Abstract
Minlog is an interactive system which implements proof-theoretic methods and applies them to verification and program extraction. We give an overview of Minlog and demonstrate how it can be used to exploit the computational content in (co)algebraic proofs and to develop correct and efficient programs. We illustrate this by means of two examples: one about parsing, the other about exact real numbers in signed digit representation.
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Berger, U., Berghofer, S., Letouzey, P., Schwichtenberg, H.: Program extraction from normalization proofs. Studia Logica 82, 27–51 (2006)
Benl, H., Berger, U., Schwichtenberg, H., Seisenberger, M., Zuber, W.: Proof theory at work: Program development in the Minlog system. In: Bibel, W., Schmitt, P.H. (eds.) Automated Deduction. Applied Logic Series, vol. II, pp. 41–71. Kluwer, Dordrecht (1998)
Berger, U., Buchholz, W., Schwichtenberg, H.: Refined program extraction from classical proofs. APAL 114, 3–25 (2002)
Berger, U.: From coinductive proofs to exact real arithmetic. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 132–146. Springer, Heidelberg (2009)
Berger, U., Eberl, M., Schwichtenberg, H.: Term rewriting for normalization by evaluation. Information and Computation 183, 19–42 (2003)
Berger, U., Hou, T.: Coinduction for exact real number computation. Theory of Computing Systems 43, 394–409 (2008)
Berger, U., Schwichtenberg, H.: An inverse of the evaluation functional for typed λ-calculus. In: Vemuri, R. (ed.) Proceedings 6’th Symposium on Logic in Computer Science, LICS 1991, pp. 203–211. IEEE Computer Society Press, Los Alamitos (1991)
Bauer, A., Stone, C.A.: RZ: A tool for bringing constructive and computable mathematics closer to programming practice. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds.) CiE 2007. LNCS, vol. 4497, pp. 28–42. Springer, Heidelberg (2007)
Berger, U., Seisenberger, M.: Proofs, programs, processes. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 39–48. Springer, Heidelberg (2010)
Ciaffaglione, A., Di Gianantonio, P.: A certified, corecursive implementation of exact real numbers. Theor. Comp. Sci. 351, 39–51 (2006)
Chuang, C.M.: Extraction of Programs for Exact Real Number Computation Using Agda. PhD thesis. Swansea University, Wales (2011)
The Coq Proof Assistant, http://coq.inria.fr/
Crosilla, L., Seisenberger, M., Schwichtenberg, H.: A Tutorial for Minlog, Version 5.0 (2011)
Geuvers, H., Niqui, M., Spitters, B., Wiedijk, F.: Constructive analysis, types and exact real numbers. Math. Struct. Comp. Sci. 17(1), 3–36 (2007)
Isabelle, http://isabelle.in.tum.de/
Kreisel, G.: Interpretation of analysis by means of constructive functionals of finite types. Constructivity in Mathematics, 101–128 (1959)
Letouzey, P.: A New Extraction for Coq. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 200–219. Springer, Heidelberg (2003)
Miller, D.: A logic programming language with lambda–abstraction, function variables and simple unification. Jour. Logic Comput. 2(4), 497–536 (1991)
The Minlog System, http://www.minlog-system.de
Marcial-Romero, J.R., Escardo, M.H.: Semantics of a sequential language for exact real-number computation. Theor. Comp. Sci. 379(1-2), 120–141 (2007)
Schwichtenberg, H.: Proof search in minimal logic. In: Buchberger, B., Campbell, J.A. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 15–25. Springer, Heidelberg (2004)
Schwichtenberg, H., Wainer, S.S.: Proofs and Computations. Perspectives in Logic. Assoc. Symb. Logic, Cambridge Univ. Press (to appear, 2011)
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Berger, U., Miyamoto, K., Schwichtenberg, H., Seisenberger, M. (2011). Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras. In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_29
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DOI: https://doi.org/10.1007/978-3-642-22944-2_29
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