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16 In this paper we present MILONGA, a language based on functional programming concepts, which was designed 17 for the implementation of a new generation of nonterm-rewriting elimination algorithms for multivariate polynomial 18 solving [J. Pure Appl. Alg. 124 (1998) 101; J. Pure Appl. Alg. 117/118 (1997) 277; Appl. Alg. Eng. Commun. 19 Comput. 11 (4) (2001) 239; J. Complex. 17 (1) (2001) 154]. 20 These new algorithms profit from an alternative representation of multivariate polynomials by means of straight21 line programs [Algebraic complexity theory, in: Handbook of Theoretical Computer Science, Elsevier, Amsterdam, 22 1990, pp. 634–671 (Chapter 11); Algebraic complexity theory, in: Grundlehren der mathematischen Wissenschaften, 23 Vol. 315, Springer, Berlin, 1997] allowing an exponential improvement of theoretical complexity—with respect to 24 computing time and memory space—upon traditional, term-rewriting procedures. 25 There is a strong analogy between the way how these algorithms employ straight-line programs and the way how 26 functional programming languages treat functions as first-class citizens. Taking advantage of this circumstance, the 27 MILONGA language enables us to analyze the relevance of the functional programming paradigm for the particular 28 kind of task of polynomial equation solving. 29 The paper contains an exhaustive do-it-yourself description of the programming philosophy of MILONGA, of the 30 development of its compiler, of the operational semantics of its run-time system and of the implementation of a 31 couple of fundamental computer algebra procedures in this language. 32 ∗Corresponding author. Present address: Departamento de Computación, Universidad Favaloro, Belgrano 1723, 1093 Buenos Aires, Argentina. Tel.: +54-11-4771-5760; fax: +54-11-4576-3351. E-mail addresses: [email protected] (N. Bruno), [email protected], [email protected] (J. Heintz), [email protected], [email protected] (G. Matera), [email protected] (R. Wachenchauzer). 1Present address: Department of Computer Science, Columbia University, New York, NY 10027-7003, USA. 1 0378-4754/02/$ – see front matter © 2002 Published by Elsevier Science B.V. on behalf of IMACS. 2 PII: S0378-4754(02)00035-6