CC BY 4.0 UnportedBotta, N.Jansson, P.Ionescu, C.Christiansen, D.R.Brady, E.2020-07-272020-07-272017https://doi.org/10.34657/3748https://oa.tib.eu/renate/handle/123456789/5119We 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.enghttps://creativecommons.org/licenses/by/4.0/510Dynamical systemsStochastic systemsCentral componentClimate impact researchesDependent typesGeneric implementationGeneric solutionsInduction algorithmsPrinciple of optimalitySequential decisionsProblem oriented languagesArticle