diff --git a/data/bibliography.bib b/data/bibliography.bib index 618f637ce..89c05f419 100644 --- a/data/bibliography.bib +++ b/data/bibliography.bib @@ -107,3 +107,42 @@ @book{Rocca:2004 publisher = {Springer}, title = {The Parametric Lambda Calculus}, year = {2004}} + +@inproceedings{Schafer:2015, + title={Autosubst: Reasoning with de Bruijn terms and parallel substitutions}, + author={Sch{\"a}fer, Steven and Tebbi, Tobias and Smolka, Gert}, + booktitle={Interactive Theorem Proving: 6th International Conference, ITP 2015, Nanjing, China, August 24-27, 2015, Proceedings 6}, + pages={359--374}, + year={2015}, + organization={Springer} +} + +@techreport{Pfenning:1992, + author = {Pfenning, Frank}, + institution = {Carnegie Mellon University}, + number = {CMU-CS-92-186}, + publisher = {Carnegie Mellon University}, + title = {A Proof of the Church-Rosser Theorem and Its Representation in a Logical Framework}, + year = {1992}} + +@article{Takahashi:1995, +title = {Parallel Reductions in λ-Calculus}, +journal = {Information and Computation}, +volume = {118}, +number = {1}, +pages = {120-127}, +year = {1995}, +doi = {https://doi.org/10.1006/inco.1995.1057}, +author = {M. Takahashi}} + +@inproceedings{Nipkow:1996, + author = {Nipkow, Tobias}, + title = {More Church-Rosser Proofs (in Isabelle/HOL)}, + year = {1996}, + publisher = {Springer-Verlag}, + address = {Berlin, Heidelberg}, + booktitle = {Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction}, + pages = {733–747}, + numpages = {15}, + series = {CADE-13} + } diff --git a/src/plfa/part2/Confluence.lagda.md b/src/plfa/part2/Confluence.lagda.md index 610831444..8bb75d6de 100644 --- a/src/plfa/part2/Confluence.lagda.md +++ b/src/plfa/part2/Confluence.lagda.md @@ -608,13 +608,13 @@ confluence L↠M₁ L↠M₂ ## Notes This mechanized proof of confluence is based on several sources. The -`subst-par` lemma is the "strong substitutivity" lemma of Shafer, -Tebbi, and Smolka (ITP 2015). The proofs of `par-triangle`, `strip`, +`subst-par` lemma is the "strong substitutivity" lemma of +@Schafer:2015. The proofs of `par-triangle`, `strip`, and `par-confluence` are based on the notion of complete development -by Takahashi (1995) and Pfenning's 1992 technical report about the +by @Takahashi:1995 and the technical report by @Pfenning:1992 about the Church-Rosser theorem. In addition, we consulted Nipkow and Berghofer's mechanization in Isabelle, which is based on an earlier -article by Nipkow (JAR 1996). +paper by @Nipkow:1996. ## Unicode