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Allows one to write `if MyType_eqb a b then ... else ...` where `MyType_eqb a b` returns a `bool`, instead of writing `if MyType_eq_dec a b then ... else ...` where `MyType_eq_dec a b` returns a `sumbool`, while still getting `a = b` and `a <> b` as hypotheses (as opposed to `MyType_eqb a b = true` and `MyType_eqb a b = false`) after destructing the `if` (need to use [`destr`](https://github.com/mit-plv/coqutil/blob/master/src/coqutil/Tactics/destr.v) instead of `destruct`). So one gets the benefits of `Sumbool` without getting its disadvantage of having to carry around proof terms, which can cause a blow-up under reduction if one is not careful.\n* [Map](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Map): A typeclass based map library allowing one to abstract over the concrete implementation of maps. The implementations have to be extensional, which excludes certain efficient implementations, but simplifies proofs, because one can `replace mapA with mapB` if one can prove that `mapA` and `mapB` have the same contents. Comes with a [solver](https://github.com/mit-plv/coqutil/blob/master/src/coqutil/Map/Solver.v) which works reasonably fast on most map goals we have encountered so far.\n* [Tactics](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Tactics): A collection of useful general-purpose tactics.\n* [Word](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Word): Fixed width words for any width, in the same typeclass based style as the map library. Designed for the case where all words have the same (potentially abstract) bit width. Therefore, it does not provide functions to concatenate and split words, which is better addressed by [bbv](https://github.com/mit-plv/bbv/).\n* [Z](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Z): Utilities to work with the `Z` type from Coq's standard library, including a tactic to prove `Z` equalities by splitting the equality into equalities on bit index ranges, a tactic to make `lia` capable of reasoning about goals with division and modulo, and a tactic to simplify expressions containing nested occurrences of `mod`, and more misc utilities.\n* Various macros, notations, and desirable default settings.\n\nEach feature is intended to be as minimal and as independent of the other features as possible, so that users can pick just what they need.","date":null,"version":"0.0.1","suite":"released","src":"https://github.com/mit-plv/coqutil/archive/refs/tags/v0.0.1.tar.gz","checksum":"sha512=fc8f334260add1d437030660e7cb79627e0e3a8603140cade9f6d83f895fc8dd49b218c350b84cc18342af357fffa9d0698b33519283dda9742a3486562b6343"},{"homepage":"https://github.com/mit-plv/coqutil","keywords":[],"categories":[],"authors":["Massachusetts Institute of Technology"],"description":"### coqutil -- Various Coq Utilities\n\nContents:\n* [Datatypes](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Datatypes): Some utilities for existing datatypes, and new datatypes.\n* [Decidable](https://github.com/mit-plv/coqutil/blob/master/src/coqutil/Decidable.v): `BoolSpec`-based decidability typeclasses. Allows one to write `if MyType_eqb a b then ... else ...` where `MyType_eqb a b` returns a `bool`, instead of writing `if MyType_eq_dec a b then ... else ...` where `MyType_eq_dec a b` returns a `sumbool`, while still getting `a = b` and `a <> b` as hypotheses (as opposed to `MyType_eqb a b = true` and `MyType_eqb a b = false`) after destructing the `if` (need to use [`destr`](https://github.com/mit-plv/coqutil/blob/master/src/coqutil/Tactics/destr.v) instead of `destruct`). So one gets the benefits of `Sumbool` without getting its disadvantage of having to carry around proof terms, which can cause a blow-up under reduction if one is not careful.\n* [Map](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Map): A typeclass based map library allowing one to abstract over the concrete implementation of maps. The implementations have to be extensional, which excludes certain efficient implementations, but simplifies proofs, because one can `replace mapA with mapB` if one can prove that `mapA` and `mapB` have the same contents. Comes with a [solver](https://github.com/mit-plv/coqutil/blob/master/src/coqutil/Map/Solver.v) which works reasonably fast on most map goals we have encountered so far.\n* [Tactics](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Tactics): A collection of useful general-purpose tactics.\n* [Word](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Word): Fixed width words for any width, in the same typeclass based style as the map library. Designed for the case where all words have the same (potentially abstract) bit width. Therefore, it does not provide functions to concatenate and split words, which is better addressed by [bbv](https://github.com/mit-plv/bbv/).\n* [Z](https://github.com/mit-plv/coqutil/tree/master/src/coqutil/Z): Utilities to work with the `Z` type from Coq's standard library, including a tactic to prove `Z` equalities by splitting the equality into equalities on bit index ranges, a tactic to make `lia` capable of reasoning about goals with division and modulo, and a tactic to simplify expressions containing nested occurrences of `mod`, and more misc utilities.\n* Various macros, notations, and desirable default settings.\n\nEach feature is intended to be as minimal and as independent of the other features as possible, so that users can pick just what they need.","date":null,"version":"dev","suite":"extra-dev","src":"git+https://github.com/mit-plv/coqutil.git#tested","checksum":null}],"most_recent":"dev"}],["coq-corn",{"versions":[{"homepage":"https://github.com/coq-community/corn","keywords":["constructive mathematics","algebra","real calculus","real numbers","Fundamental Theorem of Algebra"],"categories":["Mathematics/Algebra","Mathematics/Real Calculus and Topology","Mathematics/Exact Real computation"],"authors":["Evgeny Makarov","Robbert Krebbers","Eelis van der Weegen","Bas Spitters","Jelle Herold","Russell O'Connor","Cezary Kaliszyk","Dan Synek","Luís Cruz-Filipe","Milad Niqui","Iris Loeb","Herman Geuvers","Randy Pollack","Freek Wiedijk","Jan Zwanenburg","Dimitri Hendriks","Henk Barendregt","Mariusz Giero","Rik van Ginneken","Dimitri Hendriks","Sébastien Hinderer","Bart Kirkels","Pierre Letouzey","Lionel Mamane","Nickolay Shmyrev","Vincent Semeria"],"description":"CoRN includes the following parts:\n\n- Algebraic Hierarchy\n\n An axiomatic formalization of the most common algebraic\n structures, including setoids, monoids, groups, rings,\n fields, ordered fields, rings of polynomials, real and\n complex numbers\n\n- Model of the Real Numbers\n\n Construction of a concrete real number structure\n satisfying the previously defined axioms\n\n- Fundamental Theorem of Algebra\n\n A proof that every non-constant polynomial on the complex\n plane has at least one root\n\n- Real Calculus\n\n A collection of elementary results on real analysis,\n including continuity, differentiability, integration,\n Taylor's theorem and the Fundamental Theorem of Calculus\n\n- Exact Real Computation\n\n Fast verified computation inside Coq. 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E.g. `{{nat}}` is expanded to the type name of natural\nnumbers, or `{{A -> B}}` to the representation of a product by unfolding\n the `->` notation. Finally it provides a way to define new vernacular commands\nand\nnew tactics.","date":null,"version":"1.11.1","suite":"released","src":"https://github.com/LPCIC/coq-elpi/archive/v1.11.1.tar.gz","checksum":"sha256=53adbef161f3ade43b04438afa37d730b4b2e90404d78df2d67e0675de5c2e4a"},{"homepage":"https://github.com/LPCIC/coq-elpi","keywords":[],"categories":[],"authors":["Enrico Tassi"],"description":"Coq-elpi provides a Coq plugin that embeds ELPI.\nIt also provides a way to embed Coq's terms into λProlog using\nthe Higher-Order Abstract Syntax approach\nand a way to read terms back. 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E.g. `{{nat}}` is expanded to the type name of natural\nnumbers, or `{{A -> B}}` to the representation of a product by unfolding\n the `->` notation. Finally it provides a way to define new vernacular commands\nand\nnew tactics.","date":"2021-06-18","version":"1.10.3","suite":"released","src":"https://github.com/LPCIC/coq-elpi/archive/v1.10.3.tar.gz","checksum":"sha256=3ae232cacedb6150c78de9445d25673e0eff8a0e1d884e26fd87a36151d70214"},{"homepage":"https://github.com/LPCIC/coq-elpi","keywords":[],"categories":[],"authors":["Enrico Tassi"],"description":"Coq-elpi provides a Coq plugin that embeds ELPI.\nIt also provides a way to embed Coq's terms into λProlog using\nthe Higher-Order Abstract Syntax approach\nand a way to read terms back. 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E.g. `{{nat}}` is expanded to the type name of natural\nnumbers, or `{{A -> B}}` to the representation of a product by unfolding\n the `->` notation. Finally it provides a way to define new vernacular commands\nand\nnew tactics.","date":null,"version":"1.10.1","suite":"released","src":"https://github.com/LPCIC/coq-elpi/archive/v1.10.1.tar.gz","checksum":"sha256=e6743e11cca651f384eb3cdc89a41e9a62c75300fa80a28cd07d7076957a0620"},{"homepage":"https://github.com/LPCIC/coq-elpi","keywords":[],"categories":[],"authors":["Enrico Tassi"],"description":"Coq-elpi provides a Coq plugin that embeds ELPI.\nIt also provides a way to embed Coq's terms into λProlog using\nthe Higher-Order Abstract Syntax approach\nand a way to read terms back. 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E.g. `{{nat}}` is expanded to the type name of natural\nnumbers, or `{{A -> B}}` to the representation of a product by unfolding\n the `->` notation. Finally it provides a way to define new vernacular commands\nand\nnew tactics.","date":null,"version":"1.9.7","suite":"released","src":"https://github.com/LPCIC/coq-elpi/archive/v1.9.7.tar.gz","checksum":"sha256=96ef27381a6cbf9330dc503dea41dec85437ad8d368833bbe1d2e94022413d37"},{"homepage":"https://github.com/LPCIC/coq-elpi","keywords":[],"categories":[],"authors":["Enrico Tassi"],"description":"Coq-elpi provides a Coq plugin that embeds ELPI.\nIt also provides a way to embed Coq's terms into λProlog using\nthe Higher-Order Abstract Syntax approach\nand a way to read terms back. 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E.g. `{{nat}}` is expanded to the type name of natural\nnumbers, or `{{A -> B}}` to the representation of a product by unfolding\n the `->` notation. Finally it provides a way to define new vernacular commands\nand\nnew tactics.","date":null,"version":"1.9.5","suite":"released","src":"https://github.com/LPCIC/coq-elpi/archive/v1.9.5.tar.gz","checksum":"sha256=837728cc8c536a74757bbc36365828ce5ac8a2f3f9afa8182c98c4986861c77a"},{"homepage":"https://github.com/LPCIC/coq-elpi","keywords":[],"categories":[],"authors":["Enrico Tassi"],"description":"Coq-elpi provides a Coq plugin that embeds ELPI.\nIt also provides a way to embed Coq's terms into λProlog using\nthe Higher-Order Abstract Syntax approach\nand a way to read terms back. 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finGroupType) (G : {group gT}), odd #|G| -> solvable G\n\nFrom mathcomp Require Import all_ssreflect all_fingroup\n all_solvable stripped_odd_order_theorem.\n\nCheck stripped_Odd_Order.\n : forall (T : Type) (mul : T -> T -> T) (one : T) (inv : T -> T)\n (G : T -> Type) (n : natural),\n group_axioms T mul one inv ->\n group T mul one inv G ->\n finite_of_order T G n -> odd n -> solvable_group T mul one inv G","date":null,"version":"1.13.0","suite":"released","src":"https://github.com/math-comp/odd-order/archive/mathcomp-odd-order.1.13.0.tar.gz","checksum":"sha512=4caebcbce72976fc771a8507de4e3ed4614ae0f2f04dec3e50088b16cdafa8e29a213c8b1054c1e68765c135d4a39c0eebafd750a1c092060fc868180e129a9b"},{"homepage":"http://math-comp.github.io/math-comp/","keywords":["finite groups","Feit Thompson theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico 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all_solvable stripped_odd_order_theorem.\n\nCheck stripped_Odd_Order.\n : forall (T : Type) (mul : T -> T -> T) (one : T) (inv : T -> T)\n (G : T -> Type) (n : natural),\n group_axioms T mul one inv ->\n group T mul one inv G ->\n finite_of_order T G n -> odd n -> solvable_group T mul one inv G","date":null,"version":"1.10.0","suite":"released","src":"https://github.com/math-comp/odd-order/archive/mathcomp-odd-order.1.10.0.tar.gz","checksum":"sha256=c3ddd9f3c3882985cf01afbc72866f551cbba314f45478a248b7aec88bf8f533"},{"homepage":"http://math-comp.github.io/math-comp/","keywords":["finite groups","Feit Thompson theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"The formal proof of the Feit-Thompson theorem.\n\nFrom mathcomp Require Import all_ssreflect all_fingroup all_solvable PFsection14.\n\nCheck Feit_Thompson.\n : forall (gT : finGroupType) (G : {group gT}), odd #|G| -> solvable G\n\nFrom mathcomp Require Import all_ssreflect all_fingroup \n all_solvable stripped_odd_order_theorem.\n\nCheck stripped_Odd_Order.\n : forall (T : Type) (mul : T -> T -> T) (one : T) (inv : T -> T)\n (G : T -> Type) (n : natural),\n group_axioms T mul one inv ->\n group T mul one inv G ->\n finite_of_order T G n -> odd n -> solvable_group T mul one inv G","date":null,"version":"1.7.0","suite":"released","src":"https://github.com/math-comp/odd-order/archive/mathcomp-odd-order.1.7.0.tar.gz","checksum":"md5=e7a90d25223e257a604a8574a06a3e3c"},{"homepage":"http://ssr.msr-inria.inria.fr/","keywords":["finite groups","Feit Thompson theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea 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G","date":null,"version":"1.6.2","suite":"released","src":"https://github.com/math-comp/math-comp/archive/mathcomp-odd-order.1.6.2.tar.gz","checksum":"md5=88dbbafd24e86220157e478340478cfd"},{"homepage":"http://ssr.msr-inria.inria.fr/","keywords":["finite groups","Feit Thompson theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"The formal proof of the Feit-Thompson theorem.\n\nFrom mathcomp Require Import all_ssreflect all_fingroup all_solvable PFsection14.\n\nCheck Feit_Thompson.\n : forall (gT : finGroupType) (G : {group gT}), odd #|G| -> solvable G\n\nFrom mathcomp Require Import all_ssreflect all_fingroup \n all_solvable stripped_odd_order_theorem.\n\nCheck stripped_Odd_Order.\n : forall (T : Type) (mul : T -> T -> T) (one : T) (inv : T -> T)\n (G : T -> Type) (n : natural),\n group_axioms T mul one inv ->\n group T mul one inv G ->\n finite_of_order T G n -> odd n -> solvable_group T mul one inv G","date":null,"version":"1.6.1","suite":"released","src":"https://github.com/math-comp/math-comp/archive/mathcomp-odd-order.1.6.1.tar.gz","checksum":"md5=2303f60bbca5eaa24bef7af5d47694b9"},{"homepage":"https://math-comp.github.io/math-comp/","keywords":["Feit Thompson theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"This library contains the complete formal proof of the Odd Order\nTheorem (aka Feit Thompson Theorem).\nThe file stripped_odd_order_theorem.v contains a proof of a self\ncontained statement of the odd order.","date":null,"version":"dev","suite":"extra-dev","src":"git+https://github.com/math-comp/odd-order.git","checksum":null}],"most_recent":"dev"}],["coq-mathcomp-real-closed",{"versions":[{"homepage":"https://github.com/math-comp/real-closed","keywords":["real closed field"],"categories":[],"authors":["Cyril Cohen","Assia Mahboubi"],"description":"This library contains definitions and theorems about real closed\nfields, with a construction of the real closure and the algebraic\nclosure (including a proof of the fundamental theorem of\nalgebra). 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theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"This library contains more definitions and theorems about finite groups.","date":null,"version":"dev","suite":"extra-dev","src":"git+https://github.com/math-comp/math-comp.git","checksum":null},{"homepage":"https://math-comp.github.io/","keywords":["finite groups","Feit Thompson theorem","small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent 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boolean and boolean\npredicates, natural numbers and types with decidable equality,\nfinite types, finite sets, finite functions, finite graphs, basic arithmetics\nand prime numbers, big operators","date":null,"version":"1.15.0","suite":"released","src":"https://github.com/math-comp/math-comp/archive/mathcomp-1.15.0.tar.gz","checksum":"sha256=33105615c937ae1661e12e9bc00e0dbad143c317a6ab78b1a15e1d28339d2d95"},{"homepage":"https://math-comp.github.io/","keywords":["small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"This library includes the small scale reflection proof language\nextension and the minimal set of libraries to take advantage of it.\nThis includes libraries on 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to take advantage of it.\nThis includes libraries on lists (seq), boolean and boolean\npredicates, natural numbers and types with decidable equality,\nfinite types, finite sets, finite functions, finite graphs, basic arithmetics\nand prime numbers, big operators","date":null,"version":"1.9.0","suite":"released","src":"http://github.com/math-comp/math-comp/archive/mathcomp-1.9.0.tar.gz","checksum":"sha256=fe3d157a4db7e96f39212f76e701a7fc1e3f125c54b8c38f06a6a387eda61c96"},{"homepage":"https://math-comp.github.io/","keywords":["small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"This library includes the small scale reflection proof language\nextension and the minimal set of libraries to take advantage of it.\nThis includes libraries on lists (seq), boolean and boolean\npredicates, natural numbers and types with decidable equality,\nfinite types, finite sets, finite functions, finite graphs, basic arithmetics\nand prime numbers, big operators","date":null,"version":"1.8.0","suite":"released","src":"http://github.com/math-comp/math-comp/archive/mathcomp-1.8.0.tar.gz","checksum":"sha256=dcb3b29041d61084d21451cd38c0aeb61ef61dd136efaec96055a1ceea3b9162"},{"homepage":"https://math-comp.github.io/math-comp/","keywords":["small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"The Mathematical Components 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operators","date":null,"version":"dev","suite":"extra-dev","src":"git+https://github.com/math-comp/math-comp.git#master","checksum":null},{"homepage":"https://math-comp.github.io/","keywords":["small scale reflection","mathematical components","odd order theorem"],"categories":[],"authors":["Jeremy Avigad","Andrea Asperti","Stephane Le Roux","Yves Bertot","Laurence Rideau","Enrico Tassi","Ioana Pasca","Georges Gonthier","Sidi Ould Biha","Cyril Cohen","Francois Garillot","Alexey Solovyev","Russell O'Connor","Laurent Théry","Assia Mahboubi"],"description":"This library includes the small scale reflection proof language\nextension and the minimal set of libraries to take advantage of it.\nThis includes libraries on lists (seq), boolean and boolean\npredicates, natural numbers and types with decidable equality,\nfinite types, finite sets, finite functions, finite graphs, basic arithmetics\nand prime numbers, big operators","date":null,"version":"1.11+beta1","suite":"extra-dev","src":"https://github.com/math-comp/math-comp/archive/mathcomp-1.11+beta1.tar.gz","checksum":"sha256=412e3bd8faae4c52a4e1651a3ea3ad949ae6f93a2ffbb579f0ebd4662d5d418e"}],"most_recent":"dev"}],["coq-mathcomp-sum-of-two-square",{"versions":[{"homepage":"https://github.com/thery/twoSquare","keywords":[],"categories":[],"authors":[],"description":"gauss_int.v : the definition of gaussian integers\n\nfermat2.v : the proof of Fermat's theorem\n\nThe final statement reads:\n\n===================================================\n\nFrom mathcomp\nRequire Import all_ssreflect.\n\nFrom mathcomp.contrib.sum_of_two_square\nRequire Import gauss_int fermat2.\nCheck sum2stest.\n\nsum2stest\n : forall n : nat,\n reflect\n (forall p : nat,\n prime p ->\n odd p -> p %| n -> odd (logn p n) -> p %% 4 = 1)\n (n \\is a sum_of_two_square)\n\n===================================================","date":null,"version":"1.0.1","suite":"released","src":"https://github.com/thery/twoSquare/archive/v1.0.1.zip","checksum":"md5=1633745a81e8e3941d00ffb7e6e89883"},{"homepage":"https://github.com/thery/twoSquare","keywords":[],"categories":[],"authors":[],"description":"gauss_int.v : the definition of gaussian integers\n\nfermat2.v : the proof of Fermat's theorem\n\nThe final statement reads:\n\n===================================================\n\nFrom mathcomp\nRequire Import all_ssreflect.\n\nFrom mathcomp.contrib.sum_of_two_square\nRequire Import gauss_int fermat2.\nCheck sum2stest.\n\nsum2stest\n : forall n : nat,\n reflect\n (forall p : nat,\n prime p ->\n odd p -> p %| n -> odd (logn p n) -> p %% 4 = 1)\n (n \\is a sum_of_two_square)\n\n===================================================","date":null,"version":"1.0.0","suite":"released","src":"https://github.com/thery/twoSquare/archive/v1.0.0.zip","checksum":"md5=98739e31fac7fcda2cb52f40e5901257"}],"most_recent":"1.0.1"}],["coq-mathcomp-tarjan",{"versions":[{"homepage":"https://github.com/math-comp/tarjan","keywords":["strongly connected components","topological sorting","Kosaraju","Tarjan","acyclicity","graph theory"],"categories":["Computer Science/Graph Theory"],"authors":["Cyril Cohen","Jean-Jacques Lévy","Karl Palmskog","Laurent Théry"],"description":"This development contains formalizations and correctness proofs using Coq and the Mathematical\nComponents library of algorithms originally due to Kosaraju and Tarjan for finding strongly\nconnected components in finite graphs. 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implementations of Quicksort;\n- proofs of these implementations' worst- and average case complexity.\n\nMost of the development is documented in the TYPES 2008 paper \"A Machine-Checked Proof of the Average-Case Complexity of Quicksort in Coq\", available at the homepage.","date":"2010-06","version":"8.5.0","suite":"released","src":"https://github.com/coq-contribs/quicksort-complexity/archive/v8.5.0.tar.gz","checksum":"md5=8234353fc0384b441e777523f7542440"}],"most_recent":"8.10.0"}],["coq-railroad-crossing",{"versions":[{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna [http://www.fing.edu.uy/~cluna]"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"8.10.0","suite":"released","src":"https://github.com/coq-contribs/railroad-crossing/archive/v8.10.0.tar.gz","checksum":"md5=6b070cfc66b79c57cdbd3d4ed55a0ee4"},{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna [http://www.fing.edu.uy/~cluna]"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"8.9.0","suite":"released","src":"https://github.com/coq-contribs/railroad-crossing/archive/v8.9.0.tar.gz","checksum":"md5=98e7fada2a3a76ef365de972182d566b"},{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna [http://www.fing.edu.uy/~cluna]"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"8.8.0","suite":"released","src":"https://github.com/coq-contribs/railroad-crossing/archive/v8.8.0.tar.gz","checksum":"md5=b3d43148c290b04b040e11078b4acf26"},{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna [http://www.fing.edu.uy/~cluna]"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"8.7.0","suite":"released","src":"https://github.com/coq-contribs/railroad-crossing/archive/v8.7.0.tar.gz","checksum":"md5=ebaf56330ea9eb42892c35901c764a82"},{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna [http://www.fing.edu.uy/~cluna]"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"8.6.0","suite":"released","src":"https://github.com/coq-contribs/railroad-crossing/archive/v8.6.0.tar.gz","checksum":"md5=19438c5093df37961a84b3e40cf43b38"},{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"8.5.0","suite":"released","src":"https://github.com/coq-contribs/railroad-crossing/archive/v8.5.0.tar.gz","checksum":"md5=aa5d5cef3b3a7a723b2040f90219f866"},{"homepage":"https://github.com/coq-contribs/railroad-crossing","keywords":["CTL","TCTL","real time","timed automatas","safety","concurrency properties","invariants","non-Zeno","discrete time"],"categories":["Computer Science/Concurrent Systems and Protocols/Correctness of specific protocols"],"authors":["Carlos Daniel Luna"],"description":"This library present the specification and verification of\none real time system: the Railroad Crossing Problem, which has been\nproposed as a benchmark for the comparison of real-time formalisms. We\nspecify the system using timed automatas (timed graphs) with discrete\ntime and we prove invariants, the system safety property and the NonZeno\nproperty, using the logics CTL and TCTL.","date":"February-March 2000","version":"dev","suite":"extra-dev","src":"git+https://github.com/coq-contribs/railroad-crossing.git#master","checksum":null}],"most_recent":"dev"}],["coq-ramsey",{"versions":[{"homepage":"https://github.com/coq-contribs/ramsey","keywords":["dimension one Ramsey theorem","constructive mathematics","almost full sets"],"categories":["Mathematics/Logic","Mathematics/Combinatorics and Graph Theory","Miscellaneous/Extracted Programs/Combinatorics"],"authors":["Marc Bezem"],"description":"For dimension one, the Infinite Ramsey Theorem states that, for any\nsubset A of the natural numbers nat, either A or nat\\A is\ninfinite. This special case of the Pigeon Hole Principle is\nclassically equivalent to: if A and B are both co-finite, then so is\ntheir intersection. None of these principles is constructively\nvalid. In [VB] the notion of an almost full set is introduced,\nclassically equivalent to co-finiteness, for which closure under\nfinite intersection can be proved constructively. A is almost full if\nfor every (strictly) increasing sequence f: nat -> nat there exists an\nx in nat such that f(x) in A. The notion of almost full and its\nclosure under finite intersection are generalized to all finite\ndimensions, yielding constructive Ramsey Theorems. The proofs for\ndimension two and higher essentially use Brouwer's Bar Theorem.\n\nIn the proof development below we strengthen the notion of almost full\nfor dimension one in the following sense. A: nat -> Prop is called\nY-full if for every (strictly) increasing sequence f: nat -> nat we\nhave (A (f (Y f))). Here of course Y : (nat -> nat) -> nat. Given\nYA-full A and YB-full B we construct X from YA and YB such that the\nintersection of A and B is X-full. This is essentially [VB, Th. 5.4],\nbut now it can be done without using axioms, using only inductive\ntypes. The generalization to higher dimensions will be much more\ndifficult and is not pursued here.","date":null,"version":"8.10.0","suite":"released","src":"https://github.com/coq-contribs/ramsey/archive/v8.10.0.tar.gz","checksum":"md5=4ac9988a8896338d3f8000c5832e39f0"},{"homepage":"https://github.com/coq-contribs/ramsey","keywords":["dimension one Ramsey theorem","constructive mathematics","almost full sets"],"categories":["Mathematics/Logic","Mathematics/Combinatorics and Graph Theory","Miscellaneous/Extracted Programs/Combinatorics"],"authors":["Marc Bezem"],"description":"For dimension one, the Infinite Ramsey Theorem states that, for any\nsubset A of the natural numbers nat, either A or nat\\A is\ninfinite. This special case of the Pigeon Hole Principle is\nclassically equivalent to: if A and B are both co-finite, then so is\ntheir intersection. None of these principles is constructively\nvalid. In [VB] the notion of an almost full set is introduced,\nclassically equivalent to co-finiteness, for which closure under\nfinite intersection can be proved constructively. A is almost full if\nfor every (strictly) increasing sequence f: nat -> nat there exists an\nx in nat such that f(x) in A. The notion of almost full and its\nclosure under finite intersection are generalized to all finite\ndimensions, yielding constructive Ramsey Theorems. The proofs for\ndimension two and higher essentially use Brouwer's Bar Theorem.\n\nIn the proof development below we strengthen the notion of almost full\nfor dimension one in the following sense. A: nat -> Prop is called\nY-full if for every (strictly) increasing sequence f: nat -> nat we\nhave (A (f (Y f))). Here of course Y : (nat -> nat) -> nat. Given\nYA-full A and YB-full B we construct X from YA and YB such that the\nintersection of A and B is X-full. This is essentially [VB, Th. 5.4],\nbut now it can be done without using axioms, using only inductive\ntypes. The generalization to higher dimensions will be much more\ndifficult and is not pursued here.","date":null,"version":"8.9.0","suite":"released","src":"https://github.com/coq-contribs/ramsey/archive/v8.9.0.tar.gz","checksum":"md5=40f729767b3187f93b74a90aac4da5b4"},{"homepage":"https://github.com/coq-contribs/ramsey","keywords":["dimension one Ramsey theorem","constructive mathematics","almost full sets"],"categories":["Mathematics/Logic","Mathematics/Combinatorics and Graph Theory","Miscellaneous/Extracted Programs/Combinatorics"],"authors":["Marc Bezem"],"description":"For dimension one, the Infinite Ramsey Theorem states that, for any\nsubset A of the natural numbers nat, either A or nat\\A is\ninfinite. This special case of the Pigeon Hole Principle is\nclassically equivalent to: if A and B are both co-finite, then so is\ntheir intersection. None of these principles is constructively\nvalid. In [VB] the notion of an almost full set is introduced,\nclassically equivalent to co-finiteness, for which closure under\nfinite intersection can be proved constructively. A is almost full if\nfor every (strictly) increasing sequence f: nat -> nat there exists an\nx in nat such that f(x) in A. The notion of almost full and its\nclosure under finite intersection are generalized to all finite\ndimensions, yielding constructive Ramsey Theorems. The proofs for\ndimension two and higher essentially use Brouwer's Bar Theorem.\n\nIn the proof development below we strengthen the notion of almost full\nfor dimension one in the following sense. A: nat -> Prop is called\nY-full if for every (strictly) increasing sequence f: nat -> nat we\nhave (A (f (Y f))). Here of course Y : (nat -> nat) -> nat. Given\nYA-full A and YB-full B we construct X from YA and YB such that the\nintersection of A and B is X-full. This is essentially [VB, Th. 5.4],\nbut now it can be done without using axioms, using only inductive\ntypes. The generalization to higher dimensions will be much more\ndifficult and is not pursued here.","date":null,"version":"8.8.0","suite":"released","src":"https://github.com/coq-contribs/ramsey/archive/v8.8.0.tar.gz","checksum":"md5=9087b15e27879f3d4b7576b4e7d48aad"},{"homepage":"https://github.com/coq-contribs/ramsey","keywords":["dimension one Ramsey theorem","constructive mathematics","almost full sets"],"categories":["Mathematics/Logic","Mathematics/Combinatorics and Graph Theory","Miscellaneous/Extracted Programs/Combinatorics"],"authors":["Marc Bezem"],"description":"For dimension one, the Infinite Ramsey Theorem states that, for any\nsubset A of the natural numbers nat, either A or nat\\A is\ninfinite. This special case of the Pigeon Hole Principle is\nclassically equivalent to: if A and B are both co-finite, then so is\ntheir intersection. None of these principles is constructively\nvalid. In [VB] the notion of an almost full set is introduced,\nclassically equivalent to co-finiteness, for which closure under\nfinite intersection can be proved constructively. A is almost full if\nfor every (strictly) increasing sequence f: nat -> nat there exists an\nx in nat such that f(x) in A. The notion of almost full and its\nclosure under finite intersection are generalized to all finite\ndimensions, yielding constructive Ramsey Theorems. The proofs for\ndimension two and higher essentially use Brouwer's Bar Theorem.\n\nIn the proof development below we strengthen the notion of almost full\nfor dimension one in the following sense. A: nat -> Prop is called\nY-full if for every (strictly) increasing sequence f: nat -> nat we\nhave (A (f (Y f))). Here of course Y : (nat -> nat) -> nat. Given\nYA-full A and YB-full B we construct X from YA and YB such that the\nintersection of A and B is X-full. This is essentially [VB, Th. 5.4],\nbut now it can be done without using axioms, using only inductive\ntypes. The generalization to higher dimensions will be much more\ndifficult and is not pursued here.","date":null,"version":"8.7.0","suite":"released","src":"https://github.com/coq-contribs/ramsey/archive/v8.7.0.tar.gz","checksum":"md5=2dae4557a10bb6ab518e14e2cc8e7b8e"},{"homepage":"https://github.com/coq-contribs/ramsey","keywords":["dimension one Ramsey theorem","constructive mathematics","almost full sets"],"categories":["Mathematics/Logic","Mathematics/Combinatorics and Graph Theory","Miscellaneous/Extracted Programs/Combinatorics"],"authors":["Marc Bezem"],"description":"For dimension one, the Infinite Ramsey Theorem states that, for any\nsubset A of the natural numbers nat, either A or nat\\A is\ninfinite. This special case of the Pigeon Hole Principle is\nclassically equivalent to: if A and B are both co-finite, then so is\ntheir intersection. None of these principles is constructively\nvalid. In [VB] the notion of an almost full set is introduced,\nclassically equivalent to co-finiteness, for which closure under\nfinite intersection can be proved constructively. A is almost full if\nfor every (strictly) increasing sequence f: nat -> nat there exists an\nx in nat such that f(x) in A. The notion of almost full and its\nclosure under finite intersection are generalized to all finite\ndimensions, yielding constructive Ramsey Theorems. The proofs for\ndimension two and higher essentially use Brouwer's Bar Theorem.\n\nIn the proof development below we strengthen the notion of almost full\nfor dimension one in the following sense. A: nat -> Prop is called\nY-full if for every (strictly) increasing sequence f: nat -> nat we\nhave (A (f (Y f))). Here of course Y : (nat -> nat) -> nat. Given\nYA-full A and YB-full B we construct X from YA and YB such that the\nintersection of A and B is X-full. This is essentially [VB, Th. 5.4],\nbut now it can be done without using axioms, using only inductive\ntypes. The generalization to higher dimensions will be much more\ndifficult and is not pursued here.","date":null,"version":"8.6.0","suite":"released","src":"https://github.com/coq-contribs/ramsey/archive/v8.6.0.tar.gz","checksum":"md5=821e0a1434876b9d3263cf18a3ede913"},{"homepage":"https://github.com/coq-contribs/ramsey","keywords":["dimension one ramsey theorem","constructive mathematics","almost full sets"],"categories":["Mathematics/Combinatorics and Graph Theory","Miscellaneous/Extracted Programs/Combinatorics"],"authors":["Marc Bezem"],"description":"For dimension one, the Infinite Ramsey Theorem states that, for any\nsubset A of the natural numbers nat, either A or nat\\A is\ninfinite. This special case of the Pigeon Hole Principle is\nclassically equivalent to: if A and B are both co-finite, then so is\ntheir intersection. None of these principles is constructively\nvalid. In [VB] the notion of an almost full set is introduced,\nclassically equivalent to co-finiteness, for which closure under\nfinite intersection can be proved constructively. A is almost full if\nfor every (strictly) increasing sequence f: nat -> nat there exists an\nx in nat such that f(x) in A. The notion of almost full and its\nclosure under finite intersection are generalized to all finite\ndimensions, yielding constructive Ramsey Theorems. The proofs for\ndimension two and higher essentially use Brouwer's Bar Theorem.\n\nIn the proof development below we strengthen the notion of almost full\nfor dimension one in the following sense. A: nat -> Prop is called\nY-full if for every (strictly) increasing sequence f: nat -> nat we\nhave (A (f (Y f))). Here of course Y : (nat -> nat) -> nat. Given\nYA-full A and YB-full B we construct X from YA and YB such that the\nintersection of A and B is X-full. This is essentially [VB, Th. 5.4],\nbut now it can be done without using axioms, using only inductive\ntypes. The generalization to higher dimensions will be much more\ndifficult and is not pursued here.","date":null,"version":"8.5.0","suite":"released","src":"https://github.com/coq-contribs/ramsey/archive/v8.5.0.tar.gz","checksum":"md5=0cdb4da8829dffb56d5e6f9e36c6f4c1"}],"most_recent":"8.10.0"}],["coq-random",{"versions":[{"homepage":"https://github.com/coq-contribs/random","keywords":["randomized algorithms","monads","probability"],"categories":["Computer Science/Decision Procedures and Certified Algorithms/Correctness proofs of algorithms"],"authors":["Christine Paulin"],"description":"This contribution is a modelisation of random programs\nas measures in Coq. It started in 2004 in the context\nof the AVERROES project (http://www-verimag.imag.fr/AVERROES/).\nIt is based on comon work with Philippe Audebaud (ENS Lyon).\nIt was last updated in february 2007.\n\nIt contains the following elements\n - an axiomatisation of the interval [0,1] and derived properties\n(files Ubase.v and Uprop.v);\n\n - a definition of measures on a type A as functions of type\n(A->[0,1])->[0,1] enjoying special stability properties (files\nMonads.v and Probas.v); proofs that these constructions have a\nmonadic structure;\n\n - an interpretation of programs of type A as measures, in particular\na fixpoint construction; the definition of an axiomatic semantic for\nderiving judgements such as ``the probability of an expression e to\nevaluate to a result satisfying property q belongs to an interval [p,q]''\n(file Prog.v);\n\n - Proof of probabilistic termination of a linear random walk (file\nIterflip.v);\n\n - Proof of a program implementing a bernoulli distribution\n(Proba(bernouilli(p)=true)=p) using a coin flip and the derived binomial\nlaw (Proba(binomial p n=k)=C(n,k)p^k(1-p)^{n-k}) (file Bernoulli.v);\n\n - Proof of estimation of the combination of two random executions\n(file Choice.v)\n\n - Proof of partial termination of parameterized random walk (file Ycart.v)\n\n - Definition of a measure on traces from a mesure on transitions\nsteps (file Nelist.v, Transitions.v)\n\nThe document random.pdf contains a short introduction to the library\nassociated to the Gallina source code of the library.","date":null,"version":"8.10.0","suite":"released","src":"https://github.com/coq-contribs/random/archive/v8.10.0.tar.gz","checksum":"md5=e0d9709f1ed8622c07d9b28ca1330564"},{"homepage":"https://github.com/coq-contribs/random","keywords":["randomized algorithms","monads","probability"],"categories":["Computer Science/Decision Procedures and Certified Algorithms/Correctness proofs of algorithms"],"authors":["Christine Paulin"],"description":"This contribution is a modelisation of random programs\nas measures in Coq. It started in 2004 in the context\nof the AVERROES project (http://www-verimag.imag.fr/AVERROES/).\nIt is based on comon work with Philippe Audebaud (ENS Lyon).\nIt was last updated in february 2007.\n\nIt contains the following elements\n - an axiomatisation of the interval [0,1] and derived properties\n(files Ubase.v and Uprop.v);\n\n - a definition of measures on a type A as functions of type\n(A->[0,1])->[0,1] enjoying special stability properties (files\nMonads.v and Probas.v); proofs that these constructions have a\nmonadic structure;\n\n - an interpretation of programs of type A as measures, in particular\na fixpoint construction; the definition of an axiomatic semantic for\nderiving judgements such as ``the probability of an expression e to\nevaluate to a result satisfying property q belongs to an interval [p,q]''\n(file Prog.v);\n\n - Proof of probabilistic termination of a linear random walk (file\nIterflip.v);\n\n - Proof of a program implementing a bernoulli distribution\n(Proba(bernouilli(p)=true)=p) using a coin flip and the derived binomial\nlaw (Proba(binomial p n=k)=C(n,k)p^k(1-p)^{n-k}) (file Bernoulli.v);\n\n - Proof of estimation of the combination of two random executions\n(file Choice.v)\n\n - Proof of partial termination of parameterized random walk (file Ycart.v)\n\n - Definition of a measure on traces from a mesure on transitions\nsteps (file Nelist.v, Transitions.v)\n\nThe document random.pdf contains a short introduction to the library\nassociated to the Gallina source code of the library.","date":null,"version":"8.9.0","suite":"released","src":"https://github.com/coq-contribs/random/archive/v8.9.0.tar.gz","checksum":"md5=6ec9214028caa925a7a30b2cf3c14545"},{"homepage":"https://github.com/coq-contribs/random","keywords":["randomized algorithms","monads","probability"],"categories":["Computer Science/Decision Procedures and Certified Algorithms/Correctness proofs of algorithms"],"authors":["Christine Paulin"],"description":"This contribution is a modelisation of random programs\nas measures in Coq. 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