Using F# to prove stabilisation of biological networks

Categories:

Ocaml, F#, cufp2012, Biological

BMA is a tool for modeling and analyzing Systems Biology models, such as cellular-level descriptions of skin and blood.

One important property that these biological artifacts have is homeostasis or stability. Stability in skin, for instance, means that the epidermis is dividing at the same rate that the surface is losing cells; instability, in contrast, means either cancer or surface sores.

A tool that verifies stability is, we hope, part of a development to target drugs better, by identifying the cellular components that enable stability. The whole endeavor can be seen as an EDA for biology.

In this talk, I will describe the F# implementation of the stabilization prover of BMA.

The prover checks that, regardless of the initial values the model's variables, there is one stability point that the model always reaches and then remains in. The complexity of this analysis stems from the high number of possible states of such a system. Yet the BMA prover scales by composing a lot of local, small proofs together. The prover's underlying procedure is based on mathematical techniques for the specification and verification of properties in concurrent systems.

Though this domain (automatically proving properties of systems) is one that is known to be amenable to functional programming techniques, the BMA implementation exploits several F# features. Almost all the data structures are immutable collections like Set and Map. The main fixed-point loop is implemented using the Seq lazy sequences library: transforming the loop from a recursive function to a Seq.fold was quick, yielding code that is elegantly asynchronous, and allows the C#-based UI to pause, step, and fast-forward the proof search.

The analyzer also uses FParsec (a parser combinator library) to parse the definition of the model's update functions, and Z3 (an SMT solver) to generate counter-examples to stability.

I am normally an Emacs/OCaml functional programmer. I'll also compare my development experience of Visual Studio/F#.