Programming with algebraic structures: design of the MAGMA language

ABSTRACT

MAGMA is a new software system for computational algebra, number theory and geometry whose design is centred on the concept of algebraic structure (magma). The use of algebraic structure as a design paradigm provides a natural strong typing mechanism. Further, structures and their morphisms appear in the language as first class objects. Standard mathematical notions are used for the basic data types. The result is a powerful, clean language which deals with objects in a mathematically rigorous manner. The conceptual and implementation ideas behind MAGMA will be examined in this paper. This conceptual base differs significantly from those underlying other computer algebra systems.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems
          Subjects: Special-purpose algebraic systems

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: C
      D.3.3 Language Constructs and Features
          Subjects: Data types and structures

  F. Theory of Computation
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.3 Studies of Program Constructs
          Subjects: Type structure

General Terms:
Algorithms, Design