├── 002-shortest-path ├── path-length.opam ├── dune-project ├── dune ├── Makefile ├── Sym_network.mli ├── Floyd_warshall.mli ├── Main.ml ├── Sym_network.ml ├── README.md └── Floyd_warshall.ml ├── .gitignore ├── README.md ├── 001-max-reachability ├── sym_network.ml └── README.md └── LICENSE /002-shortest-path/path-length.opam: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # dune workspace 2 | _build 3 | -------------------------------------------------------------------------------- /002-shortest-path/dune-project: -------------------------------------------------------------------------------- 1 | (lang dune 2.1) 2 | -------------------------------------------------------------------------------- /002-shortest-path/dune: -------------------------------------------------------------------------------- 1 | (executable 2 | (public_name path-length) 3 | (name Main)) 4 | -------------------------------------------------------------------------------- /002-shortest-path/Makefile: -------------------------------------------------------------------------------- 1 | .PHONY: all 2 | all: build 3 | dune exec path-length 10 4 | dune exec path-length 1000 5 | 6 | .PHONY: build 7 | build: 8 | dune build 9 | 10 | .PHONY: clean 11 | clean: 12 | dune clean 13 | -------------------------------------------------------------------------------- /002-shortest-path/Sym_network.mli: -------------------------------------------------------------------------------- 1 | (* 2 | A symmetric graph of n nodes where each node i is connected to 3 | log n other nodes. 4 | *) 5 | 6 | (* 7 | node identifier = index 8 | Each cell of the array contains the list of nodes defining outgoing edges. 9 | *) 10 | type t = int list array 11 | 12 | val create : int -> t 13 | 14 | val print : t -> unit 15 | -------------------------------------------------------------------------------- /002-shortest-path/Floyd_warshall.mli: -------------------------------------------------------------------------------- 1 | (* 2 | Compute all shortest paths in a graph using the Floyd-Warshall algorithm. 3 | 4 | https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm 5 | *) 6 | 7 | (* Node identifiers range from 0 to n-1, where n is the number of nodes 8 | in the graph. *) 9 | type node_id = int 10 | 11 | val get_distance_matrix : 12 | ?directed:bool -> 13 | int -> 14 | (node_id * node_id * float) list -> float array array 15 | 16 | val print_matrix : float array array -> unit 17 | 18 | val print_matrix_stats : float array array -> unit 19 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # dev-random: exploring one idea per day with code 2 | 3 | The rules are: 4 | 5 | - each experiment must take no more than a day, and ideally no more 6 | than 4 hours; 7 | - there must be some text that explains the idea; 8 | - there must be some code that illustrates the idea. 9 | 10 | Why? 11 | 12 | A day is the natural unit for focusing on one thing without 13 | interruption given that we must sleep at night. 14 | 15 | What to expect: 16 | 17 | - a vague starting point; 18 | - a vague conclusion, if any at all; 19 | - incomplete explanations; 20 | - inconsistent terminology; 21 | - many mistakes; 22 | - no finished software that you could use as is. 23 | -------------------------------------------------------------------------------- /002-shortest-path/Main.ml: -------------------------------------------------------------------------------- 1 | (* 2 | Command-line handling and entry point of the program. 3 | *) 4 | 5 | let convert_edges graph = 6 | graph 7 | |> Array.mapi (fun i js -> List.map (fun j -> (i, j, 1.)) js) 8 | |> Array.to_list 9 | |> List.flatten 10 | 11 | let run n = 12 | let graph = Sym_network.create n in 13 | let mat = 14 | Floyd_warshall.get_distance_matrix ~directed:true n 15 | (convert_edges graph) 16 | in 17 | Sym_network.print graph; 18 | if n <= 20 then 19 | Floyd_warshall.print_matrix mat; 20 | Floyd_warshall.print_matrix_stats mat 21 | 22 | let main () = 23 | let n = 24 | match Sys.argv with 25 | | [| _ |] -> 100 26 | | [| _; num |] -> int_of_string num 27 | | _ -> failwith "pass the number of nodes as argument" 28 | in 29 | run n 30 | 31 | let () = main () 32 | -------------------------------------------------------------------------------- /002-shortest-path/Sym_network.ml: -------------------------------------------------------------------------------- 1 | (* 2 | A symmetric graph of n nodes where each node i is connected to 3 | log n other nodes. 4 | *) 5 | 6 | open Printf 7 | 8 | (* 9 | node identifier = index 10 | Each cell of the array contains the list of nodes defining outgoing edges. 11 | *) 12 | type t = int list array 13 | 14 | let create_offsets n = 15 | let rec aux offset = 16 | if offset < n then 17 | offset :: aux (2 * offset) 18 | else 19 | [] 20 | in 21 | aux 1 22 | 23 | let create_edge n offsets i = 24 | List.map (fun offset -> (i + offset) mod n) offsets 25 | 26 | let create n = 27 | let offsets = create_offsets n in 28 | Array.init n (create_edge n offsets) 29 | 30 | let print a = 31 | let n = Array.length a in 32 | let num_pairs = n * (n - 1) in 33 | let num_edges = 34 | Array.fold_left (fun sum dests -> sum + List.length dests) 0 a 35 | in 36 | printf "\ 37 | number of nodes: %i 38 | number of node pairs: %i 39 | number of edges: %i 40 | " 41 | n num_pairs num_edges; 42 | Array.iteri (fun i dests -> 43 | printf "%3i -> %s\n" 44 | i (List.map (sprintf "%3i") dests |> String.concat " ") 45 | ) a 46 | -------------------------------------------------------------------------------- /001-max-reachability/sym_network.ml: -------------------------------------------------------------------------------- 1 | (* 2 | A symmetric graph of n nodes where each node i is connected to 3 | log n other nodes. 4 | 5 | Usage: ocaml sym_network.ml 200 6 | *) 7 | 8 | open Printf 9 | 10 | (* 11 | node identifier = index 12 | Each cell of the array contains the list of nodes defining outgoing edges. 13 | *) 14 | type t = int list array 15 | 16 | let create_offsets n = 17 | let rec aux offset = 18 | if offset < n then 19 | offset :: aux (2 * offset) 20 | else 21 | [] 22 | in 23 | aux 1 24 | 25 | let create_edge n offsets i = 26 | List.map (fun offset -> (i + offset) mod n) offsets 27 | 28 | let create n = 29 | let offsets = create_offsets n in 30 | Array.init n (create_edge n offsets) 31 | 32 | let print a = 33 | Array.iteri (fun i dests -> 34 | printf "%i -> %s\n" 35 | i (List.map string_of_int dests |> String.concat " ") 36 | ) a 37 | 38 | let main () = 39 | let n = 40 | match Sys.argv with 41 | | [| _ |] -> 100 42 | | [| _; num |] -> int_of_string num 43 | | _ -> failwith "pass the number of nodes as argument" 44 | in 45 | let example = create n in 46 | print example 47 | 48 | let () = main () 49 | -------------------------------------------------------------------------------- /002-shortest-path/README.md: -------------------------------------------------------------------------------- 1 | Shortest paths in a graph designed for shortest paths 2 | == 3 | 4 | This a follow-up to [001-max-reachability](../001-max-reachability) 5 | where we created a directed graph with the following properties: 6 | 7 | * n nodes 8 | * O(n log n) edges 9 | * nodes are indistinguishable without being assigned an identifier, 10 | i.e. the structure of the space from the perspective of a node is 11 | the same for all the nodes. 12 | * The worst-case shortest path from one node to another was claimed to 13 | be O(log n). 14 | 15 | Let's check if the shortest path from one node to another is indeed 16 | of length O(log n). 17 | 18 | Implementation 19 | -- 20 | 21 | I'm reusing an old implementation of the Floyd-Warshall algorithm to 22 | compute all the shortest paths within a directed graph. 23 | 24 | The graph of interest is what I implemented 25 | [previously](../001-max-reachability). 26 | 27 | The program can be built and run with: 28 | ``` 29 | $ make 30 | ``` 31 | 32 | For n = 1000 nodes, we get: 33 | 34 | ``` 35 | number of nodes: 1000 36 | number of node pairs: 999000 37 | number of edges: 10000 38 | 0 -> 1 2 4 8 16 32 64 128 256 512 39 | 1 -> 2 3 5 9 17 33 65 129 257 513 40 | 2 -> 3 4 6 10 18 34 66 130 258 514 41 | ... 42 | 997 -> 998 999 1 5 13 29 61 125 253 509 43 | 998 -> 999 0 2 6 14 30 62 126 254 510 44 | 999 -> 0 1 3 7 15 31 63 127 255 511 45 | number of nodes n: 1000 46 | average distance between two distinct nodes: 4.93694 47 | maximum distance between two distinct nodes: 9 48 | ``` 49 | 50 | For n = 2000 nodes, we get: 51 | 52 | ``` 53 | number of nodes: 2000 54 | number of node pairs: 3998000 55 | number of edges: 22000 56 | 0 -> 1 2 4 8 16 32 64 128 256 512 1024 57 | 1 -> 2 3 5 9 17 33 65 129 257 513 1025 58 | 2 -> 3 4 6 10 18 34 66 130 258 514 1026 59 | ... 60 | 1997 -> 1998 1999 1 5 13 29 61 125 253 509 1021 61 | 1998 -> 1999 0 2 6 14 30 62 126 254 510 1022 62 | 1999 -> 0 1 3 7 15 31 63 127 255 511 1023 63 | number of nodes n: 2000 64 | average distance between two distinct nodes: 5.43472 65 | maximum distance between two distinct nodes: 10 66 | ``` 67 | 68 | Note that the Floyd-Warshall algorithm runs in O(n^3) which takes a 69 | while on large graphs. This is why I didn't have the patience to get 70 | the data for really large graphs. Since every node of the graph is 71 | identical, it would actually suffice to calculate the shortest paths 72 | from one node to all the other nodes. 73 | 74 | Conclusion 75 | -- 76 | 77 | It looks indeed like the maximum distance from one node to another is 78 | log n. This graph structure allows us to create only n log n edges, 79 | with log n outgoing edges for each node. An important property is that 80 | all nodes are identical and is traversed by the same traffic unlike a 81 | hierarchical network like the internet. 82 | 83 | Possible uses include "egalitarian diffusion algorithms" based on a 84 | collection of agents that broadcast data to their neighbors. Upon 85 | receiving data from a neighbor, an agent integrates it and 86 | rebroadcasts it in a modified form, as is the case with [self-organizing 87 | maps](https://en.wikipedia.org/wiki/Self-organizing_map). 88 | -------------------------------------------------------------------------------- /002-shortest-path/Floyd_warshall.ml: -------------------------------------------------------------------------------- 1 | (* 2 | Compute all shortest paths in a graph using the Floyd-Warshall algorithm. 3 | 4 | https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm 5 | *) 6 | 7 | open Printf 8 | 9 | type node_id = int 10 | 11 | let add_directed_edge dist i j w = 12 | if not (Float.is_finite w) then 13 | invalid_arg "Floyd_warshall.add_directed_edge: not a finite edge weight"; 14 | dist.(i).(j) <- w 15 | 16 | let add_undirected_edge dist i j w = 17 | add_directed_edge dist i j w; 18 | add_directed_edge dist j i w 19 | 20 | (* 21 | Load a graph and compute the distance matrix. 22 | Vertices are identified by consecutive ints starting from zero. 23 | *) 24 | let get_distance_matrix ?(directed = false) n edge_weights = 25 | let dist = Array.make_matrix n n infinity in 26 | for i = 0 to n - 1 do 27 | dist.(i).(i) <- 0. 28 | done; 29 | let add_edge = 30 | if directed then 31 | add_directed_edge 32 | else 33 | add_undirected_edge 34 | in 35 | List.iter (fun (i, j, w) -> add_edge dist i j w) edge_weights; 36 | for k = 0 to n - 1 do 37 | for i = 0 to n - 1 do 38 | for j = 0 to n - 1 do 39 | let dist_via_k = dist.(i).(k) +. dist.(k).(j) in 40 | if dist_via_k < dist.(i).(j) then 41 | dist.(i).(j) <- dist_via_k 42 | done 43 | done 44 | done; 45 | dist 46 | 47 | let print_matrix m = 48 | let n = Array.length m in 49 | for i = 0 to n - 1 do 50 | printf "[%3i]" i; 51 | let mi = m.(i) in 52 | assert (Array.length mi = n); 53 | for j = 0 to n - 1 do 54 | printf " %3g" mi.(j) 55 | done; 56 | printf "\n" 57 | done 58 | 59 | let print_matrix_stats m = 60 | let n = Array.length m in 61 | let avg_dist = 62 | (* We only care about distances between distinct nodes, 63 | giving us n * (n-1) pairs *) 64 | Array.fold_left (fun sum row -> 65 | assert (Array.length row = n); 66 | Array.fold_left (+.) sum row 67 | ) 0. m /. float (n * (n - 1)) 68 | in 69 | let max_dist = 70 | Array.fold_left (fun acc row -> 71 | Array.fold_left max acc row 72 | ) 0. m 73 | in 74 | printf "\ 75 | number of nodes n: %i 76 | average distance between two distinct nodes: %g 77 | maximum distance between two distinct nodes: %g 78 | " 79 | n avg_dist max_dist 80 | 81 | let test_distance_matrix () = 82 | assert ( 83 | let dist = 84 | get_distance_matrix 2 [ 85 | 0, 1, 10.; 86 | ] 87 | in 88 | dist = [| [| 0.; 10.; |]; 89 | [| 10.; 0.; |] |] 90 | ); 91 | assert ( 92 | let dist = 93 | get_distance_matrix 3 [ 94 | 0, 1, 10.; 95 | 1, 2, 20.; 96 | ] 97 | in 98 | dist = [| [| 0.; 10.; 30.; |]; 99 | [| 10.; 0.; 20.; |]; 100 | [| 30.; 20.; 0.; |] |] 101 | ); 102 | assert ( 103 | let dist = 104 | get_distance_matrix 4 [ 105 | 0, 1, 10.; 106 | 2, 3, 20.; 107 | ] 108 | in 109 | let inf = infinity in 110 | dist = [| [| 0.; 10.; inf; inf; |]; 111 | [| 10.; 0.; inf; inf; |]; 112 | [| inf; inf; 0.; 20.; |]; 113 | [| inf; inf; 20.; 0.; |]; |] 114 | ); 115 | assert ( 116 | let dist = 117 | get_distance_matrix 3 [ 118 | 0, 1, 10.; 119 | 0, 2, 50.; 120 | 1, 2, 20.; 121 | ] 122 | in 123 | dist = [| [| 0.; 10.; 30.; |]; 124 | [| 10.; 0.; 20.; |]; 125 | [| 30.; 20.; 0.; |] |] 126 | ) 127 | 128 | let _tests = [ 129 | "distance matrix", test_distance_matrix; 130 | ] 131 | -------------------------------------------------------------------------------- /001-max-reachability/README.md: -------------------------------------------------------------------------------- 1 | Maximum reachability 2 | == 3 | 4 | Let's explore the idea of creating a navigable space in which every 5 | point is a close as possible to any other point without requiring an 6 | unreasonable number of "roads" or connections between points. 7 | 8 | We'll consider only finite graphs where each node represents a point 9 | in space and edges represent roads connecting points. We'll also 10 | assume that all edges have the same length. 11 | 12 | We shall however keep in mind and discuss the applicability of such model, 13 | i.e. whether such spaces can be implemented in the physical world, 14 | possibly as electronic circuits and/or computer networks. 15 | 16 | In what follows, n designates the number of nodes in the graph 17 | representing the whole space unless otherwise noted. 18 | 19 | Initial assumptions 20 | -- 21 | 22 | * the graph has n nodes and e edges. The graph is may be directed or 23 | undirected. We'll consider directed graphs to be a special cases of 24 | undirected graphs. 25 | * the graph is meant to be used to transport some information along edges. 26 | * each node has a unique identifier. The unique identifier of an edge 27 | is formed by the pair of nodes. 28 | * each node is equipped with a realistic computer (bounded memory, 29 | bounded number of operations per time interval). 30 | * the question of addressing is left open i.e. we want a way to send 31 | information from one node to another but we have to figure out a good 32 | way to do so while carrying information only along the edges of the 33 | graph. For example, it's not possible to make a function call to 34 | request the path to reach another node for free. 35 | * the memory space allotted to a node is bounded while the size of the graph 36 | is unbounded. This prevents a node from storing a complete map of 37 | the space. 38 | * the graph doesn't change over time. 39 | 40 | Given these constraints, the space resembles the internet under 41 | simplifying assumptions that the network is immutable and that the 42 | travel time from one host to another is constant. We'll assume this is 43 | a solved problem. Instead, we'll focus on the graph topology. 44 | 45 | Motivations 46 | -- 47 | 48 | * model cooperative systems such as: 49 | - individual members of a society with or without technology 50 | - natural or artificial neurons 51 | - a fleet of cooperative robots 52 | * optimize acquisition and exchanges of knowledge 53 | 54 | ### Example 1: O(n) edges, O(n) average shortest path: 55 | 56 | ``` 57 | A -- B -- C -- D 58 | ``` 59 | 60 | ### Example 2: O(n^2) edges, O(1) average shortest path: 61 | 62 | Each node is connected directly to every other node: 63 | 64 | ``` 65 | A -- B 66 | A -- C 67 | A -- D 68 | B -- C 69 | B -- D 70 | C -- D 71 | ``` 72 | 73 | ### Example 3: O(n) edges, O(log n) average shortest path: balanced tree 74 | 75 | Some nodes are closer to the root than others and therefore see more 76 | traffic than the nodes that are closer to the root if all nodes are 77 | equally likely to communicate directly with one another. 78 | 79 | A hierarchical tree-like structure is suitable when most communication 80 | is done locally, each subtree corresponding to a "region" or "locality". 81 | 82 | ### Example 4: O(n log n) edges, O(log n) average shortest path 83 | 84 | Data structure: 85 | * circular array 86 | * each array element i is implicitly connected to elements i+1, i+2, 87 | i+4, i+8, i+16, etc. 88 | 89 | Implementation: see OCaml code. Run `ocaml sym_network.ml 1000` to see 90 | the structure of the graph: 91 | 92 | ``` 93 | $ ocaml sym_network.ml 1000 94 | 0 -> 1 2 4 8 16 32 64 128 256 512 95 | 1 -> 2 3 5 9 17 33 65 129 257 513 96 | 2 -> 3 4 6 10 18 34 66 130 258 514 97 | 3 -> 4 5 7 11 19 35 67 131 259 515 98 | 4 -> 5 6 8 12 20 36 68 132 260 516 99 | 5 -> 6 7 9 13 21 37 69 133 261 517 100 | ... 101 | 995 -> 996 997 999 3 11 27 59 123 251 507 102 | 996 -> 997 998 0 4 12 28 60 124 252 508 103 | 997 -> 998 999 1 5 13 29 61 125 253 509 104 | 998 -> 999 0 2 6 14 30 62 126 254 510 105 | 999 -> 0 1 3 7 15 31 63 127 255 511 106 | ``` 107 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU AFFERO GENERAL PUBLIC LICENSE 2 | Version 3, 19 November 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU Affero General Public License is a free, copyleft license for 11 | software and other kinds of works, specifically designed to ensure 12 | cooperation with the community in the case of network server software. 13 | 14 | The licenses for most software and other practical works are designed 15 | to take away your freedom to share and change the works. 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If additional permissions 338 | apply only to part of the Program, that part may be used separately 339 | under those permissions, but the entire Program remains governed by 340 | this License without regard to the additional permissions. 341 | 342 | When you convey a copy of a covered work, you may at your option 343 | remove any additional permissions from that copy, or from any part of 344 | it. (Additional permissions may be written to require their own 345 | removal in certain cases when you modify the work.) 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Any attempt otherwise to propagate or 399 | modify it is void, and will automatically terminate your rights under 400 | this License (including any patent licenses granted under the third 401 | paragraph of section 11). 402 | 403 | However, if you cease all violation of this License, then your 404 | license from a particular copyright holder is reinstated (a) 405 | provisionally, unless and until the copyright holder explicitly and 406 | finally terminates your license, and (b) permanently, if the copyright 407 | holder fails to notify you of the violation by some reasonable means 408 | prior to 60 days after the cessation. 409 | 410 | Moreover, your license from a particular copyright holder is 411 | reinstated permanently if the copyright holder notifies you of the 412 | violation by some reasonable means, this is the first time you have 413 | received notice of violation of this License (for any work) from that 414 | copyright holder, and you cure the violation prior to 30 days after 415 | your receipt of the notice. 416 | 417 | Termination of your rights under this section does not terminate the 418 | licenses of parties who have received copies or rights from you under 419 | this License. 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Automatic Licensing of Downstream Recipients. 435 | 436 | Each time you convey a covered work, the recipient automatically 437 | receives a license from the original licensors, to run, modify and 438 | propagate that work, subject to this License. You are not responsible 439 | for enforcing compliance by third parties with this License. 440 | 441 | An "entity transaction" is a transaction transferring control of an 442 | organization, or substantially all assets of one, or subdividing an 443 | organization, or merging organizations. 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Patents. 460 | 461 | A "contributor" is a copyright holder who authorizes use under this 462 | License of the Program or a work on which the Program is based. The 463 | work thus licensed is called the contributor's "contributor version". 464 | 465 | A contributor's "essential patent claims" are all patent claims 466 | owned or controlled by the contributor, whether already acquired or 467 | hereafter acquired, that would be infringed by some manner, permitted 468 | by this License, of making, using, or selling its contributor version, 469 | but do not include claims that would be infringed only as a 470 | consequence of further modification of the contributor version. For 471 | purposes of this definition, "control" includes the right to grant 472 | patent sublicenses in a manner consistent with the requirements of 473 | this License. 474 | 475 | Each contributor grants you a non-exclusive, worldwide, royalty-free 476 | patent license under the contributor's essential patent claims, to 477 | make, use, sell, offer for sale, import and otherwise run, modify and 478 | propagate the contents of its contributor version. 479 | 480 | In the following three paragraphs, a "patent license" is any express 481 | agreement or commitment, however denominated, not to enforce a patent 482 | (such as an express permission to practice a patent or covenant not to 483 | sue for patent infringement). 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"Knowingly relying" means you have 496 | actual knowledge that, but for the patent license, your conveying the 497 | covered work in a country, or your recipient's use of the covered work 498 | in a country, would infringe one or more identifiable patents in that 499 | country that you have reason to believe are valid. 500 | 501 | If, pursuant to or in connection with a single transaction or 502 | arrangement, you convey, or propagate by procuring conveyance of, a 503 | covered work, and grant a patent license to some of the parties 504 | receiving the covered work authorizing them to use, propagate, modify 505 | or convey a specific copy of the covered work, then the patent license 506 | you grant is automatically extended to all recipients of the covered 507 | work and works based on it. 508 | 509 | A patent license is "discriminatory" if it does not include within 510 | the scope of its coverage, prohibits the exercise of, or is 511 | conditioned on the non-exercise of one or more of the rights that are 512 | specifically granted under this License. You may not convey a covered 513 | work if you are a party to an arrangement with a third party that is 514 | in the business of distributing software, under which you make payment 515 | to the third party based on the extent of your activity of conveying 516 | the work, and under which the third party grants, to any of the 517 | parties who would receive the covered work from you, a discriminatory 518 | patent license (a) in connection with copies of the covered work 519 | conveyed by you (or copies made from those copies), or (b) primarily 520 | for and in connection with specific products or compilations that 521 | contain the covered work, unless you entered into that arrangement, 522 | or that patent license was granted, prior to 28 March 2007. 523 | 524 | Nothing in this License shall be construed as excluding or limiting 525 | any implied license or other defenses to infringement that may 526 | otherwise be available to you under applicable patent law. 527 | 528 | 12. No Surrender of Others' Freedom. 529 | 530 | If conditions are imposed on you (whether by court order, agreement or 531 | otherwise) that contradict the conditions of this License, they do not 532 | excuse you from the conditions of this License. If you cannot convey a 533 | covered work so as to satisfy simultaneously your obligations under this 534 | License and any other pertinent obligations, then as a consequence you may 535 | not convey it at all. For example, if you agree to terms that obligate you 536 | to collect a royalty for further conveying from those to whom you convey 537 | the Program, the only way you could satisfy both those terms and this 538 | License would be to refrain entirely from conveying the Program. 539 | 540 | 13. Remote Network Interaction; Use with the GNU General Public License. 541 | 542 | Notwithstanding any other provision of this License, if you modify the 543 | Program, your modified version must prominently offer all users 544 | interacting with it remotely through a computer network (if your version 545 | supports such interaction) an opportunity to receive the Corresponding 546 | Source of your version by providing access to the Corresponding Source 547 | from a network server at no charge, through some standard or customary 548 | means of facilitating copying of software. This Corresponding Source 549 | shall include the Corresponding Source for any work covered by version 3 550 | of the GNU General Public License that is incorporated pursuant to the 551 | following paragraph. 552 | 553 | Notwithstanding any other provision of this License, you have 554 | permission to link or combine any covered work with a work licensed 555 | under version 3 of the GNU General Public License into a single 556 | combined work, and to convey the resulting work. The terms of this 557 | License will continue to apply to the part which is the covered work, 558 | but the work with which it is combined will remain governed by version 559 | 3 of the GNU General Public License. 560 | 561 | 14. Revised Versions of this License. 562 | 563 | The Free Software Foundation may publish revised and/or new versions of 564 | the GNU Affero General Public License from time to time. Such new versions 565 | will be similar in spirit to the present version, but may differ in detail to 566 | address new problems or concerns. 567 | 568 | Each version is given a distinguishing version number. If the 569 | Program specifies that a certain numbered version of the GNU Affero General 570 | Public License "or any later version" applies to it, you have the 571 | option of following the terms and conditions either of that numbered 572 | version or of any later version published by the Free Software 573 | Foundation. If the Program does not specify a version number of the 574 | GNU Affero General Public License, you may choose any version ever published 575 | by the Free Software Foundation. 576 | 577 | If the Program specifies that a proxy can decide which future 578 | versions of the GNU Affero General Public License can be used, that proxy's 579 | public statement of acceptance of a version permanently authorizes you 580 | to choose that version for the Program. 581 | 582 | Later license versions may give you additional or different 583 | permissions. However, no additional obligations are imposed on any 584 | author or copyright holder as a result of your choosing to follow a 585 | later version. 586 | 587 | 15. Disclaimer of Warranty. 588 | 589 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 590 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 591 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 592 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 593 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 594 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 595 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 596 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 597 | 598 | 16. Limitation of Liability. 599 | 600 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 601 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 602 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 603 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 604 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 605 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 606 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 607 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 608 | SUCH DAMAGES. 609 | 610 | 17. Interpretation of Sections 15 and 16. 611 | 612 | If the disclaimer of warranty and limitation of liability provided 613 | above cannot be given local legal effect according to their terms, 614 | reviewing courts shall apply local law that most closely approximates 615 | an absolute waiver of all civil liability in connection with the 616 | Program, unless a warranty or assumption of liability accompanies a 617 | copy of the Program in return for a fee. 618 | 619 | END OF TERMS AND CONDITIONS 620 | 621 | How to Apply These Terms to Your New Programs 622 | 623 | If you develop a new program, and you want it to be of the greatest 624 | possible use to the public, the best way to achieve this is to make it 625 | free software which everyone can redistribute and change under these terms. 626 | 627 | To do so, attach the following notices to the program. It is safest 628 | to attach them to the start of each source file to most effectively 629 | state the exclusion of warranty; and each file should have at least 630 | the "copyright" line and a pointer to where the full notice is found. 631 | 632 | 633 | Copyright (C) 634 | 635 | This program is free software: you can redistribute it and/or modify 636 | it under the terms of the GNU Affero General Public License as published 637 | by the Free Software Foundation, either version 3 of the License, or 638 | (at your option) any later version. 639 | 640 | This program is distributed in the hope that it will be useful, 641 | but WITHOUT ANY WARRANTY; without even the implied warranty of 642 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 643 | GNU Affero General Public License for more details. 644 | 645 | You should have received a copy of the GNU Affero General Public License 646 | along with this program. If not, see . 647 | 648 | Also add information on how to contact you by electronic and paper mail. 649 | 650 | If your software can interact with users remotely through a computer 651 | network, you should also make sure that it provides a way for users to 652 | get its source. For example, if your program is a web application, its 653 | interface could display a "Source" link that leads users to an archive 654 | of the code. There are many ways you could offer source, and different 655 | solutions will be better for different programs; see section 13 for the 656 | specific requirements. 657 | 658 | You should also get your employer (if you work as a programmer) or school, 659 | if any, to sign a "copyright disclaimer" for the program, if necessary. 660 | For more information on this, and how to apply and follow the GNU AGPL, see 661 | . 662 | --------------------------------------------------------------------------------