1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131

(*
Copyright (c) 2009 Daniel C. Bünzli. All rights reserved.
Distributed under a BSD3 license, see license at the end of the file.
react release 1.2.0
*)
(** Declarative events and signals.
React is a module for functional reactive programming (frp). It
provides support to program with time varying values : declarative
{{!E}events} and {{!S}signals}. React
doesn't define any primitive event or signal, this lets the client
choose the concrete timeline.
Consult the {{!sem}semantics}, the {{!basics}basics} and
{{!ex}examples}. Open the module to use it, this defines only two
types and modules in your scope.
{e Release 1.2.0  Daniel Bünzli <daniel.buenzl i\@erratique.ch> } *)
(** {1 Interface} *)
type 'a event
(** The type for events of type ['a]. *)
type 'a signal
(** The type for signals of type ['a]. *)
type step
(** The type for update steps. *)
(** Event combinators.
Consult their {{!evsem}semantics.} *)
module E : sig
(** {1:prim Primitive and basics} *)
type 'a t = 'a event
(** The type for events with occurrences of type ['a]. *)
val never : 'a event
(** A never occuring event. For all t, \[[never]\]{_t} [= None]. *)
val create : unit > 'a event * (?step:step > 'a > unit)
(** [create ()] is a primitive event [e] and a [send] function. The
function [send] is such that:
{ul
{ [send v] generates an occurrence [v] of [e] at the time it is called
and triggers an {{!steps}update step}.}
{ [send ~step v] generates an occurence [v] of [e] on the step [step]
when [step] is {{!Step.execute}executed}.}
{ [send ~step v] raises [Invalid_argument] if it was previously
called with a step and this step has not executed yet or if
the given [step] was already executed.}}
{b Warning.} [send] must not be executed inside an update step. *)
val retain : 'a event > (unit > unit) > [ `R of (unit > unit) ]
(** [retain e c] keeps a reference to the closure [c] in [e] and
returns the previously retained value. [c] will {e never} be
invoked.
{b Raises.} [Invalid_argument] on {!E.never}. *)
val stop : ?strong:bool > 'a event > unit
(** [stop e] stops [e] from occuring. It conceptually becomes
{!never} and cannot be restarted. Allows to
disable {{!sideeffects}effectful} events.
The [strong] argument should only be used on platforms
where weak arrays have a strong semantics (i.e. JavaScript).
See {{!strongstop}details}.
{b Note.} If executed in an {{!steps}update step}
the event may still occur in the step. *)
val equal : 'a event > 'a event > bool
(** [equal e e'] is [true] iff [e] and [e'] are equal. If both events are
different from {!never}, physical equality is used. *)
val trace : ?iff:bool signal > ('a > unit) > 'a event > 'a event
(** [trace iff tr e] is [e] except [tr] is invoked with e's
occurence when [iff] is [true] (defaults to [S.const true]).
For all t where \[[e]\]{_t} [= Some v] and \[[iff]\]{_t} =
[true], [tr] is invoked with [v]. *)
(** {1:transf Transforming and filtering} *)
val once : 'a event > 'a event
(** [once e] is [e] with only its next occurence.
{ul
{ \[[once e]\]{_t} [= Some v] if \[[e]\]{_t} [= Some v] and
\[[e]\]{_<t} [= None].}
{ \[[once e]\]{_t} [= None] otherwise.}} *)
val drop_once : 'a event > 'a event
(** [drop_once e] is [e] without its next occurrence.
{ul
{ \[[drop_once e]\]{_t} [= Some v] if \[[e]\]{_t} [= Some v] and
\[[e]\]{_<t} [= Some _].}
{ \[[drop_once e]\]{_t} [= None] otherwise.}} *)
val app : ('a > 'b) event > 'a event > 'b event
(** [app ef e] occurs when both [ef] and [e] occur
{{!simultaneity}simultaneously}.
The value is [ef]'s occurence applied to [e]'s one.
{ul
{ \[[app ef e]\]{_t} [= Some v'] if \[[ef]\]{_t} [= Some f] and
\[[e]\]{_t} [= Some v] and [f v = v'].}
{ \[[app ef e]\]{_t} [= None] otherwise.}} *)
val map : ('a > 'b) > 'a event > 'b event
(** [map f e] applies [f] to [e]'s occurrences.
{ul
{ \[[map f e]\]{_t} [= Some (f v)] if \[[e]\]{_t} [= Some v].}
{ \[[map f e]\]{_t} [= None] otherwise.}} *)
val stamp : 'b event > 'a > 'a event
(** [stamp e v] is [map (fun _ > v) e]. *)
val filter : ('a > bool) > 'a event > 'a event
(** [filter p e] are [e]'s occurrences that satisfy [p].
{ul
{ \[[filter p e]\]{_t} [= Some v] if \[[e]\]{_t} [= Some v] and
[p v = true]}
{ \[[filter p e]\]{_t} [= None] otherwise.}} *)
val fmap : ('a > 'b option) > 'a event > 'b event
(** [fmap fm e] are [e]'s occurrences filtered and mapped by [fm].
{ul
{ \[[fmap fm e]\]{_t} [= Some v] if [fm] \[[e]\]{_t} [= Some v]}
{ \[[fmap fm e]\]{_t} [= None] otherwise.}} *)
val diff : ('a > 'a > 'b) > 'a event > 'b event
(** [diff f e] occurs whenever [e] occurs except on the next occurence.
Occurences are [f v v'] where [v] is [e]'s current
occurrence and [v'] the previous one.
{ul
{ \[[diff f e]\]{_t} [= Some r] if \[[e]\]{_t} [= Some v],
\[[e]\]{_<t} [= Some v'] and [f v v' = r].}
{ \[[diff f e]\]{_t} [= None] otherwise.}} *)
val changes : ?eq:('a > 'a > bool) > 'a event > 'a event
(** [changes eq e] is [e]'s occurrences with occurences equal to
the previous one dropped. Equality is tested with [eq] (defaults to
structural equality).
{ul
{ \[[changes eq e]\]{_t} [= Some v] if \[[e]\]{_t} [= Some v]
and either \[[e]\]{_<t} [= None] or \[[e]\]{_<t} [= Some v'] and
[eq v v' = false].}
{ \[[changes eq e]\]{_t} [= None] otherwise.}} *)
val on : bool signal > 'a event > 'a event
(** [on c e] is the occurrences of [e] when [c] is [true].
{ul
{ \[[on c e]\]{_t} [= Some v]
if \[[c]\]{_t} [= true] and \[[e]\]{_t} [= Some v].}
{ \[[on c e]\]{_t} [= None] otherwise.}} *)
val when_ : bool signal > 'a event > 'a event
(** @deprecated Use {!on}. *)
val dismiss : 'b event > 'a event > 'a event
(** [dismiss c e] is the occurences of [e] except the ones when [c] occurs.
{ul
{ \[[dimiss c e]\]{_t} [= Some v]
if \[[c]\]{_t} [= None] and \[[e]\]{_t} [= Some v].}
{ \[[dimiss c e]\]{_t} [= None] otherwise.}} *)
val until : 'a event > 'b event > 'b event
(** [until c e] is [e]'s occurences until [c] occurs.
{ul
{ \[[until c e]\]{_t} [= Some v] if \[[e]\]{_t} [= Some v] and
\[[c]\]{_<=t} [= None]}
{ \[[until c e]\]{_t} [= None] otherwise.}} *)
(** {1:accum Accumulating} *)
val accum : ('a > 'a) event > 'a > 'a event
(** [accum ef i] accumulates a value, starting with [i], using [e]'s
functional occurrences.
{ul
{ \[[accum ef i]\]{_t} [= Some (f i)] if \[[ef]\]{_t} [= Some f]
and \[[ef]\]{_<t} [= None].
}
{ \[[accum ef i]\]{_t} [= Some (f acc)] if \[[ef]\]{_t} [= Some f]
and \[[accum ef i]\]{_<t} [= Some acc].}
{ \[[accum ef i]\] [= None] otherwise.}} *)
val fold : ('a > 'b > 'a) > 'a > 'b event > 'a event
(** [fold f i e] accumulates [e]'s occurrences with [f] starting with [i].
{ul
{ \[[fold f i e]\]{_t} [= Some (f i v)] if
\[[e]\]{_t} [= Some v] and \[[e]\]{_<t} [= None].}
{ \[[fold f i e]\]{_t} [= Some (f acc v)] if
\[[e]\]{_t} [= Some v] and \[[fold f i e]\]{_<t} [= Some acc].}
{ \[[fold f i e]\]{_t} [= None] otherwise.}} *)
(** {1:combine Combining} *)
val select : 'a event list > 'a event
(** [select el] is the occurrences of every event in [el].
If more than one event occurs {{!simultaneity}simultaneously}
the leftmost is taken and the others are lost.
{ul
{ \[[select el]\]{_ t} [=] \[[List.find (fun e > ]\[[e]\]{_t}
[<> None) el]\]{_t}}.
{ \[[select el]\]{_ t} [= None] otherwise.}} *)
val merge : ('a > 'b > 'a) > 'a > 'b event list > 'a event
(** [merge f a el] merges the {{!simultaneity}simultaneous}
occurrences of every event in [el] using [f] and the accumulator [a].
\[[merge f a el]\]{_ t}
[= List.fold_left f a (List.filter (fun o > o <> None)
(List.map] \[\]{_t}[ el))]. *)
val switch : 'a event > 'a event event > 'a event
(** [switch e ee] is [e]'s occurrences until there is an
occurrence [e'] on [ee], the occurrences of [e'] are then used
until there is a new occurrence on [ee], etc..
{ul
{ \[[switch e ee]\]{_ t} [=] \[[e]\]{_t} if \[[ee]\]{_<=t} [= None].}
{ \[[switch e ee]\]{_ t} [=] \[[e']\]{_t} if \[[ee]\]{_<=t}
[= Some e'].}} *)
val fix : ('a event > 'a event * 'b) > 'b
(** [fix ef] allows to refer to the value an event had an
infinitesimal amount of time before.
In [fix ef], [ef] is called with an event [e] that represents
the event returned by [ef] delayed by an infinitesimal amount of
time. If [e', r = ef e] then [r] is returned by [fix] and [e]
is such that :
{ul
{ \[[e]\]{_ t} [=] [None] if t = 0 }
{ \[[e]\]{_ t} [=] \[[e']\]{_tdt} otherwise}}
{b Raises.} [Invalid_argument] if [e'] is directly a delayed event (i.e.
an event given to a fixing function). *)
(** {1 Lifting}
Lifting combinators. For a given [n] the semantics is:
{ul
{ \[[ln f e1 ... en]\]{_t} [= Some (f v1 ... vn)] if for all
i : \[[ei]\]{_t} [= Some vi].}
{ \[[ln f e1 ... en]\]{_t} [= None] otherwise.}} *)
val l1 : ('a > 'b) > 'a event > 'b event
val l2 : ('a > 'b > 'c) > 'a event > 'b event > 'c event
val l3 : ('a > 'b > 'c > 'd) > 'a event > 'b event > 'c event >
'd event
val l4 : ('a > 'b > 'c > 'd > 'e) > 'a event > 'b event > 'c event >
'd event > 'e event
val l5 : ('a > 'b > 'c > 'd > 'e > 'f) > 'a event > 'b event >
'c event > 'd event > 'e event > 'f event
val l6 : ('a > 'b > 'c > 'd > 'e > 'f > 'g) > 'a event > 'b event >
'c event > 'd event > 'e event > 'f event > 'g event
(** {1 Pervasives support} *)
(** Events with option occurences. *)
module Option : sig
val some : 'a event > 'a option event
(** [some e] is [map (fun v > Some v) e]. *)
val value : ?default:'a signal > 'a option event > 'a event
(** [value default e] either silences [None] occurences if [default] is
unspecified or replaces them by the value of [default] at the occurence
time.
{ul
{ \[[value ~default e]\]{_t}[ = v] if \[[e]\]{_t} [= Some (Some v)].}
{ \[[value ?default:None e]\]{_t}[ = None] if \[[e]\]{_t} = [None].}
{ \[[value ?default:(Some s) e]\]{_t}[ = v]
if \[[e]\]{_t} = [None] and \[[s]\]{_t} [= v].}} *)
end
end
(** Signal combinators.
Consult their {{!sigsem}semantics.} *)
module S : sig
(** {1:prim Primitive and basics} *)
type 'a t = 'a signal
(** The type for signals of type ['a]. *)
val const : 'a > 'a signal
(** [const v] is always [v], \[[const v]\]{_t} [= v]. *)
val create : ?eq:('a > 'a > bool) > 'a >
'a signal * (?step:step > 'a > unit)
(** [create i] is a primitive signal [s] set to [i] and a
[set] function. The function [set] is such that:
{ul
{ [set v] sets the signal's value to [v] at the time it is called and
triggers an {{!steps}update step}.}
{ [set ~step v] sets the signal's value to [v] at the time it is
called and updates it dependencies when [step] is
{{!Step.execute}executed}}
{ [set ~step v] raises [Invalid_argument] if it was previously
called with a step and this step has not executed yet or if
the given [step] was already executed.}}
{b Warning.} [set] must not be executed inside an update step. *)
val value : 'a signal > 'a
(** [value s] is [s]'s current value.
{b Warning.} If executed in an {{!steps}update
step} may return a non uptodate value or raise [Failure] if
the signal is not yet initialized. *)
val retain : 'a signal > (unit > unit) > [ `R of (unit > unit) ]
(** [retain s c] keeps a reference to the closure [c] in [s] and
returns the previously retained value. [c] will {e never} be
invoked.
{b Raises.} [Invalid_argument] on constant signals. *)
(**/**)
val eq_fun : 'a signal > ('a > 'a > bool) option
(**/**)
val stop : ?strong:bool > 'a signal > unit
(** [stop s], stops updating [s]. It conceptually becomes {!const}
with the signal's last value and cannot be restarted. Allows to
disable {{!sideeffects}effectful} signals.
The [strong] argument should only be used on platforms
where weak arrays have a strong semantics (i.e. JavaScript).
See {{!strongstop}details}.
{b Note.} If executed in an update step the signal may
still update in the step. *)
val equal : ?eq:('a > 'a > bool) > 'a signal > 'a signal > bool
(** [equal s s'] is [true] iff [s] and [s'] are equal. If both
signals are {!const}ant [eq] is used between their value
(defauts to structural equality). If both signals are not
{!const}ant, physical equality is used.*)
val trace : ?iff:bool t > ('a > unit) > 'a signal > 'a signal
(** [trace iff tr s] is [s] except [tr] is invoked with [s]'s
current value and on [s] changes when [iff] is [true] (defaults
to [S.const true]). For all t where \[[s]\]{_t} [= v] and (t = 0
or (\[[s]\]{_tdt}[= v'] and [eq v v' = false])) and
\[[iff]\]{_t} = [true], [tr] is invoked with [v]. *)
(** {1 From events} *)
val hold : ?eq:('a > 'a > bool) > 'a > 'a event > 'a signal
(** [hold i e] has the value of [e]'s last occurrence or [i] if there
wasn't any.
{ul
{ \[[hold i e]\]{_t} [= i] if \[[e]\]{_<=t} [= None]}
{ \[[hold i e]\]{_t} [= v] if \[[e]\]{_<=t} [= Some v]}} *)
(** {1:tr Transforming and filtering} *)
val app : ?eq:('b > 'b > bool) > ('a > 'b) signal > 'a signal >
'b signal
(** [app sf s] holds the value of [sf] applied
to the value of [s], \[[app sf s]\]{_t}
[=] \[[sf]\]{_t} \[[s]\]{_t}. *)
val map : ?eq:('b > 'b > bool) > ('a > 'b) > 'a signal > 'b signal
(** [map f s] is [s] transformed by [f], \[[map f s]\]{_t} = [f] \[[s]\]{_t}.
*)
val filter : ?eq:('a > 'a > bool) > ('a > bool) > 'a > 'a signal >
'a signal
(** [filter f i s] is [s]'s values that satisfy [p]. If a value does not
satisfy [p] it holds the last value that was satisfied or [i] if
there is none.
{ul
{ \[[filter p s]\]{_t} [=] \[[s]\]{_t} if [p] \[[s]\]{_t}[ = true].}
{ \[[filter p s]\]{_t} [=] \[[s]\]{_t'} if [p] \[[s]\]{_t}[ = false]
and t' is the greatest t' < t with [p] \[[s]\]{_t'}[ = true].}
{ \[[filter p e]\]{_t} [= i] otherwise.}} *)
val fmap : ?eq:('b > 'b > bool) > ('a > 'b option) > 'b > 'a signal >
'b signal
(** [fmap fm i s] is [s] filtered and mapped by [fm].
{ul
{ \[[fmap fm i s]\]{_t} [=] v if [fm] \[[s]\]{_t}[ = Some v].}
{ \[[fmap fm i s]\]{_t} [=] \[[fmap fm i s]\]{_t'} if [fm]
\[[s]\]{_t} [= None] and t' is the greatest t' < t with [fm]
\[[s]\]{_t'} [<> None].}
{ \[[fmap fm i s]\]{_t} [= i] otherwise.}} *)
val diff : ('a > 'a > 'b) > 'a signal > 'b event
(** [diff f s] is an event with occurrences whenever [s] changes from
[v'] to [v] and [eq v v'] is [false] ([eq] is the signal's equality
function). The value of the occurrence is [f v v'].
{ul
{ \[[diff f s]\]{_t} [= Some d]
if \[[s]\]{_t} [= v] and \[[s]\]{_tdt} [= v'] and [eq v v' = false]
and [f v v' = d].}
{ \[[diff f s]\]{_t} [= None] otherwise.}} *)
val changes : 'a signal > 'a event
(** [changes s] is [diff (fun v _ > v) s]. *)
val sample : ('b > 'a > 'c) > 'b event > 'a signal > 'c event
(** [sample f e s] samples [s] at [e]'s occurrences.
{ul
{ \[[sample f e s]\]{_t} [= Some (f ev sv)] if \[[e]\]{_t} [= Some ev]
and \[[s]\]{_t} [= sv].}
{ \[[sample e s]\]{_t} [= None] otherwise.}} *)
val on : ?eq:('a > 'a > bool) > bool signal > 'a > 'a signal >
'a signal
(** [on c i s] is the signal [s] whenever [c] is [true].
When [c] is [false] it holds the last value [s] had when
[c] was the last time [true] or [i] if it never was.
{ul
{ \[[on c i s]\]{_t} [=] \[[s]\]{_t} if \[[c]\]{_t} [= true]}
{ \[[on c i s]\]{_t} [=] \[[s]\]{_t'} if \[[c]\]{_t} [= false]
where t' is the greatest t' < t with \[[c]\]{_t'} [= true].}
{ \[[on c i s]\]{_t} [=] [i] otherwise.}} *)
val when_ : ?eq:('a > 'a > bool) > bool signal > 'a > 'a signal >
'a signal
(** @deprecated Use {!on}. *)
val dismiss : ?eq:('a > 'a > bool) > 'b event > 'a > 'a signal >
'a signal
(** [dismiss c i s] is the signal [s] except changes when [c] occurs
are ignored. If [c] occurs initially [i] is used.
{ul
{ \[[dismiss c i s]\]{_t} [=] \[[s]\]{_t'}
where t' is the greatest t' <= t with \[[c]\]{_t'} [= None] and
\[[s]\]{_t'dt} [<>] \[[s]\]{_t'}}
{ \[[dismiss_ c i s]\]{_0} [=] [v] where [v = i] if
\[[c]\]{_0} [= Some _] and [v =] \[[s]\]{_0} otherwise.}} *)
(** {1:acc Accumulating} *)
val accum : ?eq:('a > 'a > bool) > ('a > 'a) event > 'a > 'a signal
(** [accum e i] is [S.hold i (]{!E.accum}[ e i)]. *)
val fold : ?eq:('a > 'a > bool) > ('a > 'b > 'a) > 'a > 'b event >
'a signal
(** [fold f i e] is [S.hold i (]{!E.fold}[ f i e)]. *)
(** {1:combine Combining} *)
val merge : ?eq:('a > 'a > bool) > ('a > 'b > 'a) > 'a >
'b signal list > 'a signal
(** [merge f a sl] merges the value of every signal in [sl]
using [f] and the accumulator [a].
\[[merge f a sl]\]{_ t}
[= List.fold_left f a (List.map] \[\]{_t}[ sl)]. *)
val switch : ?eq:('a > 'a > bool) > 'a signal signal > 'a signal
(** [switch ss] is the inner signal of [ss].
{ul
{ \[[switch ss]\]{_ t} [=] \[\[[ss]\]{_t}\]{_t}.}} *)
val bind : ?eq:('b > 'b > bool) > 'a signal > ('a > 'b signal) >
'b signal
(** [bind s sf] is [switch (map ~eq:( == ) sf s)]. *)
val fix : ?eq:('a > 'a > bool) > 'a > ('a signal > 'a signal * 'b) > 'b
(** [fix i sf] allow to refer to the value a signal had an
infinitesimal amount of time before.
In [fix sf], [sf] is called with a signal [s] that represents
the signal returned by [sf] delayed by an infinitesimal amount
time. If [s', r = sf s] then [r] is returned by [fix] and [s]
is such that :
{ul
{ \[[s]\]{_ t} [=] [i] for t = 0. }
{ \[[s]\]{_ t} [=] \[[s']\]{_tdt} otherwise.}}
[eq] is the equality used by [s].
{b Raises.} [Invalid_argument] if [s'] is directly a delayed signal (i.e.
a signal given to a fixing function).
{b Note.} Regarding values depending on the result [r] of
[s', r = sf s] the following two cases need to be distinguished :
{ul
{ After [sf s] is applied, [s'] does not depend on
a value that is in a step and [s] has no dependents in a step (e.g
in the simple case where [fix] is applied outside a step).
In that case if the initial value of [s'] differs from [i],
[s] and its dependents need to be updated and a special
update step will be triggered for this. Values
depending on the result [r] will be created only after this
special update step has finished (e.g. they won't see
the [i] of [s] if [r = s]).}
{ Otherwise, values depending on [r] will be created in the same
step as [s] and [s'] (e.g. they will see the [i] of [s] if [r = s]).}}
*)
(** {1:lifting Lifting}
Lifting combinators. For a given [n] the semantics is :
\[[ln f a1] ... [an]\]{_t} = f \[[a1]\]{_t} ... \[[an]\]{_t} *)
val l1 : ?eq:('b > 'b > bool) > ('a > 'b) > ('a signal > 'b signal)
val l2 : ?eq:('c > 'c > bool) >
('a > 'b > 'c) > ('a signal > 'b signal > 'c signal)
val l3 : ?eq:('d > 'd > bool) >
('a > 'b > 'c > 'd) > ('a signal > 'b signal > 'c signal > 'd signal)
val l4 : ?eq:('e > 'e > bool) >
('a > 'b > 'c > 'd > 'e) >
('a signal > 'b signal > 'c signal > 'd signal > 'e signal)
val l5 : ?eq:('f > 'f > bool) >
('a > 'b > 'c > 'd > 'e > 'f) >
('a signal > 'b signal > 'c signal > 'd signal > 'e signal >
'f signal)
val l6 : ?eq:('g > 'g > bool) >
('a > 'b > 'c > 'd > 'e > 'f > 'g) >
('a signal > 'b signal > 'c signal > 'd signal > 'e signal >
'f signal > 'g signal)
(** The following modules lift some of [Pervasives] functions and
operators. *)
module Bool : sig
val zero : bool signal
val one : bool signal
val not : bool signal > bool signal
val ( && ) : bool signal > bool signal > bool signal
val (  ) : bool signal > bool signal > bool signal
val edge : bool signal > bool event
(** [edge s] is [changes s]. *)
val rise : bool signal > unit event
(** [rise s] is [E.fmap (fun b > if b then Some () else None) (edge s)].*)
val fall : bool signal > unit event
(** [fall s] is [E.fmap (fun b > if b then None else Some ()) (edge s)].*)
val flip : bool > 'a event > bool signal
(** [flip b e] is a signal whose boolean value flips each time
[e] occurs. [b] is the initial signal value.
{ul
{ \[[flip b e]\]{_0} [= not b] if \[[e]\]{_0} [= Some _]}
{ \[[flip b e]\]{_t} [= b] if \[[e]\]{_<=t} [= None]}
{ \[[flip b e]\]{_t} [=] [not] \[[flip b e]\]{_tdt}
if \[[e]\]{_t} [= Some _]}}
*)
end
module Int : sig
val zero : int signal
val one : int signal
val minus_one : int signal
val ( ~ ) : int signal > int signal
val succ : int signal > int signal
val pred : int signal > int signal
val ( + ) : int signal > int signal > int signal
val (  ) : int signal > int signal > int signal
val ( * ) : int signal > int signal > int signal
val ( mod ) : int signal > int signal > int signal
val abs : int signal > int signal
val max_int : int signal
val min_int : int signal
val ( land ) : int signal > int signal > int signal
val ( lor ) : int signal > int signal > int signal
val ( lxor ) : int signal > int signal > int signal
val lnot : int signal > int signal
val ( lsl ) : int signal > int signal > int signal
val ( lsr ) : int signal > int signal > int signal
val ( asr ) : int signal > int signal > int signal
end
module Float : sig
val zero : float signal
val one : float signal
val minus_one : float signal
val ( ~. ) : float signal > float signal
val ( +. ) : float signal > float signal > float signal
val ( . ) : float signal > float signal > float signal
val ( *. ) : float signal > float signal > float signal
val ( /. ) : float signal > float signal > float signal
val ( ** ) : float signal > float signal > float signal
val sqrt : float signal > float signal
val exp : float signal > float signal
val log : float signal > float signal
val log10 : float signal > float signal
val cos : float signal > float signal
val sin : float signal > float signal
val tan : float signal > float signal
val acos : float signal > float signal
val asin : float signal > float signal
val atan : float signal > float signal
val atan2 : float signal > float signal > float signal
val cosh : float signal > float signal
val sinh : float signal > float signal
val tanh : float signal > float signal
val ceil : float signal > float signal
val floor : float signal > float signal
val abs_float : float signal > float signal
val mod_float : float signal > float signal > float signal
val frexp : float signal > (float * int) signal
val ldexp : float signal > int signal > float signal
val modf : float signal > (float * float) signal
val float : int signal > float signal
val float_of_int : int signal > float signal
val truncate : float signal > int signal
val int_of_float : float signal > int signal
val infinity : float signal
val neg_infinity : float signal
val nan : float signal
val max_float : float signal
val min_float : float signal
val epsilon_float : float signal
val classify_float : float signal > fpclass signal
end
module Pair : sig
val pair : ?eq:(('a * 'b) > ('a * 'b) > bool)>
'a signal > 'b signal > ('a * 'b) signal
val fst : ?eq:('a > 'a > bool) > ('a * 'b) signal > 'a signal
val snd : ?eq:('a > 'a > bool) > ('b * 'a) signal > 'a signal
end
module Option : sig
val none : 'a option signal
(** [none] is [S.const None]. *)
val some : 'a signal > 'a option signal
(** [some s] is [S.map ~eq (fun v > Some v) None], where [eq] uses
[s]'s equality function to test the [Some v]'s equalities. *)
val value : ?eq:('a > 'a > bool) >
default:[`Init of 'a signal  `Always of 'a signal ] >
'a option signal > 'a signal
(** [value default s] is [s] with only its [Some v] values.
Whenever [s] is [None], if [default] is [`Always dv] then
the current value of [dv] is used instead. If [default]
is [`Init dv] the current value of [dv] is only used
if there's no value at creation time, otherwise the last
[Some v] value of [s] is used.
{ul
{ \[[value ~default s]\]{_t} [= v] if \[[s]\]{_t} [= Some v]}
{ \[[value ~default:(`Always d) s]\]{_t} [=] \[[d]\]{_t}
if \[[s]\]{_t} [= None]}
{ \[[value ~default:(`Init d) s]\]{_0} [=] \[[d]\]{_0}
if \[[s]\]{_0} [= None]}
{ \[[value ~default:(`Init d) s]\]{_t} [=]
\[[value ~default:(`Init d) s]\]{_t'}
if \[[s]\]{_t} [= None] and t' is the greatest t' < t
with \[[s]\]{_t'} [<> None] or 0 if there is no such [t'].}} *)
end
module Compare : sig
val ( = ) : 'a signal > 'a signal > bool signal
val ( <> ) : 'a signal > 'a signal > bool signal
val ( < ) : 'a signal > 'a signal > bool signal
val ( > ) : 'a signal > 'a signal > bool signal
val ( <= ) : 'a signal > 'a signal > bool signal
val ( >= ) : 'a signal > 'a signal > bool signal
val compare : 'a signal > 'a signal > int signal
val ( == ) : 'a signal > 'a signal > bool signal
val ( != ) : 'a signal > 'a signal > bool signal
end
(** {1:special Combinator specialization}
Given an equality function [equal] and a type [t], the functor
{!Make} automatically applies the [eq] parameter of the combinators.
The outcome is combinators whose {e results} are signals with
values in [t].
Basic types are already specialized in the module {!Special}, open
this module to use them. *)
(** Input signature of {!S.Make} *)
module type EqType = sig
type 'a t
val equal : 'a t > 'a t > bool
end
(** Output signature of {!S.Make} *)
module type S = sig
type 'a v
val create : 'a v > 'a v signal * (?step:step > 'a v > unit)
val equal : 'a v signal > 'a v signal > bool
val hold : 'a v > 'a v event > 'a v signal
val app : ('a > 'b v) signal > 'a signal > 'b v signal
val map : ('a > 'b v) > 'a signal > 'b v signal
val filter : ('a v > bool) > 'a v > 'a v signal > 'a v signal
val fmap : ('a > 'b v option) > 'b v > 'a signal > 'b v signal
val when_ : bool signal > 'a v > 'a v signal > 'a v signal
val dismiss : 'b event > 'a v > 'a v signal > 'a v signal
val accum : ('a v > 'a v) event > 'a v > 'a v signal
val fold : ('a v > 'b > 'a v) > 'a v > 'b event > 'a v signal
val merge : ('a v > 'b > 'a v) > 'a v > 'b signal list > 'a v signal
val switch : 'a v signal signal > 'a v signal
val bind : 'b signal > ('b > 'a v signal) > 'a v signal
val fix : 'a v > ('a v signal > 'a v signal * 'b) > 'b
val l1 : ('a > 'b v) > ('a signal > 'b v signal)
val l2 : ('a > 'b > 'c v) > ('a signal > 'b signal > 'c v signal)
val l3 : ('a > 'b > 'c > 'd v) > ('a signal > 'b signal >
'c signal > 'd v signal)
val l4 : ('a > 'b > 'c > 'd > 'e v) >
('a signal > 'b signal > 'c signal > 'd signal > 'e v signal)
val l5 : ('a > 'b > 'c > 'd > 'e > 'f v) >
('a signal > 'b signal > 'c signal > 'd signal > 'e signal >
'f v signal)
val l6 : ('a > 'b > 'c > 'd > 'e > 'f > 'g v) >
('a signal > 'b signal > 'c signal > 'd signal > 'e signal >
'f signal > 'g v signal)
end
(** Functor specializing the combinators for the given signal value type *)
module Make (Eq : EqType) : S with type 'a v = 'a Eq.t
(** Specialization for booleans, integers and floats.
Open this module to use it. *)
module Special : sig
(** Specialization for booleans. *)
module Sb : S with type 'a v = bool
(** Specialization for integers. *)
module Si : S with type 'a v = int
(** Specialization for floats. *)
module Sf : S with type 'a v = float
end
end
(** Update steps.
Update functions returned by {!S.create} and {!E.create}
implicitely create and execute update steps when used without
specifying their [step] argument.
Using explicit {!step} values with these functions gives more control on
the time when the update step is perfomed and allows to perform
simultaneous {{!primitives}primitive} signal updates and event
occurences. See also the documentation about {{!steps}update steps} and
{{!simultaneity}simultaneous events}. *)
module Step : sig
(** {1 Steps} *)
type t = step
(** The type for update steps. *)
val create : unit > step
(** [create ()] is a new update step. *)
val execute : step > unit
(** [execute step] executes the update step.
@raise Invalid_argument if [step] was already executed. *)
end
(** {1:sem Semantics}
The following notations are used to give precise meaning to the
combinators. It is important to note that in these semantic
descriptions the origin of time t = 0 is {e always} fixed at
the time at which the combinator creates the event or the signal and
the semantics of the dependents is evaluated relative to this timeline.
We use dt to denote an infinitesimal amount of time.
{2:evsem Events}
An event is a value with discrete occurrences over time.
The semantic function \[\] [: 'a event > time > 'a option] gives
meaning to an event [e] by mapping it to a function of time
\[[e]\] returning [Some v] whenever the event occurs with value
[v] and [None] otherwise. We write \[[e]\]{_t} the evaluation of
this {e semantic} function at time t.
As a shortcut notation we also define []{_<t} [: 'a event > 'a option]
(resp. \[\]{_<=t}) to denote the last occurrence, if any, of an
event before (resp. before or at) [t]. More precisely :
{ul
{ \[[e]\]{_<t} [=] \[[e]\]{_t'} with t' the greatest t' < t
(resp. [<=]) such that
\[[e]\]{_t'} [<> None].}
{ \[[e]\]{_<t} [= None] if there is no such t'.}}
{2:sigsem Signals}
A signal is a value that varies continuously over time. In
contrast to {{!evsem}events} which occur at specific point
in time, a signal has a value at every point in time.
The semantic function \[\] [: 'a signal > time > 'a] gives
meaning to a signal [s] by mapping it to a function of time
\[[s]\] that returns its value at a given time. We write \[[s]\]{_t}
the evaluation of this {e semantic} function at time t.
{3:sigeq Equality}
Most signal combinators have an optional [eq] parameter that
defaults to structural equality. [eq] specifies the equality
function used to detect changes in the value of the resulting
signal. This function is needed for the efficient update of
signals and to deal correctly with signals that perform
{{!sideeffects}side effects}.
Given an equality function on a type the combinators can be automatically
{{!S.special}specialized} via a functor.
{3:sigcont Continuity}
Ultimately signal updates depend on
{{!primitives}primitives} updates. Thus a signal can
only approximate a real continuous signal. The accuracy of the
approximation depends on the variation rate of the real signal and
the primitive's update frequency.
{1:basics Basics}
{2:primitives Primitive events and signals}
React doesn't define primitive events and signals, they must be
created and updated by the client.
Primitive events are created with {!E.create}. This function
returns a new event and an update function that generates an
occurrence for the event at the time it is called. The following
code creates a primitive integer event [x] and generates three
occurrences with value [1], [2], [3]. Those occurrences are printed
on stdout by the effectful event [pr_x]. {[open React;;
let x, send_x = E.create ()
let pr_x = E.map print_int x
let () = List.iter send_x [1; 2; 3]]}
Primitive signals are created with {!S.create}. This function
returns a new signal and an update function that sets the signal's value
at the time it is called. The following code creates an
integer signal [x] initially set to [1] and updates it three time with
values [2], [2], [3]. The signal's values are printed on stdout by the
effectful signal [pr_x]. Note that only updates that change
the signal's value are printed, hence the program prints [123], not [1223].
See the discussion on
{{!sideeffects}side effects} for more details.
{[open React;;
let x, set_x = S.create 1
let pr_x = S.map print_int x
let () = List.iter set_x [2; 2; 3]]}
The {{!clock}clock} example shows how a realtime time
flow can be defined.
{2:steps Update steps}
The {!E.create} and {!S.create} functions return update functions
used to generate primitive event occurences and set the value of
primitive signals. Upon invocation as in the preceding section
these functions immediatly create and invoke an update step.
The {e update step} automatically updates events and signals that
transitively depend on the updated primitive. The dependents of a
signal are updated iff the signal's value changed according to its
{{!sigeq}equality function}.
The update functions have an optional [step] argument. If they are
given a concrete [step] value created with {!Step.create}, then it
updates the event or signal but doesn't update its dependencies. It
will only do so whenever [step] is executed with
{!Step.execute}. This allows to make primitive event occurences and
signal changes simultaneous. See next section for an example.
{2:simultaneity Simultaneous events}
{{!steps}Update steps} are made under a
{{:http://dx.doi.org/10.1016/01676423(92)90005V}synchrony hypothesis} :
the update step takes no time, it is instantenous. Two event occurrences
are {e simultaneous} if they occur in the same update step.
In the code below [w], [x] and [y] will always have simultaneous
occurrences. They {e may} have simulatenous occurences with [z]
if [send_w] and [send_z] are used with the same update step.
{[let w, send_w = E.create ()
let x = E.map succ w
let y = E.map succ x
let z, send_z = E.create ()
let () =
let () = send_w 3 (* w x y occur simultaneously, z doesn't occur *) in
let step = Step.create () in
send_w ~step 3;
send_z ~step 4;
Step.execute step (* w x z y occur simultaneously *)
]}
{2:update The update step and thread safety}
{{!primitives}Primitives} are the only mean to drive the reactive
system and they are entirely under the control of the client. When
the client invokes a primitive's update function without the
[step] argument or when it invokes {!Step.execute} on a [step]
value, React performs an update step.
To ensure correctness in the presence of threads, update steps
must be executed in a critical section. Let uset([p]) be the set
of events and signals that need to be updated whenever the
primitive [p] is updated. Updating two primitives [p] and [p']
concurrently is only allowed if uset([p]) and uset([p']) are
disjoint. Otherwise the updates must be properly serialized.
Below, concurrent, updates to [x] and [y] must be serialized (or
performed on the same step if it makes sense semantically), but z
can be updated concurently to both [x] and [y].
{[open React;;
let x, set_x = S.create 0
let y, send_y = E.create ()
let z, set_z = S.create 0
let max_xy = S.l2 (fun x y > if x > y then x else y) x (S.hold 0 y)
let succ_z = S.map succ z]}
{2:sideeffects Side effects}
Effectful events and signals perform their side effect
exactly {e once} in each {{!steps}update step} in which there
is an update of at least one of the event or signal it depends on.
Remember that a signal updates in a step iff its
{{!sigeq}equality function} determined that the signal
value changed. Signal initialization is unconditionally considered as
an update.
It is important to keep references on effectful events and
signals. Otherwise they may be reclaimed by the garbage collector.
The following program prints only a [1].
{[let x, set_x = S.create 1
let () = ignore (S.map print_int x)
let () = Gc.full_major (); List.iter set_x [2; 2; 3]]}
{2:lifting Lifting}
Lifting transforms a regular function to make it act on signals.
The combinators
{!S.const} and {!S.app} allow to lift functions of arbitrary arity n,
but this involves the inefficient creation of n1 intermediary
closure signals. The fixed arity {{!S.lifting}lifting
functions} are more efficient. For example :
{[let f x y = x mod y
let fl x y = S.app (S.app ~eq:(==) (S.const f) x) y (* inefficient *)
let fl' x y = S.l2 f x y (* efficient *)
]}
Besides, some of [Pervasives]'s functions and operators are
already lifted and availables in submodules of {!S}. They can be
be opened in specific scopes. For example if you are dealing with
float signals you can open {!S.Float}.
{[open React
open React.S.Float
let f t = sqrt t *. sin t (* f is defined on float signals *)
...
open Pervasives (* back to pervasives floats *)
]}
If you are using OCaml 3.12 or later you can also use the [let open]
construct
{[let open React.S.Float in
let f t = sqrt t *. sin t in (* f is defined on float signals *)
...
]}
{2:recursion Mutual and self reference}
Mutual and self reference among time varying values occurs naturally
in programs. However a mutually recursive definition of two signals
in which both need the value of the other at time t to define
their value at time t has no least fixed point. To break this
tight loop one signal must depend on the value the other had at time
tdt where dt is an infinitesimal delay.
The fixed point combinators {!E.fix} and {!S.fix} allow to refer to
the value an event or signal had an infinitesimal amount of time
before. These fixed point combinators act on a function [f] that takes
as argument the infinitesimally delayed event or signal that [f]
itself returns.
In the example below [history s] returns a signal whose value
is the history of [s] as a list.
{[let history ?(eq = ( = )) s =
let push v = function
 [] > [ v ]
 v' :: _ as l when eq v v' > l
 l > v :: l
in
let define h =
let h' = S.l2 push s h in
h', h'
in
S.fix [] define]}
When a program has infinitesimally delayed values a
{{!primitives}primitive} may trigger more than one update
step. For example if a signal [s] is infinitesimally delayed, then
its update in a step [c] will trigger a new step [c'] at the end
of the step in which the delayed signal of [s] will have the value
[s] had in [c]. This means that the recursion occuring between a
signal (or event) and its infinitesimally delayed counterpart must
be wellfounded otherwise this may trigger an infinite number
of update steps, like in the following examples.
{[let start, send_start = E.create ()
let diverge =
let define e =
let e' = E.select [e; start] in
e', e'
in
E.fix define
let () = send_start () (* diverges *)
let diverge = (* diverges *)
let define s =
let s' = S.Int.succ s in
s', s'
in
S.fix 0 define]}
For technical reasons, delayed events and signals (those given to
fixing functions) are not allowed to directly depend on each
other. Fixed point combinators will raise [Invalid_argument] if
such dependencies are created. This limitation can be
circumvented by mapping these values with the identity.
{2:strongstop Strong stops}
Strong stops should only be used on platforms where weak arrays have
a strong semantics (i.e. JavaScript). You can safely ignore that
section and the [strong] argument of {!E.stop} and {!S.stop}
if that's not the case.
Whenever {!E.stop} and {!S.stop} is called with [~strong:true] on a
reactive value [v], it is first stopped and then it walks over the
list [prods] of events and signals that it depends on and
unregisters itself from these ones as a dependent (something that is
normally automatically done when [v] is garbage collected since
dependents are stored in a weak array). Then for each element of
[prod] that has no dependents anymore and is not a primitive it
stops them aswell and recursively.
A stop call with [~strong:true] is more involved. But it allows to
prevent memory leaks when used judiciously on the leaves of the
reactive system that are no longer used.
{b Warning.} It should be noted that if direct references are kept
on an intermediate event or signal of the reactive system it may
suddenly stop updating if all its dependents were strongly stopped. In
the example below, [e1] will {e never} occur:
{[let e, e_send = E.create ()
let e1 = E.map (fun x > x + 1) e (* never occurs *)
let () =
let e2 = E.map (fun x > x + 1) e1 in
E.stop ~strong:true e2
]}
This can be side stepped by making an artificial dependency to keep
the reference:
{[let e, e_send = E.create ()
let e1 = E.map (fun x > x + 1) e (* may still occur *)
let e1_ref = E.map (fun x > x) e1
let () =
let e2 = E.map (fun x > x + 1) e1 in
E.stop ~strong:true e2
]}
{1:ex Examples}
{2:clock Clock}
The following program defines a primitive event [seconds] holding
the UNIX time and occuring on every second. An effectful event
converts these occurences to local time and prints them on stdout
along with an
{{:http://www.ecmainternational.org/publications/standards/Ecma048.htm}ANSI
escape sequence} to control the cursor position.
{[let pr_time t =
let tm = Unix.localtime t in
Printf.printf "\x1B[8D%02d:%02d:%02d%!"
tm.Unix.tm_hour tm.Unix.tm_min tm.Unix.tm_sec
open React;;
let seconds, run =
let e, send = E.create () in
let run () =
while true do send (Unix.gettimeofday ()); Unix.sleep 1 done
in
e, run
let printer = E.map pr_time seconds
let () = run ()]}
*)
(*
Copyright (c) 2009 Daniel C. Bünzli
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the
distribution.
3. Neither the name of Daniel C. Bünzli nor the names of
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*)
