At the heart of functional programming rests the principle of referential transparency, which in particular means that a function f applied to a value x always yields one and the same value y=f(x). This principle seems to be violated when contemplating the use of functions to describe probabilistic events, such as rolling a die: It is not clear at all what exactly the outcome will be, and neither is it guaranteed that the same value will be produced repeatedly. However, these two seemingly incompatible notions can be reconciled if probabilistic values are encapsulated in a data type.

A huge discrepancy between theory and practice exists in one popular application area of functional programming-spreadsheets. Although spreadsheets are the most frequently used (functional) programs, few formal models of computation and type systems exist that would provide the foundation for creating reliable spreadsheets. Consequently, existing spreadsheets contain many errors, some of which have serious impacts. We argue in favor of creating a formal foundation for spreadsheets to help improve spreadsheet systems and make spreadsheets more reliable software assets. To this end, we have developed a table specification language that allows the definition of table templates that describe possible spreadsheet evolutions. This language is based on a table calculus that formally captures the process of creating and modifying spreadsheets. We have developed a type system for this calculus that can prevent type, reference, and omission errors from occurring in spreadsheets. On the basis of the table calculus we have developed Gencel, a system for generating reliable spreadsheets. We have implemented a prototype version of Gencel as an extension of Excel. A pilot study has indicated that the system is well accepted by end-user programmers.

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Existing spreadsheet systems allow users to change cells arbitrarily, which is a major source of spreadsheet errors. We propose a system that prevents errors in spreadsheets by restricting spreadsheet updates to only those that are logically and technically correct. The system is based on the concept of templates that describe the principal structure of the initial spreadsheet and all of its future versions. We have developed a program generator that translates a template into an initial spreadsheet together with customized update operations for changing cells and inserting/deleting rows and columns for this particular template.We have designed a type system for templates that ensures the following form of "spreadsheet maintenance safety": Update operations that are generated from a type-correct template are proved to transform the spreadsheet only according to the template and to never produce any omission, reference, or type errors.Finally, we have developed a prototype as an extension to Excel, which has been shown by a preliminary usability study to be well accepted by end users.

Abstract. Many scientific applications benefit from simulation. However, programming languages used in simulation, such as C++ or Matlab, approach problems from a deterministic procedural view, which seems to differ, in general, from many scientists' mental representation. We apply a domain-specific language for probabilistic programming to the biological field of gene modeling, showing how the mental-model gap may be bridged. Our system assisted biologists in developing a model for genome evolution by separating the concerns of model and simulation and providing implicit probabilistic non-determinism.