We present a computer-checked generic implementation for solving finite-horizon sequential decision problems. This is a wide class of problems, including inter-temporal optimizations, knapsack, optimal bracketing, scheduling, etc. The implementation can handle time-step dependent control and state spaces, and monadic representations of uncertainty (such as stochastic, non-deterministic, fuzzy, or combinations thereof). This level of genericity is achievable in a programming language with dependent types (we have used both Idris and Agda). Dependent types are also the means that allow us to obtain a formalization and computer-checked proof of the central component of our implementation: Bellman's principle of optimality and the associated backwards induction algorithm. The formalization clarifies certain aspects of backwards induction and, by making explicit notions such as viability and reachability, can serve as a starting point for a theory of controllability of monadic dynamical systems, commonly encountered in, e.g., climate impact research. Comment: 23 pages, 2 figures

@article{paperbot203,
  title = {Sequential decision problems, dependent types and generic solutions},
  author = {Nicola Botta and Patrik Jansson and Cezar Ionescu and David R. Christiansen and Edwin Brady},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 13, Issue 1},
  year = {2017},
  doi = {10.23638/lmcs-13(1:7)2017}
}