haskell programs.
Outline/Structure of the Talk
- Introductory example
- Overview of the overall Approach
- Details about the algorithm
- Results
- Future directions
Learning Outcome
- Get a taste of core FP research
- Get a deeper understanding of execution semantics of Haskell
- Say Hello to GHC Core and SMT solvers
Target Audience
Functional Programmers who are interested in the latest research in the field
Prerequisites for Attendees
- Basic understanding of Haskell
- Familiarity with other formal verification tools such as CBMC is a plus but not necessary
schedule Submitted 4 years ago
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In every domain that uses computational linear algebra (which is all of engineering and science), we encounter the 'how to optimize a linear algebra expression into an optimized sequence of BLAS (or LAPACK or $linear_algera library) kernel calls' problem.Example: (if the math equations make you want to tear your hair out and go jump off a cliff, don't worry, it is just an example, you don't have to grok it. Just skim the equations The basic problem being addressed here is that solving such equations with code takes up a lot of effort and time from experts in computational linear algebra)
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1. For different input sizes, different algorithms give the most optimal performance. Which algorithm do you code up?
2. Even for a given input size, there are multiple algorithms that compute the same result, but have differing computational characteristics depending on the hardware etc. How do you generate the optimal algorithm for your hardware ?
3. Most importantly the structure of *this* specific problem allows optimizations that are specific to the problem which are not built into generic linear algebra routines. (Obviously, one can't expect MATLAB to incorporate problem specific information for every scientific/engineering problem ever). The GLS problems are connected to others, thus saving intermediate results can save hours of computation vs calculating every GLS problem from scratchIn practice, one needs to be an expert in Computational Linear Algebra to come up with the optimized algorithm for a domain specific problem, and then write (say Fortran) code to use BLAS, LAPACK etc optimally to actualize this algorithm, often with much iteration, often consuming 100s of hours.
The Solution:
Incorporating this 'expert knowledge' into a compiler speeds up the time taken to arrive at the best solution (often by a factor of 100 or 1000), and allows Computational Linear Algebra experts to do more interesting things, like focus on their research.For this particular problem, the above equations, and additional knowledge of the problem domain are the input into an expression compiler. The output is highly efficient and 'proved correct' code
In compiler terms, incorporating domain knowldege into the compilation process results in being able to apply optimizations to the generated Syntax Trees/Graphs, resulting in optimal algorithms. (note: the output of the compiler is a program in another language- say Matlab).
In essence, "Domain Specific Compilers" consume knowledge about the structure of a problem and generate optimized code that solves that problem.Shin is one such compiler. It consumes a problem description and outputs highly efficient Julia code that solves the problem.
This talk focuses on the engineering challenges I faced in building this compiler, with a special focus on the approaches that failed [5]
Trivia:
"Shin" is the Hebrew letter, not the English word meaning 'front of the leg between knee and ankle' ;-).
Every company uses names from a common theme to name their servers and components - Athena, Zeus, Hercules , or Thor, Loki, Odin, or Jedi, Sith, Skywalker etc. We use Hebrew words, so we have Ruach, Melekh, Malkuth etc..