Kazutaka Matsuda, Shin-Cheng Mu, Zhenjiang Hu, and Masato Takeichi. A grammar-based approach to invertible programs. In 19th European Symposium on Programming (ESOP 2010), LNCS 6012, pp 448-467, March 2010.
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“I cannot prove that if a function is injective, it has an inverse,” Hideki Hashimoto posed this question to me. Is it possible at all?
Z. Hu, S-C. Mu and M. Takeichi, A programmable editor for developing structured documents based on bidirectional transformations. Higher-Order and Symbolic Computation, Vol 21(1-2), pp 89-118, May 2008.
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Back in 2003, my colleagues there were discussing about the third homomorphism theorem — if a function
By chance, I came upon a blog entry by Masahiro Sakai (酒井政裕) in which he, after reading my short comment “Do you know that the S combinator is injective?”, tried to construct the inverse of S and showed that S⁻¹ ○ S = id in, guess what, Agda!
R. S. Bird and S-C. Mu, Countdown: a case study in origami programming. In Journal of Functional Programming Vol. 15(5), pp. 679-702, 2005.
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R. S. Bird and S-C. Mu, Inverting the Burrows-Wheeler transform. In Journal of Functional Programming Vol. 14(6) Special Issue on Functional Pearls, pp. 603-612, Novermber 2004.
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S-C. Mu, Z. Hu and M. Takeichi. An algebraic approach to bidirectional updating. In The Second Asian Symposium on Programming Language and Systems, pp. 2-18. November 2004.
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Z. Hu, S-C. Mu and M. Takeichi, A programmable editor for developing structured documents based on bidirectional transformations. In Partial Evaluation and Semantics-Based Program Manipulation, pp. 178-189. August 2004.
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S-C. Mu, Z. Hu and M. Takeichi, An injective language for reversible computation. In Mathematics of Program Construction 2004, LNCS 3125, pp. 289-313, July 2004.
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