Another recent paper by Cezar Ionescu and Patrik Jansson is also freely available: Full text + abstract.
Higher-order properties arise naturally in some areas of climate impact research. For example, “vulnerability measures”, crucial in assessing the vulnerability to climate change of various regions and entities, must fulfill certain conditions which are best expressed by quantification over all increasing functions of an appropriate type. This kind of property is notoriously difficult to test. However, for the measures used in practice, it is quite easy to encode the property as a dependent type and prove it correct. Moreover, in scientific programming, one is often interested in correctness “up to implication”: the program would work as expected, say, if one would use real numbers instead of floating-point values. Such counterfactuals are impossible to test, but again, they can be easily encoded as types and proven. We show examples of such situations (encoded in Agda), encountered in actual vulnerability assessments.
Cezar Ionescu (at PIK) and Patrik Jansson (me, at Chalmers) have just got a paper accepted which fits in well in the GSS activity.
Pre-print + abstract
Computer simulations are essential in virtually every scientific discipline, even more so in those such as economics or climate change where the ability to make laboratory experiments is limited. Therefore, it is important to ensure that the models are implemented correctly, that they can be re-implemented and that the results can be reproduced. Typically, though, the models are described by a mixture of prose and mathematics which is insufficient for these purposes. We argue that using dependent types allows us to gradually reduce the gap between the mathematical description and the implementation, and we give examples from economic modelling. We discuss the consequences that our incremental approach has on programming style and the requirements it imposes on the dependently-typed programming languages used.