Garnet pegmatite and allied rock types and in certain low grade metamorphic phyllites. Spessartine of an orange-yellow is found in Madagascar. Violet-red spessartines are found in rhyolites in Colorado and Maine. Blue pyrope–spessartine garnets were discovered in the late 1990s in Bekily, Madagascar. This type has also been found in parts of the United States, Russia, Kenya, Tanzania, and Turkey. It changes color from blue-green to purple depending on the color temperature of viewing light, as a result of the relatively high amounts of vanadium (about 1 wt.% VO). Other varieties of color-changing garnets exist. In daylight, their color ranges from
Type theory of a function is denoted with an arrow formula_16 from the parameter type to the function's resulting type. Thus, formula_17. Calling or "applying" a function to an argument may be written with or without parentheses, so formula_18 or formula_12. Not using parentheses is more common, because multiple argument functions can be defined using currying. There are many different set theories and many different systems of type theory, so what follows are generalizations. The term formula_20 reduces to formula_21. Since formula_21 cannot be reduced further, it is called a normal form. A system of type theory is said to be strongly