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
|
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
<html><head><title></title></head>
<body bgcolor="#ffffff" text="#000000">
<center>
<img src="../gf-logo.gif">
<h1>Grammatical Framework Tutorial</h1>
<p>
<b>3rd Edition, for GF version 2.2 or later</b>
<p>
<a href="http://www.cs.chalmers.se/~aarne">Aarne Ranta</a>
<p>
<tt>aarne@cs.chalmers.se</tt>
<p>
12 May 2005
</center>
<!-- NEW -->
<h2>GF = Grammatical Framework</h2>
The term GF is used for different things:
<ul>
<li> a <b>program</b> used for working with grammars
<li> a <b>programming language</b> in which grammars can be written
<li> a <b>theory</b> about grammars and languages
</ul>
<p>
This tutorial is primarily about the GF program and
the GF programming language.
It will guide you
<ul>
<li> to use the GF program
<li> to write GF grammars
<li> to write programs in which GF grammars are used as components
</ul>
<!-- NEW -->
<h3>Getting the GF program</h3>
The program is open-source free software, which you can download from the
GF Homepage:<br>
<a href="http://www.cs.chalmers.se/%7Eaarne/GF">
<tt>http://www.cs.chalmers.se/~aarne/GF</tt></a>
<p>
There you can download
<ul>
<li> ready-made binaries for Linux, Solaris, Macintosh, and Windows
<li> source code and documentation
<li> grammar libraries and examples
</ul>
If you want to compile GF from source, you need Haskell and Java
compilers. But normally you don't have to compile, and you definitely
don't need to know Haskell or Java to use GF.
<p>
To start the GF program, assuming you have installed it, just type
<pre>
gf
</pre>
in the shell. You will see GF's welcome message and the prompt <tt>></tt>.
<!-- NEW -->
<h2>My first grammar</h2>
Now you are ready to try out your first grammar.
We start with one that is not written in GF language, but
in the EBNF notation (Extended Backus Naur Form), which GF can also
understand. Type (or copy) the following lines in a file named
<tt>paleolithic.ebnf</tt>:
<pre>
S ::= NP VP ;
VP ::= V | TV NP | "is" A ;
NP ::= ("this" | "that" | "the" | "a") CN ;
CN ::= A CN ;
CN ::= "boy" | "louse" | "snake" | "worm" ;
A ::= "green" | "rotten" | "thick" | "warm" ;
V ::= "laughs" | "sleeps" | "swims" ;
TV ::= "eats" | "kills" | "washes" ;
</pre>
<!-- NEW -->
<h3>Importing grammars and parsing strings</h3>
The first GF command when using a grammar is to <b>import</b> it.
The command has a long name, <tt>import</tt>, and a short name, <tt>i</tt>.
<pre>
import paleolithic.gf
</pre>
The GF program now <b>compiles</b> your grammar into an internal
representation, and shows a new prompt when it is ready.
<p>
You can use GF for <b>parsing</b>:
<pre>
> parse "the boy eats a snake"
Mks_0 (Mks_6 Mks_9) (Mks_2 Mks_20 (Mks_7 Mks_11))
> parse "the snake eats a boy"
Mks_0 (Mks_6 Mks_11) (Mks_2 Mks_20 (Mks_7 Mks_9))
</pre>
The <tt>parse</tt> (= <tt>p</tt>) command takes a <b>string</b>
(in double quotes) and returns an <b>abstract syntax tree</b> - the thing
with <tt>Mks</tt>s and parentheses. We will see soon how to make sense
of the abstract syntax trees - now you should just notice that the tree
is different for the two strings.
<p>
Strings that return a tree when parsed do so in virtue of the grammar
you imported. Try parsing something else, and you fail
<pre>
> p "hello world"
No success in cf parsing
no tree found
</pre>
<!-- NEW -->
<h3>Generating trees and strings</h3>
You can also use GF for <b>linearizing</b>
(<tt>linearize = l</tt>). This is the inverse of
parsing, taking trees into strings:
<pre>
> linearize Mks_0 (Mks_6 Mks_11) (Mks_2 Mks_20 (Mks_7 Mks_9))
the snake eats a boy
</pre>
What is the use of this? Typically not that you type in a tree at
the GF prompt. The utility of linearization comes from the fact that
you can obtain a tree from somewhere else. One way to do so is
<b>random generation</b> (<tt>generate_random = gr</tt>):
<pre>
> generate_random
Mks_0 (Mks_4 Mks_11) (Mks_3 Mks_15)
</pre>
Now you can copy the tree and paste it to the <tt>linearize command</tt>.
Or, more efficiently, feed random generation into parsing by using
a <b>pipe</b>.
<pre>
> gr | l
this worm is warm
</pre>
<!-- NEW -->
<h3>Some random-generated sentences</h3>
Random generation can be quite amusing. So you may want to
generate ten strings with one and the same command:
<pre>
> gr -number=10 | l
this boy is green
a snake laughs
the rotten boy is thick
a boy washes this worm
a boy is warm
this green warm boy is rotten
the green thick green louse is rotten
that boy is green
this thick thick boy laughs
a boy is green
</pre>
<!-- NEW -->
<h3>Systematic generation</h3>
To generate <i>all</i> sentence that a grammar
can generate, use the command <tt>generate_trees = gt</tt>.
<pre>
> generate_trees | l
this louse laughs
this louse sleeps
this louse swims
this louse is green
this louse is rotten
...
a boy is rotten
a boy is thick
a boy is warm
</pre>
You get quite a few trees but not all of them: only up to a given
<b>depth</b> of trees. To see how you can get more, use the
<tt>help = h</tt> command,
<pre>
help gr
</pre>
<b>Quiz</b>. If the command <tt>gt</tt> generated all
trees in your grammar, it would never terminate. Why?
<!-- NEW -->
<h3>More on pipes; tracing</h3>
A pipe of GF commands can have any length, but the "output type"
(either string or tree) of one command must always match the "input type"
of the next command.
<p>
The intermediate results in a pipe can be observed by putting the
<b>tracing</b> flag <tt>-tr</tt> to each command whose output you
want to see:
<pre>
> gr -tr | l -tr | p
Mks_0 (Mks_7 Mks_10) (Mks_1 Mks_18)
a louse sleeps
Mks_0 (Mks_7 Mks_10) (Mks_1 Mks_18)
</pre>
This facility is good for test purposes: for instance, you
may want to see if a grammar is <b>ambiguous</b>, i.e.
contains strings that can be parsed in more than one way.
<!-- NEW -->
<h3>Writing and reading files</h3>
To save the outputs of GF commands into a file, you can
pipe it to the <tt>write_file = wf</tt> command,
<pre>
> gr -number=10 | l | write_file exx.tmp
</pre>
You can read the file back to GF with the
<tt>read_file = rf</tt> command,
<pre>
> read_file exx.tmp | l -tr | p -lines
</pre>
Notice the flag <tt>-lines</tt> given to the parsing
command. This flag tells GF to parse each line of
the file separately. Without the flag, the grammar could
not recognize the string in the file, because it is not
a sentence but a sequence of ten sentences.
<!-- NEW -->
<h3>Labelled context-free grammars</h3>
The syntax trees returned by GF's parser in the previous examples
are not so nice to look at. The identifiers of form <tt>Mks</tt>
are <b>labels</b> of the EBNF rules. To see which label corresponds to
which rule, you can use the <tt>print_grammar = pg</tt> command
with the <tt>printer</tt> flag set to <tt>cf</tt> (which means context-free):
<pre>
> print_grammar -printer=cf
Mks_10. CN ::= "louse" ;
Mks_11. CN ::= "snake" ;
Mks_12. CN ::= "worm" ;
Mks_8. CN ::= A CN ;
Mks_9. CN ::= "boy" ;
Mks_4. NP ::= "this" CN ;
Mks_15. A ::= "thick" ;
...
</pre>
A syntax tree such as
<pre>
Mks_4 (Mks_8 Mks_15 Mks_12)
this thick worm
</pre>
encodes the sequence of grammar rules used for building the
expression. If you look at this tree, you will notice that <tt>Mks_4</tt>
is the label of the rule prefixing <tt>this</tt> to a common noun,
<tt>Mks_15</tt> is the label of the adjective <tt>thick</tt>,
and so on.
<!-- NEW -->
<h4>The labelled context-free format</h4>
The <b>labelled context-free grammar</b> format permits user-defined
labels to each rule. GF recognizes files of this format by the suffix
<tt>.cf</tt>. Let us include the following rules in the file
<tt>paleolithic.cf</tt>.
<pre>
PredVP. S ::= NP VP ;
UseV. VP ::= V ;
ComplTV. VP ::= TV NP ;
UseA. VP ::= "is" A ;
This. NP ::= "this" CN ;
That. NP ::= "that" CN ;
Def. NP ::= "the" CN ;
Indef. NP ::= "a" CN ;
ModA. CN ::= A CN ;
Boy. CN ::= "boy" ;
Louse. CN ::= "louse" ;
Snake. CN ::= "snake" ;
Worm. CN ::= "worm" ;
Green. A ::= "green" ;
Rotten. A ::= "rotten" ;
Thick. A ::= "thick" ;
Warm. A ::= "warm" ;
Laugh. V ::= "laughs" ;
Sleep. V ::= "sleeps" ;
Swim. V ::= "swims" ;
Eat. TV ::= "eats" ;
Kill. TV ::= "kills"
Wash. TV ::= "washes" ;
</pre>
<!-- NEW -->
<h4>Using the labelled context-free format</h4>
The GF commands for the <tt>.cf</tt> format are
exactly the same as for the <tt>.ebnf</tt> format.
Just the syntax trees become nicer to read and
to remember. Notice that before reading in
a new grammar in GF you often (but not always,
as we will see later) have first to give the
command (<tt>empty = e</tt>), which removes the
old grammar from the GF shell state.
<pre>
> empty
> i paleolithic.cf
> p "the boy eats a snake"
PredVP (Def Boy) (ComplTV Eat (Indef Snake))
> gr -tr | l
PredVP (Indef Louse) (UseA Thick)
a louse is thick
</pre>
<!-- NEW -->
<h2>The GF grammar format</h2>
To see what there really is in GF's shell state when a grammar
has been imported, you can give the plain command
<tt>print_grammar = pg</tt>.
<pre>
> print_grammar
</pre>
The output is quite unreadable at this stage, and you may feel happy that
you did not need to write the grammar in that notation, but that the
GF grammar compiler produced it.
<p>
However, we will now start to show how GF's own notation gives you
much more expressive power than the <tt>.cf</tt> and <tt>.ebnf</tt>
formats. We will introduce the <tt>.gf</tt> format by presenting
one more way of defining the same grammar as in
<tt>paleolithic.cf</tt> and <tt>paleolithic.ebnf</tt>.
Then we will show how the full GF grammar format enables you
to do things that are not possible in the weaker formats.
<!-- NEW -->
<h3>Abstract and concrete syntax</h3>
A GF grammar consists of two main parts:
<ul>
<li> <b>abstract syntax</b>, defining what syntax trees there are
<li> <b>concrete syntax</b>, defining how trees are linearized into strings
</ul>
The EBNF and CF formats fuse these two things together, but it is possible
to take them apart. For instance, the verb phrase predication rule
<pre>
PredVP. S ::= NP VP ;
</pre>
is interpreted as the following pair of rules:
<pre>
fun PredVP : NP -> VP -> S ;
lin PredVP x y = {s = x.s ++ y.s} ;
</pre>
The former rule, with the keyword <tt>fun</tt>, belongs to the abstract syntax.
It defines the <b>function</b>
<tt>PredVP</tt> which constructs syntax trees of form
(<tt>PredVP</tt> <i>x</i> <i>y</i>).
<p>
The latter rule, with the keyword <tt>lin</tt>, belongs to the concrete syntax.
It defines the <b>linearization function</b> for
syntax trees of form (<tt>PredVP</tt> <i>x</i> <i>y</i>).
<!-- NEW -->
<h4>Judgement forms</h4>
Rules in a GF grammar are called <b>judgements</b>, and the keywords
<tt>fun</tt> and <tt>lin</tt> are used for distinguishing between two
<b>judgement forms</b>. Here is a summary of the most important
judgement forms:
<ul>
<li> abstract syntax
<ul>
<li> cat C
<li> fun f : A
</ul>
<li> concrete syntax
<ul>
<li> lincat C = T
<li> lin f x ... y = t
</ul>
</ul>
We return to the precise meanings of these judgement forms later.
First we will look at how judgements are grouped into modules, and
show how the grammar <tt>paleolithic.cf</tt> is
expressed by using modules and judgements.
<!-- NEW -->
<h4>Module types</h4>
A GF grammar consists of <b>modules</b>,
into which judgements are grouped. The most important
module forms are
<ul>
<li> <tt>abstract</tt> A = M</tt>, abstract syntax A with judgements in
the module body M.
<li> <tt>concrete</tt> C <tt>of</tt> A = M</tt>, concrete syntax C of the
abstract syntax A, with judgements in the module body M.
</ul>
<!-- NEW -->
<h4>An abstract syntax example</h4>
Each nonterminal occurring in <tt>paleolithic.cf</tt> is
introduced by a <tt>cat</tt> judgement. Each
rule label is introduced by a <tt>fun</tt> judgement.
<pre>
abstract Paleolithic = {
cat
S ; NP ; VP ; CN ; A ; V ; TV ;
fun
PredVP : NP -> VP -> S ;
UseV : V -> VP ;
ComplTV : TV -> NP -> VP ;
UseA : A -> VP ;
ModA : A -> CN -> CN ;
This, That, Def, Indef : CN -> NP ;
Boy, Louse, Snake, Worm : CN ;
Green, Rotten, Thick, Warm : A ;
Laugh, Sleep, Swim : V ;
Eat, Kill, Wash : TV ;
}
</pre>
Notice the use of shorthands permitting the sharing of
the keyword in subsequent judgements, and of the type
in subsequent <tt>fun</tt> judgements.
<!-- NEW -->
<h4>A concrete syntax example</h4>
Each category introduced in <tt>Paleolithic.gf</tt> is
given a <tt>lincat</tt> rule, and each
function is given a <tt>fun</tt> rule. Similar shorthands
apply as in <tt>abstract</tt> modules.
<pre>
concrete PaleolithicEng of Paleolithic = {
lincat
S, NP, VP, CN, A, V, TV = {s : Str} ;
lin
PredVP np vp = {s = np.s ++ vp.s} ;
UseV v = v ;
ComplTV tv np = {s = tv.s ++ np.s} ;
UseA a = {s = "is" ++ a.s} ;
This cn = {s = "this" ++ cn.s} ;
That cn = {s = "that" ++ cn.s} ;
Def cn = {s = "the" ++ cn.s} ;
Indef cn = {s = "a" ++ cn.s} ;
ModA a cn = {s = a.s ++ cn.s} ;
Boy = {s = "boy"} ;
Louse = {s = "louse"} ;
Snake = {s = "snake"} ;
Worm = {s = "worm"} ;
Green = {s = "green"} ;
Rotten = {s = "rotten"} ;
Thick = {s = "thick"} ;
Warm = {s = "warm"} ;
Laugh = {s = "laughs"} ;
Sleep = {s = "sleeps"} ;
Swim = {s = "swims"} ;
Eat = {s = "eats"} ;
Kill = {s = "kills"} ;
Wash = {s = "washes"} ;
}
</pre>
<!-- NEW -->
<h4>Modules and files</h4>
Module name + <tt>.gf</tt> = file name
<p>
Each module is compiled into a <tt>.gfc</tt> file.
<p>
Import <tt>PaleolithicEng.gf</tt> and try what happens
<pre>
> i PaleolithicEng.gf
</pre>
The GF program does not only read the file
<tt>PaleolithicEng.gf</tt>, but also all other files that it
depends on - in this case, <tt>Paleolithic.gf</tt>.
<p>
For each file that is compiles, a <tt>.gfc</tt> file
is generated. The GFC format (="GF Canonical") is the
"machine code" of GF, which is faster to process than
GF source files. When reading a module, GF knows whether
to use an existing <tt>.gfc</tt> file or to generate
a new one, by looking at modification times.
<!-- NEW -->
<h4>Multilingual grammar</h4>
The main advantage of separating abstract from concrete syntax is that
one abstract syntax can be equipped with many concrete syntaxes.
A system with this property is called a <b>multilingual grammar</b>.
<p>
Multilingual grammars can be used for applications such as
translation. Let us buid an Italian concrete syntax for
<tt>Paleolithic</tt> and then test the resulting
multilingual grammar.
<!-- NEW -->
<h4>An Italian concrete syntax</h4>
<pre>
concrete PaleolithicIta of Paleolithic = {
lincat
S, NP, VP, CN, A, V, TV = {s : Str} ;
lin
PredVP np vp = {s = np.s ++ vp.s} ;
UseV v = v ;
ComplTV tv np = {s = tv.s ++ np.s} ;
UseA a = {s = "è" ++ a.s} ;
This cn = {s = "questo" ++ cn.s} ;
That cn = {s = "quello" ++ cn.s} ;
Def cn = {s = "il" ++ cn.s} ;
Indef cn = {s = "un" ++ cn.s} ;
ModA a cn = {s = cn.s ++ a.s} ;
Boy = {s = "ragazzo"} ;
Louse = {s = "pidocchio"} ;
Snake = {s = "serpente"} ;
Worm = {s = "verme"} ;
Green = {s = "verde"} ;
Rotten = {s = "marcio"} ;
Thick = {s = "grosso"} ;
Warm = {s = "caldo"} ;
Laugh = {s = "ride"} ;
Sleep = {s = "dorme"} ;
Swim = {s = "nuota"} ;
Eat = {s = "mangia"} ;
Kill = {s = "uccide"} ;
Wash = {s = "lava"} ;
}
</pre>
<!-- NEW -->
<h4>Using a multilingual grammar</h4>
Import without first emptying
<pre>
> i PaleolithicEng.gf
> i PaleolithicIta.gf
</pre>
Try generation now:
<pre>
> gr | l
un pidocchio uccide questo ragazzo
> gr | l -lang=PaleolithicEng
that louse eats a louse
</pre>
Translate by using a pipe:
<pre>
> p -lang=PaleolithicEng "the boy eats the snake" | l -lang=PaleolithicIta
il ragazzo mangia il serpente
</pre>
<!-- NEW -->
<h4>The multilingual shell state</h4>
A GF shell is at any time in a state, which
contains a multilingual grammar. One of the concrete
syntaxes is the "main" one, which means that parsing and linearization
are performed by using it. By default, the main concrete syntax is the
last-imported one. As we saw on previous slide, the <tt>lang</tt> flag
can be used to change the linearization and parsing grammar.
<p>
To see what the multilingual grammar is (as well as some other
things), you can use the command
<tt>print_options = po</tt>:
<pre>
> print_options
main abstract : Paleolithic
main concrete : PaleolithicIta
all concretes : PaleolithicIta PaleolithicEng
</pre>
<!-- NEW -->
<h4>Extending a grammar</h4>
The module system of GF makes it possible to <b>extend</b> a
grammar in different ways. The syntax of extension is
shown by the following example.
<pre>
abstract Neolithic = Paleolithic ** {
fun
Fire, Wheel : CN ;
Think : V ;
}
</pre>
Parallel to the abstract syntax, extensions can
be built for concrete syntaxes:
<pre>
concrete NeolithicEng of Neolithic = PaleolithicEng ** {
lin
Fire = {s = "fire"} ;
Wheel = {s = "wheel"} ;
Think = {s = "thinks"} ;
}
</pre>
The effect of extension is that all of the contents of the extended
and extending module are put together.
<!-- NEW -->
<h4>Multiple inheritance</h4>
Specialized vocabularies can be represented as small grammars that
only do "one thing" each, e.g.
<pre>
abstract Fish = {
cat Fish ;
fun Salmon, Perch : Fish ;
}
abstract Mushrooms = {
cat Mushroom ;
fun Cep, Agaric : Mushroom ;
}
</pre>
They can afterwards be combined in bigger grammars by using
<b>multiple inheritance</b>, i.e. extension of several grammars at the
same time:
<pre>
abstract Gatherer = Paleolithic, Fish, Mushrooms ** {
fun
UseFish : Fish -> CN ;
UseMushroom : Mushroom -> CN ;
}
</pre>
<!-- NEW -->
<h4>Visualizing module structure</h4>
When you have created all the abstract syntaxes and
one set of concrete syntaxes needed for <tt>Gatherer</tt>,
your grammar consists of eight GF modules. To see how their
dependences look like, you can use the command
<tt>visualize_graph = vg</tt>,
<pre>
> visualize_graph
</pre>
and the graph will pop up in a separate window. It can also
be printed out into a file, e.g. a <tt>.gif</tt> file that
can be included in an HTML document
<pre>
> pm -printer=graph | wf Gatherer.dot
> ! dot -Tgif Gatherer.dot > Gatherer.gif
</pre>
The latter command is a Unix command, issued from GF by using the
shell escape symbol <tt>!</tt>. The resulting graph is shown below.
<p>
<img src="Gatherer.gif">
</body>
</html>
|
