-
Notifications
You must be signed in to change notification settings - Fork 61
/
guide.html
1593 lines (1588 loc) · 78.2 KB
/
guide.html
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
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<!--[if IE]><meta http-equiv="X-UA-Compatible" content="IE=edge"><![endif]-->
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="generator" content="Asciidoctor 1.5.2">
<meta name="author" content="Christopher Alfeld, Sam Baskinger">
<title>Predicate Guide</title>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400">
<style>
/* Asciidoctor default stylesheet | MIT License | http://asciidoctor.org */
/* Remove the comments around the @import statement below when using this as a custom stylesheet */
/*@import "https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400";*/
article,aside,details,figcaption,figure,footer,header,hgroup,main,nav,section,summary{display:block}
audio,canvas,video{display:inline-block}
audio:not([controls]){display:none;height:0}
[hidden],template{display:none}
script{display:none!important}
html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%}
body{margin:0}
a{background:transparent}
a:focus{outline:thin dotted}
a:active,a:hover{outline:0}
h1{font-size:2em;margin:.67em 0}
abbr[title]{border-bottom:1px dotted}
b,strong{font-weight:bold}
dfn{font-style:italic}
hr{-moz-box-sizing:content-box;box-sizing:content-box;height:0}
mark{background:#ff0;color:#000}
code,kbd,pre,samp{font-family:monospace;font-size:1em}
pre{white-space:pre-wrap}
q{quotes:"\201C" "\201D" "\2018" "\2019"}
small{font-size:80%}
sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}
sup{top:-.5em}
sub{bottom:-.25em}
img{border:0}
svg:not(:root){overflow:hidden}
figure{margin:0}
fieldset{border:1px solid silver;margin:0 2px;padding:.35em .625em .75em}
legend{border:0;padding:0}
button,input,select,textarea{font-family:inherit;font-size:100%;margin:0}
button,input{line-height:normal}
button,select{text-transform:none}
button,html input[type="button"],input[type="reset"],input[type="submit"]{-webkit-appearance:button;cursor:pointer}
button[disabled],html input[disabled]{cursor:default}
input[type="checkbox"],input[type="radio"]{box-sizing:border-box;padding:0}
input[type="search"]{-webkit-appearance:textfield;-moz-box-sizing:content-box;-webkit-box-sizing:content-box;box-sizing:content-box}
input[type="search"]::-webkit-search-cancel-button,input[type="search"]::-webkit-search-decoration{-webkit-appearance:none}
button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}
textarea{overflow:auto;vertical-align:top}
table{border-collapse:collapse;border-spacing:0}
*,*:before,*:after{-moz-box-sizing:border-box;-webkit-box-sizing:border-box;box-sizing:border-box}
html,body{font-size:100%}
body{background:#fff;color:rgba(0,0,0,.8);padding:0;margin:0;font-family:"Noto Serif","DejaVu Serif",serif;font-weight:400;font-style:normal;line-height:1;position:relative;cursor:auto}
a:hover{cursor:pointer}
img,object,embed{max-width:100%;height:auto}
object,embed{height:100%}
img{-ms-interpolation-mode:bicubic}
#map_canvas img,#map_canvas embed,#map_canvas object,.map_canvas img,.map_canvas embed,.map_canvas object{max-width:none!important}
.left{float:left!important}
.right{float:right!important}
.text-left{text-align:left!important}
.text-right{text-align:right!important}
.text-center{text-align:center!important}
.text-justify{text-align:justify!important}
.hide{display:none}
.antialiased,body{-webkit-font-smoothing:antialiased}
img{display:inline-block;vertical-align:middle}
textarea{height:auto;min-height:50px}
select{width:100%}
p.lead,.paragraph.lead>p,#preamble>.sectionbody>.paragraph:first-of-type p{font-size:1.21875em;line-height:1.6}
.subheader,.admonitionblock td.content>.title,.audioblock>.title,.exampleblock>.title,.imageblock>.title,.listingblock>.title,.literalblock>.title,.stemblock>.title,.openblock>.title,.paragraph>.title,.quoteblock>.title,table.tableblock>.title,.verseblock>.title,.videoblock>.title,.dlist>.title,.olist>.title,.ulist>.title,.qlist>.title,.hdlist>.title{line-height:1.45;color:#7a2518;font-weight:400;margin-top:0;margin-bottom:.25em}
div,dl,dt,dd,ul,ol,li,h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6,pre,form,p,blockquote,th,td{margin:0;padding:0;direction:ltr}
a{color:#2156a5;text-decoration:underline;line-height:inherit}
a:hover,a:focus{color:#1d4b8f}
a img{border:none}
p{font-family:inherit;font-weight:400;font-size:1em;line-height:1.6;margin-bottom:1.25em;text-rendering:optimizeLegibility}
p aside{font-size:.875em;line-height:1.35;font-style:italic}
h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{font-family:"Open Sans","DejaVu Sans",sans-serif;font-weight:300;font-style:normal;color:#ba3925;text-rendering:optimizeLegibility;margin-top:1em;margin-bottom:.5em;line-height:1.0125em}
h1 small,h2 small,h3 small,#toctitle small,.sidebarblock>.content>.title small,h4 small,h5 small,h6 small{font-size:60%;color:#e99b8f;line-height:0}
h1{font-size:2.125em}
h2{font-size:1.6875em}
h3,#toctitle,.sidebarblock>.content>.title{font-size:1.375em}
h4,h5{font-size:1.125em}
h6{font-size:1em}
hr{border:solid #ddddd8;border-width:1px 0 0;clear:both;margin:1.25em 0 1.1875em;height:0}
em,i{font-style:italic;line-height:inherit}
strong,b{font-weight:bold;line-height:inherit}
small{font-size:60%;line-height:inherit}
code{font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;font-weight:400;color:rgba(0,0,0,.9)}
ul,ol,dl{font-size:1em;line-height:1.6;margin-bottom:1.25em;list-style-position:outside;font-family:inherit}
ul,ol,ul.no-bullet,ol.no-bullet{margin-left:1.5em}
ul li ul,ul li ol{margin-left:1.25em;margin-bottom:0;font-size:1em}
ul.square li ul,ul.circle li ul,ul.disc li ul{list-style:inherit}
ul.square{list-style-type:square}
ul.circle{list-style-type:circle}
ul.disc{list-style-type:disc}
ul.no-bullet{list-style:none}
ol li ul,ol li ol{margin-left:1.25em;margin-bottom:0}
dl dt{margin-bottom:.3125em;font-weight:bold}
dl dd{margin-bottom:1.25em}
abbr,acronym{text-transform:uppercase;font-size:90%;color:rgba(0,0,0,.8);border-bottom:1px dotted #ddd;cursor:help}
abbr{text-transform:none}
blockquote{margin:0 0 1.25em;padding:.5625em 1.25em 0 1.1875em;border-left:1px solid #ddd}
blockquote cite{display:block;font-size:.9375em;color:rgba(0,0,0,.6)}
blockquote cite:before{content:"\2014 \0020"}
blockquote cite a,blockquote cite a:visited{color:rgba(0,0,0,.6)}
blockquote,blockquote p{line-height:1.6;color:rgba(0,0,0,.85)}
@media only screen and (min-width:768px){h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{line-height:1.2}
h1{font-size:2.75em}
h2{font-size:2.3125em}
h3,#toctitle,.sidebarblock>.content>.title{font-size:1.6875em}
h4{font-size:1.4375em}}table{background:#fff;margin-bottom:1.25em;border:solid 1px #dedede}
table thead,table tfoot{background:#f7f8f7;font-weight:bold}
table thead tr th,table thead tr td,table tfoot tr th,table tfoot tr td{padding:.5em .625em .625em;font-size:inherit;color:rgba(0,0,0,.8);text-align:left}
table tr th,table tr td{padding:.5625em .625em;font-size:inherit;color:rgba(0,0,0,.8)}
table tr.even,table tr.alt,table tr:nth-of-type(even){background:#f8f8f7}
table thead tr th,table tfoot tr th,table tbody tr td,table tr td,table tfoot tr td{display:table-cell;line-height:1.6}
h1,h2,h3,#toctitle,.sidebarblock>.content>.title,h4,h5,h6{line-height:1.2;word-spacing:-.05em}
h1 strong,h2 strong,h3 strong,#toctitle strong,.sidebarblock>.content>.title strong,h4 strong,h5 strong,h6 strong{font-weight:400}
.clearfix:before,.clearfix:after,.float-group:before,.float-group:after{content:" ";display:table}
.clearfix:after,.float-group:after{clear:both}
*:not(pre)>code{font-size:.9375em;font-style:normal!important;letter-spacing:0;padding:.1em .5ex;word-spacing:-.15em;background-color:#f7f7f8;-webkit-border-radius:4px;border-radius:4px;line-height:1.45;text-rendering:optimizeSpeed}
pre,pre>code{line-height:1.45;color:rgba(0,0,0,.9);font-family:"Droid Sans Mono","DejaVu Sans Mono",monospace;font-weight:400;text-rendering:optimizeSpeed}
.keyseq{color:rgba(51,51,51,.8)}
kbd{display:inline-block;color:rgba(0,0,0,.8);font-size:.75em;line-height:1.4;background-color:#f7f7f7;border:1px solid #ccc;-webkit-border-radius:3px;border-radius:3px;-webkit-box-shadow:0 1px 0 rgba(0,0,0,.2),0 0 0 .1em white inset;box-shadow:0 1px 0 rgba(0,0,0,.2),0 0 0 .1em #fff inset;margin:-.15em .15em 0 .15em;padding:.2em .6em .2em .5em;vertical-align:middle;white-space:nowrap}
.keyseq kbd:first-child{margin-left:0}
.keyseq kbd:last-child{margin-right:0}
.menuseq,.menu{color:rgba(0,0,0,.8)}
b.button:before,b.button:after{position:relative;top:-1px;font-weight:400}
b.button:before{content:"[";padding:0 3px 0 2px}
b.button:after{content:"]";padding:0 2px 0 3px}
p a>code:hover{color:rgba(0,0,0,.9)}
#header,#content,#footnotes,#footer{width:100%;margin-left:auto;margin-right:auto;margin-top:0;margin-bottom:0;max-width:62.5em;*zoom:1;position:relative;padding-left:.9375em;padding-right:.9375em}
#header:before,#header:after,#content:before,#content:after,#footnotes:before,#footnotes:after,#footer:before,#footer:after{content:" ";display:table}
#header:after,#content:after,#footnotes:after,#footer:after{clear:both}
#content{margin-top:1.25em}
#content:before{content:none}
#header>h1:first-child{color:rgba(0,0,0,.85);margin-top:2.25rem;margin-bottom:0}
#header>h1:first-child+#toc{margin-top:8px;border-top:1px solid #ddddd8}
#header>h1:only-child,body.toc2 #header>h1:nth-last-child(2){border-bottom:1px solid #ddddd8;padding-bottom:8px}
#header .details{border-bottom:1px solid #ddddd8;line-height:1.45;padding-top:.25em;padding-bottom:.25em;padding-left:.25em;color:rgba(0,0,0,.6);display:-ms-flexbox;display:-webkit-flex;display:flex;-ms-flex-flow:row wrap;-webkit-flex-flow:row wrap;flex-flow:row wrap}
#header .details span:first-child{margin-left:-.125em}
#header .details span.email a{color:rgba(0,0,0,.85)}
#header .details br{display:none}
#header .details br+span:before{content:"\00a0\2013\00a0"}
#header .details br+span.author:before{content:"\00a0\22c5\00a0";color:rgba(0,0,0,.85)}
#header .details br+span#revremark:before{content:"\00a0|\00a0"}
#header #revnumber{text-transform:capitalize}
#header #revnumber:after{content:"\00a0"}
#content>h1:first-child:not([class]){color:rgba(0,0,0,.85);border-bottom:1px solid #ddddd8;padding-bottom:8px;margin-top:0;padding-top:1rem;margin-bottom:1.25rem}
#toc{border-bottom:1px solid #efefed;padding-bottom:.5em}
#toc>ul{margin-left:.125em}
#toc ul.sectlevel0>li>a{font-style:italic}
#toc ul.sectlevel0 ul.sectlevel1{margin:.5em 0}
#toc ul{font-family:"Open Sans","DejaVu Sans",sans-serif;list-style-type:none}
#toc a{text-decoration:none}
#toc a:active{text-decoration:underline}
#toctitle{color:#7a2518;font-size:1.2em}
@media only screen and (min-width:768px){#toctitle{font-size:1.375em}
body.toc2{padding-left:15em;padding-right:0}
#toc.toc2{margin-top:0!important;background-color:#f8f8f7;position:fixed;width:15em;left:0;top:0;border-right:1px solid #efefed;border-top-width:0!important;border-bottom-width:0!important;z-index:1000;padding:1.25em 1em;height:100%;overflow:auto}
#toc.toc2 #toctitle{margin-top:0;font-size:1.2em}
#toc.toc2>ul{font-size:.9em;margin-bottom:0}
#toc.toc2 ul ul{margin-left:0;padding-left:1em}
#toc.toc2 ul.sectlevel0 ul.sectlevel1{padding-left:0;margin-top:.5em;margin-bottom:.5em}
body.toc2.toc-right{padding-left:0;padding-right:15em}
body.toc2.toc-right #toc.toc2{border-right-width:0;border-left:1px solid #efefed;left:auto;right:0}}@media only screen and (min-width:1280px){body.toc2{padding-left:20em;padding-right:0}
#toc.toc2{width:20em}
#toc.toc2 #toctitle{font-size:1.375em}
#toc.toc2>ul{font-size:.95em}
#toc.toc2 ul ul{padding-left:1.25em}
body.toc2.toc-right{padding-left:0;padding-right:20em}}#content #toc{border-style:solid;border-width:1px;border-color:#e0e0dc;margin-bottom:1.25em;padding:1.25em;background:#f8f8f7;-webkit-border-radius:4px;border-radius:4px}
#content #toc>:first-child{margin-top:0}
#content #toc>:last-child{margin-bottom:0}
#footer{max-width:100%;background-color:rgba(0,0,0,.8);padding:1.25em}
#footer-text{color:rgba(255,255,255,.8);line-height:1.44}
.sect1{padding-bottom:.625em}
@media only screen and (min-width:768px){.sect1{padding-bottom:1.25em}}.sect1+.sect1{border-top:1px solid #efefed}
#content h1>a.anchor,h2>a.anchor,h3>a.anchor,#toctitle>a.anchor,.sidebarblock>.content>.title>a.anchor,h4>a.anchor,h5>a.anchor,h6>a.anchor{position:absolute;z-index:1001;width:1.5ex;margin-left:-1.5ex;display:block;text-decoration:none!important;visibility:hidden;text-align:center;font-weight:400}
#content h1>a.anchor:before,h2>a.anchor:before,h3>a.anchor:before,#toctitle>a.anchor:before,.sidebarblock>.content>.title>a.anchor:before,h4>a.anchor:before,h5>a.anchor:before,h6>a.anchor:before{content:"\00A7";font-size:.85em;display:block;padding-top:.1em}
#content h1:hover>a.anchor,#content h1>a.anchor:hover,h2:hover>a.anchor,h2>a.anchor:hover,h3:hover>a.anchor,#toctitle:hover>a.anchor,.sidebarblock>.content>.title:hover>a.anchor,h3>a.anchor:hover,#toctitle>a.anchor:hover,.sidebarblock>.content>.title>a.anchor:hover,h4:hover>a.anchor,h4>a.anchor:hover,h5:hover>a.anchor,h5>a.anchor:hover,h6:hover>a.anchor,h6>a.anchor:hover{visibility:visible}
#content h1>a.link,h2>a.link,h3>a.link,#toctitle>a.link,.sidebarblock>.content>.title>a.link,h4>a.link,h5>a.link,h6>a.link{color:#ba3925;text-decoration:none}
#content h1>a.link:hover,h2>a.link:hover,h3>a.link:hover,#toctitle>a.link:hover,.sidebarblock>.content>.title>a.link:hover,h4>a.link:hover,h5>a.link:hover,h6>a.link:hover{color:#a53221}
.audioblock,.imageblock,.literalblock,.listingblock,.stemblock,.videoblock{margin-bottom:1.25em}
.admonitionblock td.content>.title,.audioblock>.title,.exampleblock>.title,.imageblock>.title,.listingblock>.title,.literalblock>.title,.stemblock>.title,.openblock>.title,.paragraph>.title,.quoteblock>.title,table.tableblock>.title,.verseblock>.title,.videoblock>.title,.dlist>.title,.olist>.title,.ulist>.title,.qlist>.title,.hdlist>.title{text-rendering:optimizeLegibility;text-align:left;font-family:"Noto Serif","DejaVu Serif",serif;font-size:1rem;font-style:italic}
table.tableblock>caption.title{white-space:nowrap;overflow:visible;max-width:0}
.paragraph.lead>p,#preamble>.sectionbody>.paragraph:first-of-type p{color:rgba(0,0,0,.85)}
table.tableblock #preamble>.sectionbody>.paragraph:first-of-type p{font-size:inherit}
.admonitionblock>table{border-collapse:separate;border:0;background:none;width:100%}
.admonitionblock>table td.icon{text-align:center;width:80px}
.admonitionblock>table td.icon img{max-width:none}
.admonitionblock>table td.icon .title{font-weight:bold;font-family:"Open Sans","DejaVu Sans",sans-serif;text-transform:uppercase}
.admonitionblock>table td.content{padding-left:1.125em;padding-right:1.25em;border-left:1px solid #ddddd8;color:rgba(0,0,0,.6)}
.admonitionblock>table td.content>:last-child>:last-child{margin-bottom:0}
.exampleblock>.content{border-style:solid;border-width:1px;border-color:#e6e6e6;margin-bottom:1.25em;padding:1.25em;background:#fff;-webkit-border-radius:4px;border-radius:4px}
.exampleblock>.content>:first-child{margin-top:0}
.exampleblock>.content>:last-child{margin-bottom:0}
.sidebarblock{border-style:solid;border-width:1px;border-color:#e0e0dc;margin-bottom:1.25em;padding:1.25em;background:#f8f8f7;-webkit-border-radius:4px;border-radius:4px}
.sidebarblock>:first-child{margin-top:0}
.sidebarblock>:last-child{margin-bottom:0}
.sidebarblock>.content>.title{color:#7a2518;margin-top:0;text-align:center}
.exampleblock>.content>:last-child>:last-child,.exampleblock>.content .olist>ol>li:last-child>:last-child,.exampleblock>.content .ulist>ul>li:last-child>:last-child,.exampleblock>.content .qlist>ol>li:last-child>:last-child,.sidebarblock>.content>:last-child>:last-child,.sidebarblock>.content .olist>ol>li:last-child>:last-child,.sidebarblock>.content .ulist>ul>li:last-child>:last-child,.sidebarblock>.content .qlist>ol>li:last-child>:last-child{margin-bottom:0}
.literalblock pre,.listingblock pre:not(.highlight),.listingblock pre[class="highlight"],.listingblock pre[class^="highlight "],.listingblock pre.CodeRay,.listingblock pre.prettyprint{background:#f7f7f8}
.sidebarblock .literalblock pre,.sidebarblock .listingblock pre:not(.highlight),.sidebarblock .listingblock pre[class="highlight"],.sidebarblock .listingblock pre[class^="highlight "],.sidebarblock .listingblock pre.CodeRay,.sidebarblock .listingblock pre.prettyprint{background:#f2f1f1}
.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{-webkit-border-radius:4px;border-radius:4px;word-wrap:break-word;padding:1em;font-size:.8125em}
.literalblock pre.nowrap,.literalblock pre[class].nowrap,.listingblock pre.nowrap,.listingblock pre[class].nowrap{overflow-x:auto;white-space:pre;word-wrap:normal}
@media only screen and (min-width:768px){.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{font-size:.90625em}}@media only screen and (min-width:1280px){.literalblock pre,.literalblock pre[class],.listingblock pre,.listingblock pre[class]{font-size:1em}}.literalblock.output pre{color:#f7f7f8;background-color:rgba(0,0,0,.9)}
.listingblock pre.highlightjs{padding:0}
.listingblock pre.highlightjs>code{padding:1em;-webkit-border-radius:4px;border-radius:4px}
.listingblock pre.prettyprint{border-width:0}
.listingblock>.content{position:relative}
.listingblock code[data-lang]:before{display:none;content:attr(data-lang);position:absolute;font-size:.75em;top:.425rem;right:.5rem;line-height:1;text-transform:uppercase;color:#999}
.listingblock:hover code[data-lang]:before{display:block}
.listingblock.terminal pre .command:before{content:attr(data-prompt);padding-right:.5em;color:#999}
.listingblock.terminal pre .command:not([data-prompt]):before{content:"$"}
table.pyhltable{border-collapse:separate;border:0;margin-bottom:0;background:none}
table.pyhltable td{vertical-align:top;padding-top:0;padding-bottom:0}
table.pyhltable td.code{padding-left:.75em;padding-right:0}
pre.pygments .lineno,table.pyhltable td:not(.code){color:#999;padding-left:0;padding-right:.5em;border-right:1px solid #ddddd8}
pre.pygments .lineno{display:inline-block;margin-right:.25em}
table.pyhltable .linenodiv{background:none!important;padding-right:0!important}
.quoteblock{margin:0 1em 1.25em 1.5em;display:table}
.quoteblock>.title{margin-left:-1.5em;margin-bottom:.75em}
.quoteblock blockquote,.quoteblock blockquote p{color:rgba(0,0,0,.85);font-size:1.15rem;line-height:1.75;word-spacing:.1em;letter-spacing:0;font-style:italic;text-align:justify}
.quoteblock blockquote{margin:0;padding:0;border:0}
.quoteblock blockquote:before{content:"\201c";float:left;font-size:2.75em;font-weight:bold;line-height:.6em;margin-left:-.6em;color:#7a2518;text-shadow:0 1px 2px rgba(0,0,0,.1)}
.quoteblock blockquote>.paragraph:last-child p{margin-bottom:0}
.quoteblock .attribution{margin-top:.5em;margin-right:.5ex;text-align:right}
.quoteblock .quoteblock{margin-left:0;margin-right:0;padding:.5em 0;border-left:3px solid rgba(0,0,0,.6)}
.quoteblock .quoteblock blockquote{padding:0 0 0 .75em}
.quoteblock .quoteblock blockquote:before{display:none}
.verseblock{margin:0 1em 1.25em 1em}
.verseblock pre{font-family:"Open Sans","DejaVu Sans",sans;font-size:1.15rem;color:rgba(0,0,0,.85);font-weight:300;text-rendering:optimizeLegibility}
.verseblock pre strong{font-weight:400}
.verseblock .attribution{margin-top:1.25rem;margin-left:.5ex}
.quoteblock .attribution,.verseblock .attribution{font-size:.9375em;line-height:1.45;font-style:italic}
.quoteblock .attribution br,.verseblock .attribution br{display:none}
.quoteblock .attribution cite,.verseblock .attribution cite{display:block;letter-spacing:-.05em;color:rgba(0,0,0,.6)}
.quoteblock.abstract{margin:0 0 1.25em 0;display:block}
.quoteblock.abstract blockquote,.quoteblock.abstract blockquote p{text-align:left;word-spacing:0}
.quoteblock.abstract blockquote:before,.quoteblock.abstract blockquote p:first-of-type:before{display:none}
table.tableblock{max-width:100%;border-collapse:separate}
table.tableblock td>.paragraph:last-child p>p:last-child,table.tableblock th>p:last-child,table.tableblock td>p:last-child{margin-bottom:0}
table.spread{width:100%}
table.tableblock,th.tableblock,td.tableblock{border:0 solid #dedede}
table.grid-all th.tableblock,table.grid-all td.tableblock{border-width:0 1px 1px 0}
table.grid-all tfoot>tr>th.tableblock,table.grid-all tfoot>tr>td.tableblock{border-width:1px 1px 0 0}
table.grid-cols th.tableblock,table.grid-cols td.tableblock{border-width:0 1px 0 0}
table.grid-all *>tr>.tableblock:last-child,table.grid-cols *>tr>.tableblock:last-child{border-right-width:0}
table.grid-rows th.tableblock,table.grid-rows td.tableblock{border-width:0 0 1px 0}
table.grid-all tbody>tr:last-child>th.tableblock,table.grid-all tbody>tr:last-child>td.tableblock,table.grid-all thead:last-child>tr>th.tableblock,table.grid-rows tbody>tr:last-child>th.tableblock,table.grid-rows tbody>tr:last-child>td.tableblock,table.grid-rows thead:last-child>tr>th.tableblock{border-bottom-width:0}
table.grid-rows tfoot>tr>th.tableblock,table.grid-rows tfoot>tr>td.tableblock{border-width:1px 0 0 0}
table.frame-all{border-width:1px}
table.frame-sides{border-width:0 1px}
table.frame-topbot{border-width:1px 0}
th.halign-left,td.halign-left{text-align:left}
th.halign-right,td.halign-right{text-align:right}
th.halign-center,td.halign-center{text-align:center}
th.valign-top,td.valign-top{vertical-align:top}
th.valign-bottom,td.valign-bottom{vertical-align:bottom}
th.valign-middle,td.valign-middle{vertical-align:middle}
table thead th,table tfoot th{font-weight:bold}
tbody tr th{display:table-cell;line-height:1.6;background:#f7f8f7}
tbody tr th,tbody tr th p,tfoot tr th,tfoot tr th p{color:rgba(0,0,0,.8);font-weight:bold}
p.tableblock>code:only-child{background:none;padding:0}
p.tableblock{font-size:1em}
td>div.verse{white-space:pre}
ol{margin-left:1.75em}
ul li ol{margin-left:1.5em}
dl dd{margin-left:1.125em}
dl dd:last-child,dl dd:last-child>:last-child{margin-bottom:0}
ol>li p,ul>li p,ul dd,ol dd,.olist .olist,.ulist .ulist,.ulist .olist,.olist .ulist{margin-bottom:.625em}
ul.unstyled,ol.unnumbered,ul.checklist,ul.none{list-style-type:none}
ul.unstyled,ol.unnumbered,ul.checklist{margin-left:.625em}
ul.checklist li>p:first-child>.fa-square-o:first-child,ul.checklist li>p:first-child>.fa-check-square-o:first-child{width:1em;font-size:.85em}
ul.checklist li>p:first-child>input[type="checkbox"]:first-child{width:1em;position:relative;top:1px}
ul.inline{margin:0 auto .625em auto;margin-left:-1.375em;margin-right:0;padding:0;list-style:none;overflow:hidden}
ul.inline>li{list-style:none;float:left;margin-left:1.375em;display:block}
ul.inline>li>*{display:block}
.unstyled dl dt{font-weight:400;font-style:normal}
ol.arabic{list-style-type:decimal}
ol.decimal{list-style-type:decimal-leading-zero}
ol.loweralpha{list-style-type:lower-alpha}
ol.upperalpha{list-style-type:upper-alpha}
ol.lowerroman{list-style-type:lower-roman}
ol.upperroman{list-style-type:upper-roman}
ol.lowergreek{list-style-type:lower-greek}
.hdlist>table,.colist>table{border:0;background:none}
.hdlist>table>tbody>tr,.colist>table>tbody>tr{background:none}
td.hdlist1{padding-right:.75em;font-weight:bold}
td.hdlist1,td.hdlist2{vertical-align:top}
.literalblock+.colist,.listingblock+.colist{margin-top:-.5em}
.colist>table tr>td:first-of-type{padding:0 .75em;line-height:1}
.colist>table tr>td:last-of-type{padding:.25em 0}
.thumb,.th{line-height:0;display:inline-block;border:solid 4px #fff;-webkit-box-shadow:0 0 0 1px #ddd;box-shadow:0 0 0 1px #ddd}
.imageblock.left,.imageblock[style*="float: left"]{margin:.25em .625em 1.25em 0}
.imageblock.right,.imageblock[style*="float: right"]{margin:.25em 0 1.25em .625em}
.imageblock>.title{margin-bottom:0}
.imageblock.thumb,.imageblock.th{border-width:6px}
.imageblock.thumb>.title,.imageblock.th>.title{padding:0 .125em}
.image.left,.image.right{margin-top:.25em;margin-bottom:.25em;display:inline-block;line-height:0}
.image.left{margin-right:.625em}
.image.right{margin-left:.625em}
a.image{text-decoration:none}
span.footnote,span.footnoteref{vertical-align:super;font-size:.875em}
span.footnote a,span.footnoteref a{text-decoration:none}
span.footnote a:active,span.footnoteref a:active{text-decoration:underline}
#footnotes{padding-top:.75em;padding-bottom:.75em;margin-bottom:.625em}
#footnotes hr{width:20%;min-width:6.25em;margin:-.25em 0 .75em 0;border-width:1px 0 0 0}
#footnotes .footnote{padding:0 .375em;line-height:1.3;font-size:.875em;margin-left:1.2em;text-indent:-1.2em;margin-bottom:.2em}
#footnotes .footnote a:first-of-type{font-weight:bold;text-decoration:none}
#footnotes .footnote:last-of-type{margin-bottom:0}
#content #footnotes{margin-top:-.625em;margin-bottom:0;padding:.75em 0}
.gist .file-data>table{border:0;background:#fff;width:100%;margin-bottom:0}
.gist .file-data>table td.line-data{width:99%}
div.unbreakable{page-break-inside:avoid}
.big{font-size:larger}
.small{font-size:smaller}
.underline{text-decoration:underline}
.overline{text-decoration:overline}
.line-through{text-decoration:line-through}
.aqua{color:#00bfbf}
.aqua-background{background-color:#00fafa}
.black{color:#000}
.black-background{background-color:#000}
.blue{color:#0000bf}
.blue-background{background-color:#0000fa}
.fuchsia{color:#bf00bf}
.fuchsia-background{background-color:#fa00fa}
.gray{color:#606060}
.gray-background{background-color:#7d7d7d}
.green{color:#006000}
.green-background{background-color:#007d00}
.lime{color:#00bf00}
.lime-background{background-color:#00fa00}
.maroon{color:#600000}
.maroon-background{background-color:#7d0000}
.navy{color:#000060}
.navy-background{background-color:#00007d}
.olive{color:#606000}
.olive-background{background-color:#7d7d00}
.purple{color:#600060}
.purple-background{background-color:#7d007d}
.red{color:#bf0000}
.red-background{background-color:#fa0000}
.silver{color:#909090}
.silver-background{background-color:#bcbcbc}
.teal{color:#006060}
.teal-background{background-color:#007d7d}
.white{color:#bfbfbf}
.white-background{background-color:#fafafa}
.yellow{color:#bfbf00}
.yellow-background{background-color:#fafa00}
span.icon>.fa{cursor:default}
.admonitionblock td.icon [class^="fa icon-"]{font-size:2.5em;text-shadow:1px 1px 2px rgba(0,0,0,.5);cursor:default}
.admonitionblock td.icon .icon-note:before{content:"\f05a";color:#19407c}
.admonitionblock td.icon .icon-tip:before{content:"\f0eb";text-shadow:1px 1px 2px rgba(155,155,0,.8);color:#111}
.admonitionblock td.icon .icon-warning:before{content:"\f071";color:#bf6900}
.admonitionblock td.icon .icon-caution:before{content:"\f06d";color:#bf3400}
.admonitionblock td.icon .icon-important:before{content:"\f06a";color:#bf0000}
.conum[data-value]{display:inline-block;color:#fff!important;background-color:rgba(0,0,0,.8);-webkit-border-radius:100px;border-radius:100px;text-align:center;font-size:.75em;width:1.67em;height:1.67em;line-height:1.67em;font-family:"Open Sans","DejaVu Sans",sans-serif;font-style:normal;font-weight:bold}
.conum[data-value] *{color:#fff!important}
.conum[data-value]+b{display:none}
.conum[data-value]:after{content:attr(data-value)}
pre .conum[data-value]{position:relative;top:-.125em}
b.conum *{color:inherit!important}
.conum:not([data-value]):empty{display:none}
h1,h2{letter-spacing:-.01em}
dt,th.tableblock,td.content{text-rendering:optimizeLegibility}
p,td.content{letter-spacing:-.01em}
p strong,td.content strong{letter-spacing:-.005em}
p,blockquote,dt,td.content{font-size:1.0625rem}
p{margin-bottom:1.25rem}
.sidebarblock p,.sidebarblock dt,.sidebarblock td.content,p.tableblock{font-size:1em}
.exampleblock>.content{background-color:#fffef7;border-color:#e0e0dc;-webkit-box-shadow:0 1px 4px #e0e0dc;box-shadow:0 1px 4px #e0e0dc}
.print-only{display:none!important}
@media print{@page{margin:1.25cm .75cm}
*{-webkit-box-shadow:none!important;box-shadow:none!important;text-shadow:none!important}
a{color:inherit!important;text-decoration:underline!important}
a.bare,a[href^="#"],a[href^="mailto:"]{text-decoration:none!important}
a[href^="http:"]:not(.bare):after,a[href^="https:"]:not(.bare):after{content:"(" attr(href) ")";display:inline-block;font-size:.875em;padding-left:.25em}
abbr[title]:after{content:" (" attr(title) ")"}
pre,blockquote,tr,img{page-break-inside:avoid}
thead{display:table-header-group}
img{max-width:100%!important}
p,blockquote,dt,td.content{font-size:1em;orphans:3;widows:3}
h2,h3,#toctitle,.sidebarblock>.content>.title{page-break-after:avoid}
#toc,.sidebarblock,.exampleblock>.content{background:none!important}
#toc{border-bottom:1px solid #ddddd8!important;padding-bottom:0!important}
.sect1{padding-bottom:0!important}
.sect1+.sect1{border:0!important}
#header>h1:first-child{margin-top:1.25rem}
body.book #header{text-align:center}
body.book #header>h1:first-child{border:0!important;margin:2.5em 0 1em 0}
body.book #header .details{border:0!important;display:block;padding:0!important}
body.book #header .details span:first-child{margin-left:0!important}
body.book #header .details br{display:block}
body.book #header .details br+span:before{content:none!important}
body.book #toc{border:0!important;text-align:left!important;padding:0!important;margin:0!important}
body.book #toc,body.book #preamble,body.book h1.sect0,body.book .sect1>h2{page-break-before:always}
.listingblock code[data-lang]:before{display:block}
#footer{background:none!important;padding:0 .9375em}
#footer-text{color:rgba(0,0,0,.6)!important;font-size:.9em}
.hide-on-print{display:none!important}
.print-only{display:block!important}
.hide-for-print{display:none!important}
.show-for-print{display:inherit!important}}
</style>
</head>
<body class="article toc2 toc-left">
<div id="header">
<h1>Predicate Guide</h1>
<div class="details">
<span id="author" class="author">Christopher Alfeld</span><br>
<span id="email" class="email"><a href="mailto:calfeld@qualys.com">calfeld@qualys.com</a></span><br>
<span id="author2" class="author">Sam Baskinger</span><br>
<span id="email2" class="email"><a href="mailto:sbaskinger@qualys.com">sbaskinger@qualys.com</a></span><br>
</div>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_introduction">Introduction</a></li>
<li><a href="#_orientation">Orientation</a>
<ul class="sectlevel2">
<li><a href="#_terminology">Terminology</a></li>
<li><a href="#_first_steps">First Steps</a></li>
<li><a href="#_second_steps">Second Steps</a></li>
<li><a href="#s.composition">Composition</a></li>
<li><a href="#_configuration_time">Configuration Time</a></li>
<li><a href="#_expressions_and_the_dag">Expressions and the DAG</a></li>
<li><a href="#_values">Values</a></li>
</ul>
</li>
<li><a href="#s.templates">Templates</a></li>
<li><a href="#s.functions">Functions</a>
<ul class="sectlevel2">
<li><a href="#_boolean">Boolean</a></li>
<li><a href="#_list">List</a></li>
<li><a href="#_string">String</a></li>
<li><a href="#_filters">Filters</a></li>
<li><a href="#_predicates">Predicates</a></li>
<li><a href="#_math">Math</a></li>
<li><a href="#_phase">Phase</a></li>
<li><a href="#_ironbee">IronBee</a></li>
<li><a href="#_development">Development</a></li>
<li><a href="#_templates">Templates</a></li>
</ul>
</li>
<li><a href="#_specific_advice">Specific Advice</a>
<ul class="sectlevel2">
<li><a href="#_phaseless_rules">Phaseless Rules</a></li>
<li><a href="#s.operator_and_foperator">Operator and FOperator</a></li>
<li><a href="#_short_circuited_boolean_functions">Short-Circuited Boolean Functions</a></li>
<li><a href="#_the_pushname_flatten_idiom">The PushName-Flatten Idiom</a></li>
<li><a href="#_interaction_with_actions_and_code_set_predicate_vars_code">Interaction with actions and <code>set_predicate_vars</code></a></li>
</ul>
</li>
<li><a href="#_tools">Tools</a>
<ul class="sectlevel2">
<li><a href="#_predicatetrace">PredicateTrace</a></li>
<li><a href="#_pp">PP</a></li>
<li><a href="#s.pp_dot">PP Dot</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph">
<p>For an overview and discussion of the system, see <a href="introduction.html">introduction</a>. For a comprehensive reference to the language, see <a href="reference.html">reference</a>. For details on the modules, see <a href="modules.html">modules</a>.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_introduction">Introduction</h2>
<div class="sectionbody">
<div class="paragraph">
<p>This document is intended as a tutorial and initial reference to orient rule writers to using Predicate. Predicate is an alternative rule system for the IronBee web application firewall. It is assumed that you are familiar with IronBee and web application firewalls.</p>
</div>
<div class="paragraph">
<p>Predicate associates a predicate 'expression' with a rule and fires the rule if and only if the predicate expression evaluates to true. In comparison to the default rule system, Predicate has superior support for composition and configuration time optimization; on the downside, it does not support rule ordering and can be unintuitive.</p>
</div>
<div class="paragraph">
<p>SExpressions (sexprs) are the underlying language of Predicate. It is not expected that you, a rule writer, will write SExpressions directly. However, you will see them in error messages and tools and is worthwhile to be familiar with them. As such, for most Lua code in this document, I have added Lua comments containing the equivalent SExpression, e.g.,</p>
</div>
<div class="listingblock">
<div class="title">Example: Equivalent SExpression</div>
<div class="content">
<pre>P.Gt(1000, P.Length(P.Var('REQUEST_URI')))
-- (gt 1000 (length (var 'REQUEST_URI')))</pre>
</div>
</div>
<div class="paragraph">
<p>The second line is the S-Expression corresponding to the first line, prefixed with the Lua comment designator, <code>--</code>.</p>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_orientation">Orientation</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_terminology">Terminology</h3>
<div class="dlist">
<dl>
<dt class="hdlist1">Top-Level Expression</dt>
<dd>
<p>An expression associated with a rule. The rule will fire if and when the expression becomes truthy.</p>
</dd>
<dt class="hdlist1">Truthy</dt>
<dd>
<p>An expression or value that is interpreted as true.</p>
</dd>
<dt class="hdlist1">Falsy</dt>
<dd>
<p>An expression or value that is interpreted as false.</p>
</dd>
<dt class="hdlist1">Waggle</dt>
<dd>
<p>A Lua interface to writing IronBee rules.</p>
</dd>
<dt class="hdlist1">Frontend</dt>
<dd>
<p>A Lua interface to writing Predicate expressions.</p>
</dd>
<dt class="hdlist1">SExpr</dt>
<dd>
<p>The low level representation of Predicate expressions.</p>
</dd>
</dl>
</div>
</div>
<div class="sect2">
<h3 id="_first_steps">First Steps</h3>
<div class="paragraph">
<p>Let’s begin with a series of basic examples. Consider the following logic:</p>
</div>
<div class="quoteblock">
<blockquote>
If the URI of the request is really long, then …​
</blockquote>
</div>
<div class="paragraph">
<p>Interpreting, <code>is really long'' to mean </code>has a length greater than 1000'', we can write this in the frontend as:</p>
</div>
<div class="listingblock">
<div class="title">Example: First Steps 1</div>
<div class="content">
<pre>P.Gt(1000, P.Length(P.Var('REQUEST_URI')))
-- (gt 1000 (length (var 'REQUEST_URI')))</pre>
</div>
</div>
<div class="paragraph">
<p>This is Lua code. <code>P.Gt()</code> is a Lua function that produces a 'predicate object' from its arguments, which are in turn predicate objects (or Lua literals). The Waggle <code>predicate()</code> directive understands predicate objects and turns them into sexprs to pass on to Predicate, e.g.,</p>
</div>
<div class="listingblock">
<div class="title">Example: Waggle Rule</div>
<div class="content">
<pre>Action("predicate_example", "1"):
phase([[REQUEST_HEADER]]):
action([[clipp_announce:predicate_example]]):
predicate(P.Gt(1000, P.Length(P.Var('REQUEST_URI'))))</pre>
</div>
</div>
<div class="admonitionblock note">
<table>
<tr>
<td class="icon">
<div class="title">Note</div>
</td>
<td class="content">
Predicate is usually used with <code>Action</code> rather than <code>Rule</code> in waggle. Using <code>Action</code> ensures that whether to fire the rule is entirely up to Predicate.
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>Predicate expressions are built up by composing 'predicate functions' along with literals.</p>
</div>
<div class="paragraph">
<p>Let’s extend our logic to:</p>
</div>
<div class="quoteblock">
<blockquote>
If the URI of the request is really long and the request is a GET request, then …​
</blockquote>
</div>
<div class="listingblock">
<div class="title">Example: First Steps 2</div>
<div class="content">
<pre>P.And(
P.Gt(1000, P.Length(P.Var('REQUEST_URI'))),
P.Eq('GET', P.Var('REQUEST_METHOD'))
)
-- (and
-- (gt 1000 (length (var 'REQUEST_URI')))
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>The frontend provides some additional interfaces to more easily express certain patterns. In particular, it allows using the <code>+</code> operator for logical AND. This changes our expression to:</p>
</div>
<div class="listingblock">
<div class="title">Example: First Steps 3</div>
<div class="content">
<pre> P.Gt(1000, P.Length(P.Var('REQUEST_URI')))
+ P.Eq('GET', P.Var('REQUEST_METHOD'))
-- (and
-- (gt 1000 (length (var 'REQUEST_URI')))
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>The frontend also allows us to use object method syntax, where the object is passed in to the function as the last argument:</p>
</div>
<div class="listingblock">
<div class="title">Example: First Steps 4</div>
<div class="content">
<pre> P.Var('REQUEST_URI'):length():gt(1000)
+ P.Var('REQUEST_METHOD'):eq('GET')
-- (and
-- (gt 1000 (length (var 'REQUEST_URI')))
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>When and whether to use such shortcuts is a matter of style. Use them if you believe they make the logic clearer.</p>
</div>
</div>
<div class="sect2">
<h3 id="_second_steps">Second Steps</h3>
<div class="paragraph">
<p>Let’s look for a suspicious filename in every parameter:</p>
</div>
<div class="listingblock">
<div class="title">Example: Second Steps 1</div>
<div class="content">
<pre>P.FOperator('rx', '/etc/(?:passwd|shadow)', P.Var('ARGS'))
-- (foperator 'rx' '/etc/(?:passwd|shadow)' (var 'ARGS'))</pre>
</div>
</div>
<div class="paragraph">
<p><code>P.FOperator()</code> is an example of using an IronBee operator. IronBee operators are functions provided by modules that can be used by any rule system, not just Predicate.</p>
</div>
<div class="admonitionblock note">
<table>
<tr>
<td class="icon">
<div class="title">Note</div>
</td>
<td class="content">
See <a href="#s.operator_and_foperator">Operator and FOperator</a> for discussion on why <code>P.FOperator()</code> is used here.
</td>
</tr>
</table>
</div>
<div class="paragraph">
<p>Now let’s limit to only GET and POST requests:</p>
</div>
<div class="listingblock">
<div class="title">Example: Second Steps 2</div>
<div class="content">
<pre>P.And(
P.FOperator('rx', '/etc/(?:passwd|shadow)', P.Var('ARGS')),
P.Or(
P.Eq('GET', P.Var('REQUEST_METHOD')),
P.Eq('POST', P.Var('REQUEST_METHOD'))
)
)
-- (and
-- (foperator 'rx' '/etc/(?:passwd|shadow)' (var 'ARGS'))
-- (or
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- (eq 'POST' (var 'REQUEST_METHOD'))
-- )
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>There is a shortcut for logical OR, <code>/</code>. Using that and our other alternatives:</p>
</div>
<div class="listingblock">
<div class="title">Example: Second Steps 3</div>
<div class="content">
<pre> P.Var('ARGS'):foperator('rx', '/etc/(?:passwd|shadow)')
+ (
P.Var('REQUEST_METHOD'):eq('GET')
/ P.Var('REQUEST_METHOD'):eq('POST')
)
-- (and
-- (foperator 'rx' '/etc/(?:passwd|shadow)' (var 'ARGS'))
-- (or
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- (eq 'POST' (var 'REQUEST_METHOD'))
-- )
-- )</pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="s.composition">Composition</h3>
<div class="paragraph">
<p>A primary motivation for Predicate is to allow easy composition of rule logic. The previous examples have not directly taken advantage of that. Since we are writing our Predicate expressions in Lua when can make use of Lua features such as variables and functions to compose logic.</p>
</div>
<div class="paragraph">
<p>Let’s factor out some common pieces of logic, such as ``is a GET request'':</p>
</div>
<div class="listingblock">
<div class="title">Example: <code>IsGet</code></div>
<div class="content">
<pre>local IsGet = P.Var('REQUEST_METHOD'):eq('GET')
-- (eq 'GET' (var 'REQUEST_METHOD))</pre>
</div>
</div>
<div class="paragraph">
<p>And ``is a POST request'':</p>
</div>
<div class="listingblock">
<div class="title">Example: <code>IsPost</code></div>
<div class="content">
<pre>local IsPost = P.Var('REQUEST_METHOD'):eq('POST')
-- (eq 'POST' (var 'REQUEST_METHOD))</pre>
</div>
</div>
<div class="paragraph">
<p>The example from the previous section then becomes:</p>
</div>
<div class="listingblock">
<div class="title">Example: Composition</div>
<div class="content">
<pre> P.Var('ARGS'):foperator('rx', '/etc/(?:passwd|shadow)')
+ (IsGet / IsPost)
-- (and
-- (foperator 'rx' '/etc/(?:passwd|shadow)' (var 'ARGS'))
-- (or
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- (eq 'POST' (var 'REQUEST_METHOD'))
-- )
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>Note how the use of intermediate Lua variables to hold pieces of expressions does not affect the resulting sexpr. I.e., this sort of composition is at the Lua level and happens before conversion to an sexpr. For a way to do composition post-sexpr, see <a href="#s.templates">Templates</a>.</p>
</div>
<div class="paragraph">
<p>We are not limited to variables. Consider:</p>
</div>
<div class="quoteblock">
<blockquote>
Header X is longer than 1000 bytes.
</blockquote>
</div>
<div class="paragraph">
<p>First, let’s define a function to find the value of the ``Header X'':</p>
</div>
<div class="listingblock">
<div class="title">Example: <code>RequestHeader</code></div>
<div class="content">
<pre>local function RequestHeader(which)
return P.Sub(which, P.Var('REQUEST_HEADERS'))
end</pre>
</div>
</div>
<div class="paragraph">
<p>This function takes the name of a header and provides a predicate object representing the value of that header. It uses a new function, <code>P.Sub()</code>, which is used to select a specific member from a collection.</p>
</div>
<div class="paragraph">
<p>We can now use <code>RequestHeader()</code> to define a notion of a long header:</p>
</div>
<div class="listingblock">
<div class="title">Example: <code>LongHeader</code></div>
<div class="content">
<pre>local function LongHeader(which)
return RequestHeader(which):length():gt(1000)
end</pre>
</div>
</div>
<div class="paragraph">
<p>We can now use <code>LongHeader()</code> to express:</p>
</div>
<div class="quoteblock">
<blockquote>
The Host header is longer than 1000 bytes.
</blockquote>
</div>
<div class="listingblock">
<div class="title">Example: <code>LongHeader</code> usage</div>
<div class="content">
<pre>LongHeader('HOST')
-- (gt 1000 (length (sub 'Host' (var 'REQUEST_HEADERS))))</pre>
</div>
</div>
<div class="paragraph">
<p>There is additional value to reusing pieces of logic. Predicate automatically detects any reused expressions across all Predicate expressions and only evaluates them once, reusing the result. This reuse can provide significant performance benefits.</p>
</div>
</div>
<div class="sect2">
<h3 id="_configuration_time">Configuration Time</h3>
<div class="paragraph">
<p>IronBee operates at two different times. At configuration time, it interprets its configuration and sets up any data structures it needs to evaluate traffic. At runtime (also called evaluation time), it interprets web traffic, determines which rules should be fired (involves evaluating predicate expressions), and fires those rules.</p>
</div>
<div class="paragraph">
<p>When using Predicate, there is a further distinction to be made at configuration time. There is computation that occurs in Lua and computation that occurs in Predicate. In Lua, the Lua code is executed to produce predicate objects which are turned into sexprs. Those sexprs are then passed to Predicate. Predicate merges all sexprs together and, once it has everything, performs validation and optimization passes.</p>
</div>
<div class="paragraph">
<p>This division has a number of implications. Two important ones are:</p>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p>Some warnings and errors occur at the close of a configuration context and are in terms of sexprs rather than Lua code. In most cases, the Lua file and line number are provided with the error message.</p>
</li>
<li>
<p>Since Lua based composition is performed in Lua, the resulting SExprs that are communicated to Predicate can become quite large.</p>
</li>
</ol>
</div>
<div class="paragraph">
<p>The use of <a href="#s.templates">Templates</a> can alleviate both of these problems.</p>
</div>
<div class="paragraph">
<p>Many Predicate functions support configuration time evaluation if all of their arguments are known at configuration time. For example, consider setting a policy variable in Lua:</p>
</div>
<div class="listingblock">
<div class="title">Example: Policy Variable</div>
<div class="content">
<pre>-- Change this to true to apply rule to Post requests.
local ApplyToPost = false</pre>
</div>
</div>
<div class="paragraph">
<p>And then using it in a predicate expression, where <code>something_complicated</code> is some complex logic:</p>
</div>
<div class="listingblock">
<div class="title">Example: Using a Policy Variable</div>
<div class="content">
<pre>(IsGet / (ApplyToPost + IsPost)) + something_complicated
-- (and
-- (or
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- (and (false) (eq 'POST' (var 'REQUEST_METHOD')))
-- )
-- something_complicated
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>Since <code>ApplyToPost</code> is false, this expressions will always be false, no matter what <code>something_complicated</code> turns out to be. Predicate understands this and transforms the entire expression to false at configuration time. These transformations allows for easy configuration or customization of rules while paying the performance cost only once, at configuration time.</p>
</div>
</div>
<div class="sect2">
<h3 id="_expressions_and_the_dag">Expressions and the DAG</h3>
<div class="paragraph">
<p>Any predicate expression can be represented as a tree. For example:</p>
</div>
<div class="listingblock">
<div class="title">Example: Expression 1</div>
<div class="content">
<pre> P.Var('ARGS'):foperator('rx', '/etc/(?:passwd|shadow)')
+ (IsGet / IsPost)
-- (and
-- (foperator 'rx' '/etc/(?:passwd|shadow)' (var 'ARGS'))
-- (or
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- (eq 'POST' (var 'REQUEST_METHOD'))
-- )
-- )</pre>
</div>
</div>
<div class="paragraph">
<p>Corresponds to:</p>
</div>
<div class="imageblock">
<div class="content">
<img src="guide_1.png" alt="Expression 1 as Tree">
</div>
<div class="title">Figure 1. Expression 1 as Tree</div>
</div>
<div class="paragraph">
<p>(All of the images in this section were generated via the <a href="#s.pp_dot"><code>pp_dot</code></a> tool.)</p>
</div>
<div class="paragraph">
<p>The DAG (directed acyclic graph) is the heart of Predicate. It is initially generated by taking the trees from the predicate expressions of every rule and merging common subtrees together.</p>
</div>
<div class="paragraph">
<p>For example, consider this expression/tree:</p>
</div>
<div class="listingblock">
<div class="title">Example: Expressions 2</div>
<div class="content">
<pre> P.Gt(1000, P.Length(P.Var('REQUEST_URI')))
+ (IsGet / IsPost)
-- (and
-- (gt 1000 (length (var 'REQUEST_URI')))
-- (or
-- (eq 'GET' (var 'REQUEST_METHOD'))
-- (eq 'POST' (var 'REQUEST_METHOD'))
-- )
-- )</pre>
</div>
</div>
<div class="imageblock">
<div class="content">
<img src="guide_2.png" alt="Expression 2 as Tree">
</div>
<div class="title">Figure 2. Expression 2 as Tree</div>
</div>
<div class="paragraph">
<p>We can add both of these expressions to the DAG, merging common subtrees, to end up with:</p>
</div>
<div class="imageblock">
<div class="content">
<img src="guide_3.png" alt="Expression 1 and 2 as DAG">
</div>
<div class="title">Figure 3. Expression 1 and 2 as DAG</div>
</div>
<div class="paragraph">
<p>Merging common subexpressions enables cross-expression optimization and result sharing.</p>
</div>
<div class="sect3">
<h4 id="_one_dag_per_context">One DAG per Context</h4>
<div class="paragraph">
<p>Every configuration context has its own DAG. Each context also inherits any rules and associated predicate expressions from its parent context. Having per-context DAGs allows for differing policy to simplify each DAG in different ways.</p>
</div>
</div>
<div class="sect3">
<h4 id="_dag_lifecycle">DAG Lifecycle</h4>
<div class="paragraph">
<p>A DAG goes through a sequence of changes once all expression trees are known.</p>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p>All expression trees are combined to create the initial DAG, merging any common subtrees.</p>
</li>
<li>
<p>A validation pass is performed, in which every node does a number of sanity checks.</p>
</li>
<li>
<p>A transformation pass is performed, in which every node is allowed to manipulate the DAG. For example, <code>(not (true))</code> will transform into a falsy value.</p>
</li>
<li>
<p>Repeat step 3 until the DAG doesn’t change, i.e., there is nothing more to transform.</p>
</li>
<li>
<p>A final validation pass is performed.</p>
</li>
</ol>
</div>
<div class="paragraph">
<p>After this process completes, the DAG is fixed. It will never again change in structure and can be used for evaluation.</p>
</div>
</div>
<div class="sect3">
<h4 id="_dag_evaluation">DAG Evaluation</h4>
<div class="paragraph">
<p>DAG Evaluation is the process by which the values of nodes in the DAG are determined. When a node associated with a rule becomes truthy, that rule is fired. A DAG is evaluated on a per-transaction basis.</p>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_values">Values</h3>
<div class="paragraph">
<p>We have made it this far without actually worrying about what the value returned by a function is. As an example of how values can be complex, consider the following expressions:</p>
</div>
<div class="listingblock">
<div class="title">Example: Expression</div>
<div class="content">
<pre>P.Var('ARGS'):sub('a'):length():gt(5)
-- (gt 5 (length (sub 'a' (var 'ARGS'))))</pre>
</div>
</div>
<div class="paragraph">
<p>And consider the expression in the context of the following request:</p>
</div>
<div class="listingblock">
<div class="title">Example: Request</div>
<div class="content">
<pre>GET /example?a=123&a=123456</pre>
</div>
</div>
<div class="paragraph">
<p>Here there are two parameters (members of <code>ARGS</code>) named <code>a</code>, one of which is longer than 5 bytes and one of which is not. How do we interpret the expression in this situation?</p>
</div>
<div class="paragraph">
<p>In a boolean sense, the expression is truthy and can accurately be interpreted as:</p>
</div>
<div class="quoteblock">
<blockquote>
Does any member of <code>ARGS</code> named <code>a</code> have length greater than 5.
</blockquote>
</div>
<div class="paragraph">