This document is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. The copyright holder grants you permission to redistribute this document freely as a verbatim copy. Furthermore, the copyright holder permits you to develop any derived work from this document provided that the following conditions are met. a) The derived work acknowledges the fact that it is derived from this document, and maintains a prominent reference in the work to the original source. b) The fact that the derived work is not the original OpenMath document is stated prominently in the derived work. Moreover if both this document and the derived work are Content Dictionaries then the derived work must include a different CDName element, chosen so that it cannot be confused with any works adopted by the OpenMath Society. In particular, if there is a Content Dictionary Group whose name is, for example, `math' containing Content Dictionaries named `math1', `math2' etc., then you should not name a derived Content Dictionary `mathN' where N is an integer. However you are free to name it `private_mathN' or some such. This is because the names `mathN' may be used by the OpenMath Society for future extensions. c) The derived work is distributed under terms that allow the compilation of derived works, but keep paragraphs a) and b) intact. The simplest way to do this is to distribute the derived work under the OpenMath license, but this is not a requirement. If you have questions about this license please contact the OpenMath society at http://www.openmath.org. sts http://www.openmath.org/cd http://www.openmath.org/cd/sts.ocd 2006-03-30 2004-03-30 4 0 official Definitions of the symbols used by the OpenMath Small Type System. type semantic-attribution A symbol to be used within an OpenMath attribute to specify the type of the object. The variable z is attributed with a type for complex numbers. mapsto application This symbol represents the construction of a function type. The first n-1 children denote the types of the arguments, the last denotes the return type. The signature of the power function: (Real , Integer) -> Real nary application Constructs a child of mapsto which denotes an arbitrary number of copies of the argument of nary. The signature for list, an n-ary function: nassoc application Constructs a child of mapsto which denotes an arbitrary number of copies of the argument of nassoc. The operator is associative on these arguments which means that repeated uses may be flattened/unflattened. The signature for plus, an associative n-ary function: error constant The error symbol is the 'return type' of error symbols in the error signature file. structure application The structure element is used to represent a structure of a particular (algebraic) type. The signature of a function which given a set will return an element of that set: binder constant An `OMBIND' object has three parts: a "binder" such as "lambda" or "for all", a (list of) bound variables, and an expression. The use of `binder' in a signature indicates that we are describing something which can only be used as the first child of an OMBIND construct. The signature of forall is: attribution constant An `attribution' object consists of pairs of keys and values. The use of the symbol `attribution' in a signature indicates that the symbol is to be used as a key. Object constant Denotes any OpenMath object. The signature for list, to show that list has the signature: Object* -> Object NumericalValue constant Denotes an OpenMath object that is to be thought of as something that represents a numerical value, or a numerical value. The generic signature for the function power: SetNumericalValue constant Denotes an OpenMath object that is to be thought of as something that represents a set of numerical values, or a set of numerical values. The generic signature for the function arctan from transc3: