We present the type theory LTT, intended to form a basis for typed target languages, providing an internal notion of logical proposition and proof. The inclusion of explicit proofs allows the type system to guarantee properties that would otherwise be incompatible with decidable type checking. LTT also provides linear facilities for tracking ephemeral properties that hold only for certain program states.Our type theory allows for re-use of typechecking software by casting a variety of type systems within a single language. We illustrate our methodology of representation by means of two examples, one functional and one stateful, and describe the associated operational semantics and proofs of type safety.

The ability to identify the mineral composition of rocks and soils is an important tool for the exploration of geological sites. For instance, NASA intends to design robots that are sufficiently autonomous to perform this task on planetary missions. Spectrometer readings provide one important source of data for identifying sites with minerals of interest. Reflectance spectrometers measure intensities of light reflected from surfaces over a range of wavelengths. Spectral intensity patterns may in some cases be sufficiently distinctive for proper identification of minerals or classes of minerals. For some mineral classes, carbonates for example, specific short spectral intervals are known to carry a distinctive signature. Finding similar distinctive spectral ranges for other mineral classes is not an easy problem. We propose and evaluate data-driven techniques that automatically search for spectral ranges optimized for specific minerals. In one set of studies, we partition the whole interval of wavelengths available in our data into sub-intervals, or bins, and use a genetic algorithm to evaluate a candidate selection of subintervals. As alternatives to this computationally expensive search technique, we present an entropy-based heuristic that gives higher scores for wavelengths more likely to distinguish between classes, as well as other greedy search procedures. Results are presented for four different classes, showing reasonable improvements in identifying some, but not all, of the mineral classes tested.