ALLTYPES: An algebraic language and TYPE system

Abstract

The software system ALLTYPES provides an environment that is particularly designed for developing computer algebra software in the realm of differential equations. Its most important features may be described as follows: A set of about thirty parametrized algebraic types is defined. Data objects represented by these types may be manipulated by more than one hundred polymorphic functions. Reusability of code is achieved by genericity and inheritance. The user may extend the system by defining new types and polymorphic functions. A language comprising seven basic language constructs is defined for implementing mathematical algorithms. The easy manipulation of types is particularly supported by ALLTYPES. To this end a special portion of the language that is enclosed by a pair of absolute bars is dedicated to manipulating typed objects, i. e. user-defined or automatic type coercions. Type inquiries are also included in the language. A small amount of parallelism is supported in terms of two language constructs pand and por where the letter p indicates a parallel version of the respective logical function. Currently ALLTYPES is implemented in Reduce and Macsyma (to be completed soon). Software implemented on top of ALLTYPES should work independent of the underlying computer algebra language.