A Type Calculus for Executable Modelling Languages

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Abstract
There is considerable current interest in the design and construction of directly executable modelling languages for mathematical programming. The present research extends contemporary modelling languages by specifying a type calculus for an extended dimensional system that determines if the model is well formed in the sense that the objective function and constraints consist of homogeneous components. Each variable, coefficient, constant, function, constraint, input, and output of the model is assigned a type that consists of its concepts, quantities, and units of measurement with optional scale factors. In checking the composition of functions and constraints, the system can do automatic unit conversions and apply user-supplied conversions. The system allows a hierarchy of concepts that provides inheritance of quantities and automatic concept conversion. In addition, each set in a model is typed so the system can check the validity of operations on indices.

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