-The term GF is used for different things:
@@ -166,16 +194,16 @@ It will guide you -A grammar is a definition of a language. From this definition, different language processing components can be derived:
@@ -184,13 +212,14 @@ processing tasks can be automatically derived. In addition, many other tasks are readily available for GF grammars:
@@ -235,7 +264,7 @@ the target language. and all theoretical knowledge about its grammar is given by the libraries.
-This tutorial is mainly for programmers who want to learn to write application grammars. It will go through GF's programming concepts @@ -243,12 +272,24 @@ without entering too deep into linguistics. Thus it should be accessible to anyone who has some previous programming experience.
-A separate document is being written on how to write resource grammars. -This includes the ways in which linguistic problems posed by different -languages are solved in GF. +A separate document has been written on how to write resource grammars: the +Resource HOWTO. +In this tutorial, we will just cover the programming concepts that are used for +solving linguistic problems in the resource grammars. +
++The easiest way to use GF is probably via the interactive syntax editor. +Its use does not require any knowledge of the GF formalism. There is +a separate +Editor User Manual +by Janna Khegai, covering the use of the editor. The editor is also a platform for many +kinds of GF applications, implementing the slogan +
++write a document in a language you don't know, while seeing it in a language you know.
-The tutorial gives a hands-on introduction to grammar writing. We start by building a small grammar for the domain of food: @@ -300,8 +341,7 @@ belongs to resource grammars, this tutorial will explain the programming concepts involved in morphology. This will moreover make it possible to grow the fragment covered by the food example. The tutorial will in fact build a miniature resource grammar in order -to illustrate the module structure of library-based application -grammar writing. +to give an introduction to linguistically oriented grammar writing.
Thus it is by elaborating the initial food.cf example that
@@ -312,45 +352,62 @@ are needed.
To learn how to write GF grammars is not the only goal of -this tutorial. To learn the commands of the GF system means -that simple applications of grammars, such as translation and +this tutorial. We will also explain the most important +commands of the GF system. With these commands, +simple applications of grammars, such as translation and quiz systems, can be built simply by writing scripts for the -system. More complicated applications, such as natural-language -interfaces and dialogue systems, also require programming in -some general-purpose language. We will briefly explain how -GF grammars are used as components of Haskell, Java, Javascript, -and Prolog grammars. The tutorial concludes with a couple of -case studies showing how such complete systems can be built. +system. +
+
+More complicated applications, such as natural-language
+interfaces and dialogue systems, moreover require programming in
+some general-purpose language. Thus we will briefly explain how
+GF grammars are used as components of Haskell programs.
+Chapters on using them in Java and Javascript programs are
+forthcoming; a comprehensive manual on GF embedded in Java, by Björn Bringert, is
+available in
+http://www.cs.chalmers.se/~bringert/gf/gf-java.html.
The GF program is open-source free software, which you can download via the GF Homepage: +
+
http://www.cs.chalmers.se/~aarne/GF
There you can download
-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 +If you want to compile GF from source, you need a Haskell compiler. +To compile the interactive editor, you also need a Java compilers. +But normally you don't have to compile, and you definitely don't need to know Haskell or Java to use GF.
+We are assuming the availability of a Unix shell. Linux and Mac OS X users +have it automatically, the latter under the name "terminal". +Windows users are recommended to install Cywgin, the free Unix shell for Windows. +
+ +To start the GF program, assuming you have installed it, just type
% gf
-in the shell. You will see GF's welcome message and the prompt >.
+in the shell.
+You will see GF's welcome message and the prompt >.
The command
@@ -371,8 +428,8 @@ As a common convention in this Tutorial, we will use Thus you should not type these prompts, but only the lines that follow them. - -- -The .cf grammar format
+ +The .cf grammar format
Now you are ready to try out your first grammar. We start with one that is not written in the GF language, but @@ -420,8 +477,8 @@ following sentence can be built using this grammar: this delicious Italian wine is very very expensive
The first GF command needed when using a grammar is to import it.
The command has a long name, import, and a short name, i.
@@ -439,8 +496,15 @@ or
to get the same effect. The effect is that the GF program compiles your grammar into an internal -representation, and shows a new prompt when it is ready. +representation, and shows a new prompt when it is ready. It will also show how much +CPU time is consumed:
++ > i food.cf + - parsing cf food.cf 12 msec + 16 msec + > +
You can now use GF for parsing:
@@ -465,12 +529,35 @@ you imported. Try parsing something else, and you fail
> p "hello world"
- No success in cf parsing hello world
- no tree found
+ Unknown words: hello world
-
-
+Exercise. Extend the grammar food.cf by ten new food kinds and
+qualities, and run the parser with new kinds of examples.
+
+Exercise. Add a rule that enables questions of the form +is this cheese Italian. +
++Exercise. Add the rule +
++ IsVery. S ::= Item "is" "very" Quality ; ++
+and see what happens when parsing this wine is very very Italian.
+You have just made the grammar ambiguous: it now assigns several
+trees to some strings.
+
+Exercise. Modify the grammar so that at most one Quality may
+attach to a given Kind. Thus boring Italian fish will no longer
+be recognized.
+
You can also use GF for linearizing
(linearize = l). This is the inverse of
@@ -499,9 +586,12 @@ a pipe.
> gr | l
this Italian fish is fresh
-
+Pipes in GF work much the same way as Unix pipes: they feed the output +of one command into another command as its input. +
+ +
The gibberish code with parentheses returned by the parser does not
look like trees. Why is it called so? From the abstract mathematical
@@ -513,17 +603,21 @@ for this purpose, GF provides the command visualizre_tree = vt, to
parsing (and any other tree-producing command) can be piped:
- parse "this delicious cheese is very Italian" | vt + > parse "this delicious cheese is very Italian" | vt
+This command uses the programs Graphviz and Ghostview, which you +might not have, but which are freely available on the web. +
+ +Random generation is a good way to test a grammar; it can also -be quite amusing. So you may want to +be fun. So you may want to generate ten strings with one and the same command:
@@ -540,8 +634,8 @@ generate ten strings with one and the same command:
this fish is boring
-
-
To generate all sentence that a grammar
can generate, use the command generate_trees = gt.
@@ -565,14 +659,25 @@ You get quite a few trees but not all of them: only up to a given
help = h command,
- help gt + > help gt+
-Quiz. If the command gt generated all
+Exercise. If the command gt generated all
trees in your grammar, it would never terminate. Why?
+Exercise. Measure how many trees the grammar gives with depths 4 and 5,
+respectively. You use the Unix word count command wc to count lines.
+Hint. You can pipe the output of a GF command into a Unix command by
+using the escape ?, as follows:
+
+ > generate_trees | ? wc ++ + +
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" @@ -595,8 +700,12 @@ This facility is good for test purposes: for instance, you may want to see if a grammar is ambiguous, i.e. contains strings that can be parsed in more than one way.
- -
+Exercise. Extend the grammar food.cf so that it produces ambiguous strings,
+and try out the ambiguity test.
+
To save the outputs of GF commands into a file, you can
pipe it to the write_file = wf command,
@@ -618,8 +727,8 @@ 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.
To see GF's internal representation of a grammar that you have imported, you can give the command @@ -643,8 +752,8 @@ another way of defining the same grammar as in Then we will show how the full GF grammar format enables you to do things that are not possible in the context-free format.
- -A GF grammar consists of two main parts:
@@ -678,8 +787,8 @@ The latter rule, with the keywordlin, belongs to the concrete synt
It defines the linearization function for
syntax trees of form (Is item quality).
-
-
Rules in a GF grammar are called judgements, and the keywords
fun and lin are used for distinguishing between two
@@ -706,6 +815,7 @@ judgement forms:
+
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 food grammar is expressed by using modules and judgements.
- -A GF grammar consists of modules, into which judgements are grouped. The most important @@ -746,8 +857,23 @@ module forms are abstract syntax A, with judgements in the module body M.
+The nonterminals of a context-free grammar, i.e. categories, +are called basic types in the type system of GF. In addition +to them, there are function types such as +
++ Item -> Quality -> S ++
+This type is read "a function from iterms and qualities to sentences". +The last type in the arrow-separated sequence is the value type +of the function type, the earlier types are its argument types. +
+ +The linearization type of a category is a record type, with zero of more fields of different types. The simplest record @@ -795,19 +921,19 @@ not work with the lexical analysis that precedes parsing. A shorthand exemplified by
- ["hello world and people"] === "hello" ++ "world" ++ "and" ++ "people" + ["hello world and people"] === "hello" ++ "world" ++ "and" ++ "people"
can be used for lists of tokens. The expression
- [] + []
denotes the empty token list.
- -
To express the abstract syntax of food.cf in
a file Food.gf, we write two kinds of judgements:
@@ -851,8 +977,13 @@ and of the type in subsequent fun judgements,
The order of judgements in a module is free.
- -
+Exercise. Extend the abstract syntax Food with ten new
+kinds and qualities, and with questions of the form
+is this wine Italian.
+
Each category introduced in Food.gf is
given a lincat rule, and each
@@ -883,19 +1014,30 @@ apply as in abstract modules.
}
-Source files: Module name + .gf = file name
+Exercise. Extend the concrete syntax FoodEng so that it
+matches the abstract syntax defined in the exercise of the previous
+section. What happens if the concrete syntax lacks some of the
+new functions?
-Target files: each module is compiled into a .gfc file.
+GF uses suffixes to recognize different file formats. The most
+important ones are:
.gf = file name
+.gfc file.
+
-Import FoodEng.gf and see what happens
+Import FoodEng.gf and see what happens:
> i FoodEng.gf
+ - compiling Food.gf... wrote file Food.gfc 16 msec
+ - compiling FoodEng.gf... wrote file FoodEng.gfc 20 msec
The GF program does not only read the file
@@ -910,8 +1052,21 @@ GF source files. When reading a module, GF decides whether
to use an existing .gfc file or to generate
a new one, by looking at modification times.
+Exercise. What happens when you import FoodEng.gf for
+a second time? Try this in different situations:
+
empty (e), which clears the memory
+ of GF.
+FoodEng.gf, be it only an added space.
+Food.gf.
+
The main advantage of separating abstract from concrete syntax is that
one abstract syntax can be equipped with many concrete syntaxes.
@@ -923,8 +1078,8 @@ translation. Let us build an Italian concrete syntax for
Food and then test the resulting
multilingual grammar.
concrete FoodIta of Food = {
@@ -948,11 +1103,21 @@ multilingual grammar.
Boring = {s = "noioso"} ;
}
-
-
-
+Exercise. Write a concrete syntax of Food for some other language.
+You will probably end up with grammatically incorrect output - but don't
+worry about this yet.
+
+Exercise. If you have written Food for German, Swedish, or some
+other language, test with random or exhaustive generation what constructs
+come out incorrect, and prepare a list of those ones that cannot be helped
+with the currently available fragment of GF.
+
Import the two grammars in the same GF session.
@@ -978,6 +1143,21 @@ Translate by using a pipe: questo formaggio è molto delizioso+Generate a multilingual treebank, i.e. a set of trees with their +translations in different languages: +
++ > gr -number=2 | tree_bank + + Is (That Cheese) (Very Boring) + quello formaggio è molto noioso + that cheese is very boring + + Is (That Cheese) Fresh + quello formaggio è fresco + that cheese is fresh ++
The lang flag tells GF which concrete syntax to use in parsing and
linearization. By default, the flag is set to the last-imported grammar.
To see what grammars are in scope and which is the main one, use the command
@@ -989,9 +1169,18 @@ To see what grammars are in scope and which is the main one, use the command
main concrete : FoodIta
actual concretes : FoodIta FoodEng
+
+You can change the main grammar by the command change_main = cm:
+
+ > change_main FoodEng + main abstract : Food + main concrete : FoodEng + actual concretes : FoodIta FoodEng +- -
If translation is what you want to do with a set of grammars, a convenient
way to do it is to open a translation_session = ts. In this session,
@@ -1013,8 +1202,8 @@ A dot . terminates the translation session.
>
This is a simple language exercise that can be automatically
generated from a multilingual grammar. The system generates a set of
@@ -1048,15 +1237,15 @@ You can also generate a list of translation exercises and save it in a
file for later use, by the command translation_list = tl
- > translation_list -number=25 FoodEng FoodIta + > translation_list -number=25 FoodEng FoodIta | write_file transl.txt
The number flag gives the number of sentences generated.
The module system of GF makes it possible to extend a grammar in different ways. The syntax of extension is @@ -1088,10 +1277,11 @@ be built for concrete syntaxes:
The effect of extension is that all of the contents of the extended -and extending module are put together. +and extending module are put together. We also say that the new +module inherits the contents of the old module.
- -
Specialized vocabularies can be represented as small grammars that
only do "one thing" each. For instance, the following are grammars
@@ -1125,8 +1315,8 @@ At this point, you would perhaps like to go back to
Food and take apart Wine to build a special
Drink module.
When you have created all the abstract syntaxes and
one set of concrete syntaxes needed for Foodmarket,
@@ -1153,14 +1343,18 @@ The graph uses
+Just as the visualize_tree = vt command, the open source tools
+Ghostview and Graphviz are needed.
+
To document your grammar, you may want to print the
graph into a file, e.g. a .png file that
can be included in an HTML document. You can do this
by first printing the graph into a file .dot and then
-processing this file with the dot program.
+processing this file with the dot program (from the Graphviz package).
> pm -printer=graph | wf Foodmarket.dot
@@ -1179,12 +1373,20 @@ are available:
> help pm
> help -printer
+ > help help
+
+
+Another form of system commands are those usable in GF pipes. The escape symbol
+is then ?.
+
+
+ > generate_trees | ? wc
-
-Resource modules
-
-The golden rule of functional programming
+
+Resource modules
+
+The golden rule of functional programming
In comparison to the .cf format, the .gf format looks rather
verbose, and demands lots more characters to be written. You have probably
@@ -1201,12 +1403,13 @@ method. The golden rule of functional programming says that
A function separates the shared parts of different computations from the
-changing parts, parameters. In functional programming languages, such as
-Haskell, it is possible to share much more than in
-languages such as C and Java.
+changing parts, its arguments, or parameters.
+In functional programming languages, such as
+Haskell, it is possible to share much more
+code with functions than in imperative languages such as C and Java.
-
-Operation definitions
+
+Operation definitions
GF is a functional programming language, not only in the sense that
the abstract syntax is a system of functions (fun), but also because
@@ -1223,10 +1426,10 @@ The operation can be applied to an argument, and GF will
compute the application into a value. For instance,
- ss "boy" ---> {s = "boy"}
+ ss "boy" ===> {s = "boy"}
-(We use the symbol ---> to indicate how an expression is
+(We use the symbol ===> to indicate how an expression is
computed into a value; this symbol is not a part of GF)
@@ -1235,8 +1438,8 @@ its type, and an expression defining it. As for the syntax of the defining
expression, notice the lambda abstraction form \x -> t of
the function.
-
-The ``resource`` module type
+
+The ``resource`` module type
Operator definitions can be included in a concrete syntax.
But they are not really tied to a particular set of linearization rules.
@@ -1263,8 +1466,8 @@ Resource modules can extend other resource modules, in the
same way as modules of other types can extend modules of the
same type. Thus it is possible to build resource hierarchies.
-
-Opening a ``resource``
+
+Opening a resource
Any number of resource modules can be
opened in a concrete syntax, which
@@ -1281,9 +1484,9 @@ opened in a new version of FoodEng.
lin
Is item quality = cc item (prefix "is" quality) ;
- This = prefix "this" ;
- That = prefix "that" ;
- QKind = cc ;
+ This k = prefix "this" k ;
+ That k = prefix "that" k ;
+ QKind k q = cc k q ;
Wine = ss "wine" ;
Cheese = ss "cheese" ;
Fish = ss "fish" ;
@@ -1298,23 +1501,95 @@ opened in a new version of FoodEng.
}
-The same string operations could be used to write FoodIta
+Exercise. Use the same string operations to write FoodIta
more concisely.
+GF, like Haskell, permits partial application of +functions. An example of this is the rule +
++ lin This k = prefix "this" k ; ++
+which can be written more concisely +
++ lin This = prefix "this" ; ++
+The first form is perhaps more intuitive to write +but, once you get used to partial application, you will appreciate its +conciseness and elegance. The logic of partial application +is known as currying, with a reference to Haskell B. Curry. +The idea is that any n-place function can be defined as a 1-place +function whose value is an n-1 -place function. Thus +
++ oper prefix : Str -> SS -> SS ; ++
+can be used as a 1-place function that takes a Str into a
+function SS -> SS. The expected linearization of This is exactly
+a function of such a type, operating on an argument of type Kind
+whose linearization is of type SS. Thus we can define the
+linearization directly as prefix "this".
+
+Exercise. Define an operation infix analogous to prefix,
+such that it allows you to write
+
+ lin Is = infix "is" ; ++ + +
+To test a resource module independently, you must import it
+with the flag -retain, which tells GF to retain oper definitions
+in the memory; the usual behaviour is that oper definitions
+are just applied to compile linearization rules
+(this is called inlining) and then thrown away.
+
+ > i -retain StringOper.gf ++
+The command compute_concrete = cc computes any expression
+formed by operations and other GF constructs. For example,
+
+ > compute_concrete prefix "in" (ss "addition")
+ {
+ s : Str = "in" ++ "addition"
+ }
+
+
+
+Using operations defined in resource modules is a way to avoid repetitive code. In addition, it enables a new kind of modularity and division of labour in grammar writing: grammarians familiar with -the linguistic details of a language can make this knowledge +the linguistic details of a language can make their knowledge available through resource grammar modules, whose users only need to pick the right operations and not to know their implementation -details. +details.
- -+In the following sections, we will go through some +such linguistic details. The programming constructs needed when +doing this are useful for all GF programmers, even if they don't +hand-code the linguistics of their applications but get them +from libraries. It is also useful to know something about the +linguistic concepts of inflection, agreement, and parts of speech. +
+ +
Suppose we want to say, with the vocabulary included in
Food.gf, things like
@@ -1348,8 +1623,12 @@ and many new expression forms.
We also need to generalize linearization types
from strings to more complex types.
+Exercise. Make a list of the possible forms that nouns, +adjectives, and verbs can have in some languages that you know. +
+ +
We define the parameter type of number in Englisn by
using a new form of judgement:
@@ -1394,10 +1673,22 @@ operator !. For instance,
is a selection that computes into the value "cheeses".
This computation is performed by pattern matching: return
the value from the first branch whose pattern matches the
-selection argument.
+selection argument. Thus
+ table {Sg => "cheese" ; Pl => "cheeses"} ! Pl
+ ===> "cheeses"
+
+
+
+Exercise. In a previous exercise, we make a list of the possible
+forms that nouns, adjectives, and verbs can have in some languages that
+you know. Now take some of the results and implement them by
+using parameter type definitions and tables. Write them into a resource
+module, which you can test by using the command compute_concrete.
+
All English common nouns are inflected in number, most of them in the same way: the plural form is obtained from the singular by adding the @@ -1430,8 +1721,19 @@ are written together to form one token. Thus, for instance, (regNoun "cheese").s ! Pl ---> "cheese" + "s" ---> "cheeses"
- -
+Exercise. Identify cases in which the regNoun paradigm does not
+apply in English, and implement some alternative paradigms.
+
+Exercise. Implement a paradigm for regular verbs in English. +
++Exercise. Implement some regular paradigms for other languages you have +considered in earlier exercises. +
+ +
Some English nouns, such as mouse, are so irregular that
it makes no sense to see them as instances of a paradigm. Even
@@ -1448,7 +1750,7 @@ operation, a worst-case function for nouns:
} ;
-Thus we could define +Thus we can define
lin Mouse = mkNoun "mouse" "mice" ;
@@ -1461,7 +1763,7 @@ and
mkNoun x (x + "s") ;
-instead of writing the inflection table explicitly. +instead of writing the inflection tables explicitly.
The grammar engineering advantage of worst-case functions is that
@@ -1471,15 +1773,15 @@ interface (i.e. the system of type signatures) that makes it
correct to use these functions in concrete modules. In programming
terms, Noun is then treated as an abstract datatype.
In addition to the completely regular noun paradigm regNoun,
some other frequent noun paradigms deserve to be
defined, for instance,
- sNoun : Str -> Noun = \kiss -> mkNoun kiss (kiss + "es") ; + sNoun : Str -> Noun = \kiss -> mkNoun kiss (kiss + "es") ;
What about nouns like fly, with the plural flies? The already @@ -1487,7 +1789,7 @@ available solution is to use the longest common prefix fl (also known as the technical stem) as argument, and define
- yNoun : Str -> Noun = \fl -> mkNoun (fl + "y") (fl + "ies") ; + yNoun : Str -> Noun = \fl -> mkNoun (fl + "y") (fl + "ies") ;
But this paradigm would be very unintuitive to use, because the technical stem
@@ -1496,45 +1798,40 @@ the lemma and a string operator init, which returns the initial seg
all characters but the last) of a string:
- yNoun : Str -> Noun = \fly -> mkNoun fly (init fly + "ies") ; + yNoun : Str -> Noun = \fly -> mkNoun fly (init fly + "ies") ;
The operation init belongs to a set of operations in the
resource module Prelude, which therefore has to be
-opened so that init can be used.
-
-It may be hard for the user of a resource morphology to pick the right
-inflection paradigm. A way to help this is to define a more intelligent
-paradigm, which chooses the ending by first analysing the lemma.
-The following variant for English regular nouns puts together all the
-previously shown paradigms, and chooses one of them on the basis of
-the final letter of the lemma (found by the prelude operator last).
+opened so that init can be used. Its dual is last:
- regNoun : Str -> Noun = \s -> case last s of {
- "s" | "z" => mkNoun s (s + "es") ;
- "y" => mkNoun s (init s + "ies") ;
- _ => mkNoun s (s + "s")
- } ;
+ > cc init "curry"
+ "curr"
+
+ > cc last "curry"
+ "y"
-This definition displays many GF expression forms not shown befores;
-these forms are explained in the next section.
+As generalizations of the library functions init and last, GF has
+two predefined funtions:
+Predef.dp, which "drops" suffixes of any length,
+and Predef.tk, which "takes" a prefix
+just omitting a number of characters from the end. For instance,
+ > cc Predef.tk 3 "worried" + "worr" + > cc Predef.dp 3 "worried" + "ied" +
-The paradigms regNoun does not give the correct forms for
-all nouns. For instance, mouse - mice and
-fish - fish must be given by using mkNoun.
-Also the word boy would be inflected incorrectly; to prevent
-this, either use mkNoun or modify
-regNoun so that the "y" case does not
-apply if the second-last character is a vowel.
+The prefix Predef is given to a handful of functions that could
+not be defined internally in GF. They are available in all modules
+without explicit open of the module Predef.
We have so far built all expressions of the table form
from branches whose patterns are constants introduced in
@@ -1567,8 +1864,53 @@ programming languages are syntactic sugar for table selections:
case e of {...} === table {...} ! e
+It may be hard for the user of a resource morphology to pick the right
+inflection paradigm. A way to help this is to define a more intelligent
+paradigm, which chooses the ending by first analysing the lemma.
+The following variant for English regular nouns puts together all the
+previously shown paradigms, and chooses one of them on the basis of
+the final letter of the lemma (found by the prelude operator last).
+
+ regNoun : Str -> Noun = \s -> case last s of {
+ "s" | "z" => mkNoun s (s + "es") ;
+ "y" => mkNoun s (init s + "ies") ;
+ _ => mkNoun s (s + "s")
+ } ;
+
++This definition displays many GF expression forms not shown befores; +these forms are explained in the next section. +
+
+The paradigms regNoun does not give the correct forms for
+all nouns. For instance, mouse - mice and
+fish - fish must be given by using mkNoun.
+Also the word boy would be inflected incorrectly; to prevent
+this, either use mkNoun or modify
+regNoun so that the "y" case does not
+apply if the second-last character is a vowel.
+
+Exercise. Extend the regNoun paradigm so that it takes care
+of all variations there are in English. Test it with the nouns
+ax, bamboo, boy, bush, hero, match.
+Hint. The library functions Predef.dp and Predef.tk
+are useful in this task.
+
+Exercise. The same rules that form plural nouns in English also
+apply in the formation of third-person singular verbs.
+Write a regular verb paradigm that uses this idea, but first
+rewrite regNoun so that the analysis needed to build s-forms
+is factored out as a separate oper, which is shared with
+regVerb.
+
A common idiom is to
gather the oper and param definitions
@@ -1618,50 +1960,8 @@ module depends on. The directory prelude is a subdirectory of
set the environment variable GF_LIB_PATH to point to this
directory.
-To test a resource module independently, you must import it
-with the flag -retain, which tells GF to retain oper definitions
-in the memory; the usual behaviour is that oper definitions
-are just applied to compile linearization rules
-(this is called inlining) and then thrown away.
-
- > i -retain MorphoEng.gf --
-The command compute_concrete = cc computes any expression
-formed by operations and other GF constructs. For example,
-
- > cc regVerb "echo"
- {s : Number => Str = table Number {
- Sg => "echoes" ;
- Pl => "echo"
- }
- }
-
-
-
-The command show_operations = so` shows the type signatures
-of all operations returning a given value type:
-
- > so Verb
- MorphoEng.mkNoun : Str -> Str -> {s : {MorphoEng.Number} => Str}
- MorphoEng.mkVerb : Str -> Str -> {s : {MorphoEng.Number} => Str}
- MorphoEng.regNoun : Str -> {s : {MorphoEng.Number} => Str}
- MorphoEng.regVerb : Str -> { s : {MorphoEng.Number} => Str}
-
-
-Why does the command also show the operations that form
-Nouns? The reason is that the type expression
-Verb is first computed, and its value happens to be
-the same as the value of Noun.
-
We can now enrich the concrete syntax definitions to comprise morphology. This will involve a more radical @@ -1671,8 +1971,8 @@ parameters and linearization types are different in different languages - but this does not prevent the use of a common abstract syntax.
- -
The rule of subject-verb agreement in English says that the verb
phrase must be inflected in the number of the subject. This
@@ -1706,8 +2006,8 @@ plural determiners These and Those.
The reader is invited to inspect the way in which agreement works in
the formation of sentences.
The grammar uses both
Prelude and
@@ -1749,12 +2049,11 @@ and parametrized modules.
s = d ++ cn.s ! n ;
n = n
} ;
-
}
The reader familiar with a functional programming language such as Haskell must have noticed the similarity @@ -1806,8 +2105,8 @@ can be defined }
- -
Even though morphology is in GF
mostly used as an auxiliary for syntax, it
@@ -1824,7 +2123,8 @@ be generated, by the command morpho_quiz = mq. Usually,
the category is set to be something else than S. For instance,
- > i lib/resource/french/VerbsFre.gf
+ > cd GF/lib/resource-1.0/
+ > i french/IrregFre.gf
> morpho_quiz -cat=V
Welcome to GF Morphology Quiz.
@@ -1847,8 +2147,8 @@ file for later use, by the command morpho_list = ml
The number flag gives the number of exercises generated.
-
-Discontinuous constituents
+
+Discontinuous constituents
A linearization type may contain more strings than one.
An example of where this is useful are English particle
@@ -1888,8 +2188,8 @@ valued field labelled s. Therefore, discontinuous constituents
are not a good idea in top-level categories accessed by the users
of a grammar application.
-
-Free variation
+
+Free variation
Sometimes there are many alternative ways to define a concrete syntax.
For instance, the verb negation in English can be expressed both by
@@ -1914,8 +2214,8 @@ In general, variants should be used cautiously. It is not
recommended for modules aimed to be libraries, because the
user of the library has no way to choose among the variants.
-
-Overloading of operations
+
+Overloading of operations
Large libraries, such as the GF Resource Grammar Library, may define
hundreds of names, which can be unpractical
@@ -1950,201 +2250,17 @@ All of the following uses of mkN are easy to resolve:
lin Man = mkN "uomo" "uomini" ; -- Str -> Str -> N
-
--A resource grammar is a grammar built on linguistic grounds, -to describe a language rather than a domain. -The GF resource grammar library, which contains resource grammars for -10 languages, is described more closely in the following -documents: -
-
-The simplest way is to open a top-level Lang module
-and a Paradigms module:
-
- abstract Foo = ... - - concrete FooEng = open LangEng, ParadigmsEng in ... - concrete FooSwe = open LangSwe, ParadigmsSwe in ... --
-Here is an example. -
-
- abstract Arithm = {
- cat
- Prop ;
- Nat ;
- fun
- Zero : Nat ;
- Succ : Nat -> Nat ;
- Even : Nat -> Prop ;
- And : Prop -> Prop -> Prop ;
- }
-
- --# -path=.:alltenses:prelude
-
- concrete ArithmEng of Arithm = open LangEng, ParadigmsEng in {
- lincat
- Prop = S ;
- Nat = NP ;
- lin
- Zero =
- UsePN (regPN "zero" nonhuman) ;
- Succ n =
- DetCN (DetSg (SgQuant DefArt) NoOrd) (ComplN2 (regN2 "successor") n) ;
- Even n =
- UseCl TPres ASimul PPos
- (PredVP n (UseComp (CompAP (PositA (regA "even"))))) ;
- And x y =
- ConjS and_Conj (BaseS x y) ;
-
- }
-
- --# -path=.:alltenses:prelude
-
- concrete ArithmSwe of Arithm = open LangSwe, ParadigmsSwe in {
- lincat
- Prop = S ;
- Nat = NP ;
- lin
- Zero =
- UsePN (regPN "noll" neutrum) ;
- Succ n =
- DetCN (DetSg (SgQuant DefArt) NoOrd)
- (ComplN2 (mkN2 (mk2N "efterföljare" "efterföljare")
- (mkPreposition "till")) n) ;
- Even n =
- UseCl TPres ASimul PPos
- (PredVP n (UseComp (CompAP (PositA (regA "jämn"))))) ;
- And x y =
- ConjS and_Conj (BaseS x y) ;
- }
-
-
--The definitions in this example were found by parsing: -
-- > i LangEng.gf - - -- for Successor: - > p -cat=NP -mcfg -parser=topdown "the mother of Paris" - - -- for Even: - > p -cat=S -mcfg -parser=topdown "Paris is old" - - -- for And: - > p -cat=S -mcfg -parser=topdown "Paris is old and I am old" --
-The use of parsing can be systematized by example-based grammar writing, -to which we will return later. -
- -
-The interesting thing now is that the
-code in ArithmSwe is similar to the code in ArithmEng, except for
-some lexical items ("noll" vs. "zero", "efterföljare" vs. "successor",
-"jämn" vs. "even"). How can we exploit the similarities and
-actually share code between the languages?
-
-The solution is to use a functor: an incomplete module that opens
-an abstract as an interface, and then instantiate it to different
-languages that implement the interface. The structure is as follows:
-
- abstract Foo ... - - incomplete concrete FooI = open Lang, Lex in ... - - concrete FooEng of Foo = FooI with (Lang=LangEng), (Lex=LexEng) ; - concrete FooSwe of Foo = FooI with (Lang=LangSwe), (Lex=LexSwe) ; --
-where Lex is an abstract lexicon that includes the vocabulary
-specific to this application:
-
- abstract Lex = Cat ** ... - - concrete LexEng of Lex = CatEng ** open ParadigmsEng in ... - concrete LexSwe of Lex = CatSwe ** open ParadigmsSwe in ... --
-Here, again, a complete example (abstract Arithm is as above):
-
- incomplete concrete ArithmI of Arithm = open Lang, Lex in {
- lincat
- Prop = S ;
- Nat = NP ;
- lin
- Zero =
- UsePN zero_PN ;
- Succ n =
- DetCN (DetSg (SgQuant DefArt) NoOrd) (ComplN2 successor_N2 n) ;
- Even n =
- UseCl TPres ASimul PPos
- (PredVP n (UseComp (CompAP (PositA even_A)))) ;
- And x y =
- ConjS and_Conj (BaseS x y) ;
- }
-
- --# -path=.:alltenses:prelude
- concrete ArithmEng of Arithm = ArithmI with
- (Lang = LangEng),
- (Lex = LexEng) ;
-
- --# -path=.:alltenses:prelude
- concrete ArithmSwe of Arithm = ArithmI with
- (Lang = LangSwe),
- (Lex = LexSwe) ;
-
- abstract Lex = Cat ** {
- fun
- zero_PN : PN ;
- successor_N2 : N2 ;
- even_A : A ;
- }
-
- concrete LexSwe of Lex = CatSwe ** open ParadigmsSwe in {
- lin
- zero_PN = regPN "noll" neutrum ;
- successor_N2 =
- mkN2 (mk2N "efterföljare" "efterföljare") (mkPreposition "till") ;
- even_A = regA "jämn" ;
- }
-
-
-
-In this chapter, we go through constructs that are not necessary in simple grammars -or when the concrete syntax relies on libraries, but very useful when writing advanced -concrete syntax implementations, such as resource grammar libraries. +or when the concrete syntax relies on libraries. But they are useful when +writing advanced concrete syntax implementations, such as resource grammar libraries. +This chapter can safely be skipped if the reader prefers to continue to the +chapter on using libraries.
- -
Local definitions ("let expressions") are used in functional
programming for two reasons: to structure the code into smaller
@@ -2165,8 +2281,8 @@ the same expression. Here is an example, from
} ;
Record types and records can be extended with new fields. For instance, in German it is natural to see transitive verbs as verbs with a case. @@ -2195,8 +2311,8 @@ be used whenever a verb is required. Contravariance means that a function taking an R as argument can also be applied to any object of a subtype T.
- -Product types and tuples are syntactic sugar for record types and records:
@@ -2207,8 +2323,8 @@ Product types and tuples are syntactic sugar for record types and records:
Thus the labels p1, p2,... are hard-coded.
Record types of parameter types are also parameter types. A typical example is a record of agreement features, e.g. French @@ -2245,8 +2361,8 @@ possible to write, slightly surprisingly, }
- -To define string operations computed at compile time, such as in morphology, it is handy to use regular expression patterns: @@ -2268,7 +2384,7 @@ third-person present-tense verbs.
add_s : Str -> Str = \w -> case w of {
- _ + "oo" => s + "s" ; -- bamboo
+ _ + "oo" => w + "s" ; -- bamboo
_ + ("s" | "z" | "x" | "sh" | "o") => w + "es" ; -- bus, hero
_ + ("a" | "o" | "u" | "e") + "y" => w + "s" ; -- boy
x + "y" => x + "ies" ; -- fly
@@ -2292,10 +2408,10 @@ unstressed pre-final vowel e disappears in the plural
Semantics: variables are always bound to the first match, which is the first
in the sequence of binding lists Match p v defined as follows. In the definition,
-p is a pattern and v is a value.
+p is a pattern and v is a value. The semantics is given in Haskell notation.
- Match (p1|p2) v = Match p1 v ++ Match p2 v
+ Match (p1|p2) v = Match p1 ++ U Match p2 v
Match (p1+p2) s = [Match p1 s1 ++ Match p2 s2 |
i <- [0..length s], (s1,s2) = splitAt i s]
Match p* s = [[]] if Match "" s ++ Match p s ++ Match (p+p) s ++... /= []
@@ -2313,8 +2429,16 @@ Examples:
x + "er"* matches "burgerer" with ``x = "burg"
-
-+Exercise. Implement the German Umlaut operation on word stems. +The operation changes the vowel of the stressed stem syllable as follows: +a to ä, au to äu, o to ö, and u to ü. You +can assume that the operation only takes syllables as arguments. Test the +operation to see whether it correctly changes Arzt to Ärzt, +Baum to Bäum, Topf to Töpf, and Kuh to Küh. +
+ +Sometimes a token has different forms depending on the token that follows. An example is the English indefinite article, @@ -2347,8 +2471,8 @@ This very example does not work in all situations: the prefix } ;
- -GF has the following predefined categories in abstract syntax:
@@ -2372,16 +2496,931 @@ they can be used as arguments. For example:
FIXME: The linearization type is {s : Str} for all these categories.
-This section is about the use of the type theory part of GF for
-including more semantics in grammars. Some of the subsections present
-ideas that have not yet been used in real-world applications, and whose
-tool support outside the GF program is not complete.
+In this chapter, we will take a look at the GF resource grammar library.
+We will use the library to implement a slightly extended Food grammar
+and port it to some new languages.
+
+The GF Resource Grammar Library contains grammar rules for +10 languages (in addition, 2 languages are available as incomplete +implementations, and a few more are under construction). Its purpose +is to make these rules available for application programmers, +who can thereby concentrate on the semantic and stylistic +aspects of their grammars, without having to think about +grammaticality. The targeted level of application grammarians +is that of a skilled programmer with +a practical knowledge of the target languages, but without +theoretical knowledge about their grammars. +Such a combination of +skills is typical of programmers who, for instance, want to localize +software to new languages. +
++The current resource languages are +
+Arabic (incomplete)
+Catalan (incomplete)
+Danish
+English
+Finnish
+French
+German
+Italian
+Norwegian
+Russian
+Spanish
+Swedish
+
+The first three letters (Eng etc) are used in grammar module names.
+The incomplete Arabic and Catalan implementations are
+enough to be used in many applications; they both contain, amoung other
+things, complete inflectional morphology.
+
+The resource library API is devided into language-specific +and language-independent parts. To put it roughly, +
+SyntaxL for each language L
+ParadigmsL for each language L
++A full documentation of the API is available on-line in the +resource synopsis. For our +examples, we will only need a fragment of the full API. +
+
+In the first examples,
+we will make use of the following categories, from the module Syntax.
+
| Category | +Explanation | +Example | +|
|---|---|---|---|
Utt |
+sentence, question, word... | +"be quiet" | +|
Adv |
+verb-phrase-modifying adverb, | +"in the house" | +|
AdA |
+adjective-modifying adverb, | +"very" | +|
S |
+declarative sentence | +"she lived here" | +|
Cl |
+declarative clause, with all tenses | +"she looks at this" | +|
AP |
+adjectival phrase | +"very warm" | +|
CN |
+common noun (without determiner) | +"red house" | +|
NP |
+noun phrase (subject or object) | +"the red house" | +|
Det |
+determiner phrase | +"those seven" | +|
Predet |
+predeterminer | +"only" | +|
Quant |
+quantifier with both sg and pl | +"this/these" | +|
Prep |
+preposition, or just case | +"in" | +|
A |
+one-place adjective | +"warm" | +|
N |
+common noun | +"house" | +|
+We will need the following syntax rules from Syntax.
+
| Function | +Type | +Example | +|
|---|---|---|---|
mkUtt |
+S -> Utt |
+John walked | +|
mkUtt |
+Cl -> Utt |
+John walks | +|
mkCl |
+NP -> AP -> Cl |
+John is very old | +|
mkNP |
+Det -> CN -> NP |
+the first old man | +|
mkNP |
+Predet -> NP -> NP |
+only John | +|
mkDet |
+Quant -> Det |
+this | +|
mkCN |
+N -> CN |
+house | +|
mkCN |
+AP -> CN -> CN |
+very big blue house | +|
mkAP |
+A -> AP |
+old | +|
mkAP |
+AdA -> AP -> AP |
+very very old | +|
+We will also need the following structural words from Syntax.
+
| Function | +Type | +Example | +|
|---|---|---|---|
all_Predet |
+Predet |
+all | +|
defPlDet |
+Det |
+the (houses) | +|
this_Quant |
+Quant |
+this | +|
very_AdA |
+AdA |
+very | +|
+For French, we will use the following part of ParadigmsFre.
+
| Function | +Type | +Example | +|
|---|---|---|---|
Gender |
+Type |
+- | +|
masculine |
+Gender |
+- | +|
feminine |
+Gender |
+- | +|
mkN |
+(cheval : Str) -> N |
+- | +|
mkN |
+(foie : Str) -> Gender -> N |
+- | +|
mkA |
+(cher : Str) -> A |
+- | +|
mkA |
+(sec,seche : Str) -> A |
+- | +|
+For German, we will use the following part of ParadigmsGer.
+
| Function | +Type | +Example | +|
|---|---|---|---|
Gender |
+Type |
+- | +|
masculine |
+Gender |
+- | +|
feminine |
+Gender |
+- | +|
neuter |
+Gender |
+- | +|
mkN |
+(Stufe : Str) -> N |
+- | +|
mkN |
+(Bild,Bilder : Str) -> Gender -> N |
+- | +|
mkA |
+Str -> A |
+- | +|
mkA |
+(gut,besser,beste : Str) -> A |
+gut,besser,beste | +|
+Exercise. Try out the morphological paradigms in different languages. Do +in this way: +
++ > i -path=alltenses:prelude -retain alltenses/ParadigmsGer.gfr + > cc mkN "Farbe" + > cc mkA "gut" "besser" "beste" ++ + +
+We start with an abstract syntax that is like Food before, but
+has a plural determiner (all wines) and some new nouns that will
+need different genders in most languages.
+
+ abstract Food = {
+ cat
+ S ; Item ; Kind ; Quality ;
+ fun
+ Is : Item -> Quality -> S ;
+ This, All : Kind -> Item ;
+ QKind : Quality -> Kind -> Kind ;
+ Wine, Cheese, Fish, Beer, Pizza : Kind ;
+ Very : Quality -> Quality ;
+ Fresh, Warm, Italian, Expensive, Delicious, Boring : Quality ;
+ }
+
+
+The French implementation opens SyntaxFre and ParadigmsFre
+to get access to the resource libraries needed. In order to find
+the libraries, a path directive is prepended; it is interpreted
+relative to the environment variable GF_LIB_PATH.
+
+ --# -path=.:present:prelude
+
+ concrete FoodFre of Food = open SyntaxFre,ParadigmsFre in {
+ lincat
+ S = Utt ;
+ Item = NP ;
+ Kind = CN ;
+ Quality = AP ;
+ lin
+ Is item quality = mkUtt (mkCl item quality) ;
+ This kind = mkNP (mkDet this_Quant) kind ;
+ All kind = mkNP all_Predet (mkNP defPlDet kind) ;
+ QKind quality kind = mkCN quality kind ;
+ Wine = mkCN (mkN "vin") ;
+ Beer = mkCN (mkN "bière") ;
+ Pizza = mkCN (mkN "pizza" feminine) ;
+ Cheese = mkCN (mkN "fromage" masculine) ;
+ Fish = mkCN (mkN "poisson") ;
+ Very quality = mkAP very_AdA quality ;
+ Fresh = mkAP (mkA "frais" "fraîche") ;
+ Warm = mkAP (mkA "chaud") ;
+ Italian = mkAP (mkA "italien") ;
+ Expensive = mkAP (mkA "cher") ;
+ Delicious = mkAP (mkA "délicieux") ;
+ Boring = mkAP (mkA "ennuyeux") ;
+ }
+
+
+The lincat definitions in FoodFre assign resource categories
+to application categories. In a sense, the application categories
+are semantic, as they correspond to concepts in the grammar application,
+whereas the resource categories are syntactic: they give the linguistic
+means to express concepts in any application.
+
+The lin definitions likewise assign resource functions to application
+functions. Under the hood, there is a lot of matching with parameters to
+take care of word order, inflection, and agreement. But the user of the
+library sees nothing of this: the only parameters you need to give are
+the genders of some nouns, which cannot be correctly inferred from the word.
+
+In French, for example, the one-argument mkN assigns the noun the feminine
+gender if and only if it ends with an e. Therefore the words fromage and
+pizza are given genders. One can of course always give genders manually, to
+be on the safe side.
+
+As for inflection, the one-argument adjective pattern mkA takes care of
+completely regular adjective such as chaud-chaude, but also of special
+cases such as italien-italienne, cher-chère, and délicieux-délicieuse.
+But it cannot form frais-fraîche properly. Once again, you can give more
+forms to be on the safe side. You can also test the paradigms in the GF
+program.
+
+Exercise. Compile the grammar FoodFre and generate and parse some sentences.
+
+Exercise. Write a concrete syntax of Food for English or some other language
+included in the resource library. You can also compare the output with the hand-written
+grammars presented earlier in this tutorial.
+
+Exercise. In particular, try to write a concrete syntax for Italian, even if +you don't know Italian. What you need to know is that "beer" is birra and +"pizza" is pizza, and that all the nouns and adjectives in the grammar +are regular.
-
+If you did the exercise of writing a concrete syntax of Food for some other
+language, you probably noticed that much of the code looks exactly the same
+as for French. The immediate reason for this is that the Syntax API is the
+same for all languages; the deeper reason is that all languages (at least those
+in the resource package) implement the same syntactic structures and tend to use them
+in similar ways. Thus it is only the lexical parts of a concrete syntax that
+you need to write anew for a new language. In brief,
+
+But programming by copy-and-paste is not worthy of a functional programmer.
+Can we write a function that takes care of the shared parts of grammar modules?
+Yes, we can. It is not a function in the fun or oper sense, but
+a function operating on modules, called a functor. This construct
+is familiar from the functional languages ML and OCaml, but it does not
+exist in Haskell. It also bears some resemblance to templates in C++.
+Functors are also known as parametrized modules.
+
+In GF, a functor is a module that opens one or more interfaces.
+An interface is a module similar to a resource, but it only
+contains the types of opers, not their definitions. You can think
+of an interface as a kind of a record type. Thus a functor is a kind
+of a function taking records as arguments and producins a module
+as value.
+
+Let us look at a functor implementation of the Food grammar.
+Consider its module header first:
+
+ incomplete concrete FoodI of Food = open Syntax, LexFood in ++
+In the functor-function analogy, FoodI would be presented as a function
+with the following type signature:
+
+ FoodI : instance of Syntax -> instance of LexFood -> concrete of Food ++
+It takes as arguments two interfaces: +
+Syntax, the resource grammar interface
+LexFood, the domain-specific lexicon interface
+
+Functors opening Syntax and a domain lexicon interface are in fact
+so typical in GF applications, that this structure could be called a design patter
+for GF grammars. The idea in this pattern is, again, that
+the languages use the same syntactic structures but different words.
+
+Before going to the details of the module bodies, let us look at how functors +are concretely used. An interface has a header such as +
++ interface LexFood = open Syntax in ++
+To give an instance of it means that all opers are given definitione (of
+appropriate types). For example,
+
+ instance LexFoodGer of LexFood = open SyntaxGer, ParadigmsGer in ++
+Notice that when an interface opens an interface, such as Syntax, then its instance
+opens an instance of it. But the instance may also open some resources - typically,
+a domain lexicon instance opens a Paradigms module.
+
+In the function-functor analogy, we now have +
++ SyntaxGer : instance of Syntax + LexFoodGer : instance of LexFood ++
+Thus we can complete the German implementation by "applying" the functor: +
++ FoodI SyntaxGer LexFoodGer : concrete of Food ++
+The GF syntax for doing so is +
++ concrete FoodGer of Food = FoodI with + (Syntax = SyntaxGer), + (LexFood = LexFoodGer) ; ++
+Notice that this is the complete module, not just a header of it.
+The module body is received from FoodI, by instantiating the
+interface constants with their definitions given in the German
+instances.
+
+A module of this form, characterized by the keyword with, is
+called a functor instantiation.
+
+Here is the complete code for the functor FoodI:
+
+ incomplete concrete FoodI of Food = open Syntax, LexFood in {
+ lincat
+ S = Utt ;
+ Item = NP ;
+ Kind = CN ;
+ Quality = AP ;
+ lin
+ Is item quality = mkUtt (mkCl item quality) ;
+ This kind = mkNP (mkDet this_Quant) kind ;
+ All kind = mkNP all_Predet (mkNP defPlDet kind) ;
+ QKind quality kind = mkCN quality kind ;
+ Wine = mkCN wine_N ;
+ Beer = mkCN beer_N ;
+ Pizza = mkCN pizza_N ;
+ Cheese = mkCN cheese_N ;
+ Fish = mkCN fish_N ;
+ Very quality = mkAP very_AdA quality ;
+ Fresh = mkAP fresh_A ;
+ Warm = mkAP warm_A ;
+ Italian = mkAP italian_A ;
+ Expensive = mkAP expensive_A ;
+ Delicious = mkAP delicious_A ;
+ Boring = mkAP boring_A ;
+ }
+
+
+
+
+Let us now define the LexFood interface:
+
+ interface LexFood = open Syntax in {
+ oper
+ wine_N : N ;
+ beer_N : N ;
+ pizza_N : N ;
+ cheese_N : N ;
+ fish_N : N ;
+ fresh_A : A ;
+ warm_A : A ;
+ italian_A : A ;
+ expensive_A : A ;
+ delicious_A : A ;
+ boring_A : A ;
+ }
+
+
+In this interface, only lexical items are declared. In general, an
+interface can declare any functions and also types. The Syntax
+interface does so.
+
+Here is the German instance of the interface: +
+
+ instance LexFoodGer of LexFood = open SyntaxGer, ParadigmsGer in {
+ oper
+ wine_N = mkN "Wein" ;
+ beer_N = mkN "Bier" "Biere" neuter ;
+ pizza_N = mkN "Pizza" "Pizzen" feminine ;
+ cheese_N = mkN "Käse" "Käsen" masculine ;
+ fish_N = mkN "Fisch" ;
+ fresh_A = mkA "frisch" ;
+ warm_A = mkA "warm" "wärmer" "wärmste" ;
+ italian_A = mkA "italienisch" ;
+ expensive_A = mkA "teuer" ;
+ delicious_A = mkA "köstlich" ;
+ boring_A = mkA "langweilig" ;
+ }
+
+
+Just to complete the picture, we repeat the German functor instantiation
+for FoodI, this time with a path directive that makes it compilable.
+
+ --# -path=.:present:prelude + + concrete FoodGer of Food = FoodI with + (Syntax = SyntaxGer), + (LexFood = LexFoodGer) ; ++ +
+Exercise. Compile and test FoodGer.
+
+Exercise. Refactor FoodFre into a functor instantiation.
+
+Once we have an application grammar defined by using a functor, +adding a new language is simple. Just two modules need to be written: +
++The functor instantiation is completely mechanical to write. +Here is one for Finnish: +
++ --# -path=.:present:prelude + + concrete FoodFin of Food = FoodI with + (Syntax = SyntaxFin), + (LexFood = LexFoodFin) ; ++
+The domain lexicon instance requires some knowledge of the words of the +language: what words are used for which concepts, how the words are +inflected, plus features such as genders. Here is a lexicon instance for +Finnish: +
+
+ instance LexFoodFin of LexFood = open SyntaxFin, ParadigmsFin in {
+ oper
+ wine_N = mkN "viini" ;
+ beer_N = mkN "olut" ;
+ pizza_N = mkN "pizza" ;
+ cheese_N = mkN "juusto" ;
+ fish_N = mkN "kala" ;
+ fresh_A = mkA "tuore" ;
+ warm_A = mkA "lämmin" ;
+ italian_A = mkA "italialainen" ;
+ expensive_A = mkA "kallis" ;
+ delicious_A = mkA "herkullinen" ;
+ boring_A = mkA "tylsä" ;
+ }
+
+
+
+Exercise. Instantiate the functor FoodI to some language of
+your choice.
+
+One purpose with the resource grammars was stated to be a division +of labour between linguists and application grammarians. We can now +reflect on what this means more precisely, by asking ourselves what +skills are required of grammarians working on different components. +
++Building a GF application starts from the abstract syntax. Writing +an abstract syntax requires +
++If the concrete syntax is written by means of a functor, the programmer +has to decide what parts of the implementation are put to the interface +and what parts are shared in the functor. This requires +
++Instantiating a ready-made functor to a new language is less demanding. +It requires essentially +
++Notice that none of these tasks requires the use of GF records, tables, +or parameters. Thus only a small fragment of GF is needed; the rest of +GF is only relevant for those who write the libraries. +
++Of course, grammar writing is not always straightforward usage of libraries. +For example, GF can be used for other languages than just those in the +libraries - for both natural and formal languages. A knowledge of records +and tables can, unfortunately, also be needed for understanding GF's error +messages. +
++Exercise. Design a small grammar that can be used for controlling +an MP3 player. The grammar should be able to recognize commands such +as play this song, with the following variations: +
++The implementation goes in the following phases: +
+
+A functor implementation using the resource Syntax interface
+works as long as all concepts are expressed by using the same structures
+in all languages. If this is not the case, the deviant linearization can
+be made into a parameter and moved to the domain lexicon interface.
+
+Let us take a slightly contrived example: assume that English has
+no word for Pizza, but has to use the paraphrase Italian pie.
+This paraphrase is no longer a noun N, but a complex phrase
+in the category CN. An obvious way to solve this problem is
+to change interface LexEng so that the constant declared for
+Pizza gets a new type:
+
+ oper pizza_CN : CN ; ++
+But this solution is unstable: we may end up changing the interface +and the function with each new language, and we must every time also +change the interface instances for the old languages to maintain +type correctness. +
+
+A better solution is to use restricted inheritance: the English
+instantiation inherits the functor implementation except for the
+constant Pizza. This is how we write:
+
+ --# -path=.:present:prelude
+
+ concrete FoodEng of Food = FoodI - [Pizza] with
+ (Syntax = SyntaxEng),
+ (LexFood = LexFoodEng) **
+ open SyntaxEng, ParadigmsEng in {
+
+ lin Pizza = mkCN (mkA "Italian") (mkN "pie") ;
+ }
+
+
+Restricted inheritance is available for all inherited modules. One can for
+instance exclude some mushrooms and pick up just some fruit in
+the FoodMarket example:
+
+ abstract Foodmarket = Food, Fruit [Peach], Mushroom - [Agaric] ++
+A concrete syntax of Foodmarket must then indicate the same inheritance
+restrictions.
+
+Exercise. Change FoodGer in such a way that it says, instead of
+X is Y, the equivalent of X must be Y (X muss Y sein).
+You will have to browse the full resource API to find all
+the functions needed.
+
+In addition to reading the
+resource synopsis, you
+can find resource function combinations by using the parser. This
+is so because the resource library is in the end implemented as
+a top-level abstract-concrete grammar, on which parsing
+and linearization work.
+
+Unfortunately, only English and the Scandinavian languages can be +parsed within acceptable computer resource limits when the full +resource is used. +
++To look for a syntax tree in the overload API by parsing, do like this: +
++ > $GF_LIB_PATH + > i -path=alltenses:prelude alltenses/OverLangEng.gfc + > p -cat=S -overload "this grammar is too big" + mkS (mkCl (mkNP (mkDet this_Quant) grammar_N) (mkAP too_AdA big_A)) ++
+To view linearizations in all languages by parsing from English: +
++ > i alltenses/langs.gfcm + > p -cat=S -lang=LangEng "this grammar is too big" | tb + UseCl TPres ASimul PPos (PredVP (DetCN (DetSg (SgQuant this_Quant) + NoOrd) (UseN grammar_N)) (UseComp (CompAP (AdAP too_AdA (PositA big_A))))) + Den här grammatiken är för stor + Esta gramática es demasiado grande + (Cyrillic: eta grammatika govorit des'at' jazykov) + Denne grammatikken er for stor + Questa grammatica è troppo grande + Diese Grammatik ist zu groß + Cette grammaire est trop grande + Tämä kielioppi on liian suuri + This grammar is too big + Denne grammatik er for stor ++
+Unfortunately, the Russian grammar uses at the moment a different +character encoding than the rest and is therefore not displayed correctly +in a terminal window. However, the GF syntax editor does display all +examples correctly: +
++ % gfeditor alltenses/langs.gfcm ++
+When you have constructed the tree, you will see the following screen: +
++
+ 
+
+
+Exercise. Find the resource grammar translations for the following
+English phrases (parse in the category Phr). You can first try to
+build the terms manually.
+
+every man loves a woman +
++this grammar speaks more than ten languages +
++which languages aren't in the grammar +
++which languages did you want to speak +
+ +
In this section, we will show how
to encode advanced semantic concepts in an abstract syntax.
@@ -2408,184 +3447,318 @@ of such a theory, represented as an abstract module in GF.
And : Prop -> Prop -> Prop ; -- A and B
}
+
-A concrete syntax is given below, as an example of using the resource grammar
-library.
+Exercise. Give a concrete syntax of Arithm, either from scatch or
+by using the resource library.
Dependent types are a characteristic feature of GF, -inherited from the -constructive type theory of Martin-Löf and +inherited from the constructive type theory of Martin-Löf and distinguishing GF from most other grammar formalisms and functional programming languages. -The initial main motivation for developing GF was, indeed, -to have a grammar formalism with dependent types. -As can be inferred from the fact that we introduce them only now, -after having written lots of grammars without them, -dependent types are no longer the only motivation for GF. -But they are still important and interesting.
Dependent types can be used for stating stronger -conditions of well-formedness than non-dependent types. -A simple example is postal addresses. Ignoring the other details, -let us take a look at addresses consisting of -a street, a city, and a country. +conditions of well-formedness than ordinary types. +A simple example is a "smart house" system, which +defines voice commands for household appliances. This example +is borrowed from the +Regulus Book +(Rayner & al. 2006). +
+
+One who enters a smart house can use speech to dim lights, switch
+on the fan, etc. For each Kind of a device, there is a set of
+Actions that can be performed on it; thus one can dim the lights but
+ not the fan, for example. These dependencies can be expressed by
+by making the type Action dependent on Kind. We express this
+as follows in cat declarations:
- abstract Address = {
- cat
- Address ; Country ; City ; Street ;
+ cat
+ Command ;
+ Kind ;
+ Action Kind ;
+ Device Kind ;
+
++The crucial use of the dependencies is made in the rule for forming commands: +
++ fun CAction : (k : Kind) -> Action k -> Device k -> Command ; ++
+In other words: an action and a device can be combined into a command only
+if they are of the same Kind k. If we have the functions
+
+ DKindOne : (k : Kind) -> Device k ; -- the light - fun - mkAddress : Country -> City -> Street -> Address ; + light, fan : Kind ; + dim : Action light ; ++
+we can form the syntax tree +
++ CAction light dim (DKindOne light) ++
+but we cannot form the trees +
++ CAction light dim (DKindOne fan) + CAction fan dim (DKindOne light) + CAction fan dim (DKindOne fan) ++
+Linearization rules are written as usual: the concrete syntax does not +know if a category is a dependent type. In English, you can write as follows: +
+
+ lincat Action = {s : Str} ;
+ lin CAction kind act dev = {s = act.s ++ dev.s} ;
+
+
+Notice that the argument kind does not appear in the linearization.
+The type checker will be able to reconstruct it from the dev argument.
+
+Parsing with dependent types is performed in two phases: +
+
+If you just parse in the usual way, you don't enter the second phase, and
+the kind argument is not found:
+
+ > parse "dim the light" + CAction ? dim (DKindOne light) ++
+Moreover, type-incorrect commands are not rejected: +
++ > parse "dim the fan" + CAction ? dim (DKindOne fan) ++
+The question mark ? is a metavariable, and is returned by the parser
+for any subtree that is suppressed by a linearization rule.
+
+To get rid of metavariables, you must feed the parse result into the
+second phase of solving them. The solve process uses the dependent
+type checker to restore the values of the metavariables. It is invoked by
+the command put_tree = pt with the flag -transform=solve:
+
+ > parse "dim the light" | put_tree -transform=solve + CAction light dim (DKindOne light) ++
+The solve process may fail, in which case no tree is returned:
+
+ > parse "dim the fan" | put_tree -transform=solve + no tree found ++ +
+Exercise. Write an abstract syntax module with above contents
+and an appropriate English concrete syntax. Try to parse the commands
+dim the light and dim the fan, with and without solve filtering.
+
+Exercise. Perform random and exhaustive generation, with and without
+solve filtering.
+
+Exercise. Add some device kinds and actions to the grammar. +
+ +
+Sometimes an action can be performed on all kinds of devices. It would be
+possible to introduce separate fun constants for each kind-action pair,
+but this would be tedious. Instead, one can use polymorphic actions,
+i.e. actions that take a Kind as an argument and produce an Action
+for that Kind:
+
+ fun switchOn, switchOff : (k : Kind) -> Action k ; ++
+Functions that are not polymorphic are monomorphic. However, the +dichotomy into monomorphism and full polymorphism is not always sufficien +for good semantic modelling: very typically, some actions are defined +for a proper subset of devices, but not just one. For instance, both doors and +windows can be opened, whereas lights cannot. +We will return to this problem by introducing the +concept of restricted polymorphism later, +after a chapter on proof objects. +
+ ++We have used dependent types to control semantic well-formedness +in grammars. This is important in traditional type theory +applications such as proof assistants, where only mathematically +meaningful formulas should be constructed. But semantic filtering has +also proved important in speech recognition, because it reduces the +ambiguity of the results. +
+ +
+The standard way of using GF in speech recognition is by building
+grammar-based language models. To this end, GF comes with compilers
+into several formats that are used in speech recognition systems.
+One such format is GSL, used in the Nuance speech recognizer.
+It is produced from GF simply by printing a grammar with the flag
+-printer=gsl.
+
+ > import -conversion=finite SmartEng.gf + > print_grammar -printer=gsl - UK, France : Country ; - Paris, London, Grenoble : City ; - OxfordSt, ShaftesburyAve, BdRaspail, RueBlondel, AvAlsaceLorraine : Street ; - } --
-The linearization rules are straightforward, -
-
- lin
- mkAddress country city street =
- ss (street.s ++ "," ++ city.s ++ "," ++ country.s) ;
- UK = ss ("U.K.") ;
- France = ss ("France") ;
- Paris = ss ("Paris") ;
- London = ss ("London") ;
- Grenoble = ss ("Grenoble") ;
- OxfordSt = ss ("Oxford" ++ "Street") ;
- ShaftesburyAve = ss ("Shaftesbury" ++ "Avenue") ;
- BdRaspail = ss ("boulevard" ++ "Raspail") ;
- RueBlondel = ss ("rue" ++ "Blondel") ;
- AvAlsaceLorraine = ss ("avenue" ++ "Alsace-Lorraine") ;
-
-
-Notice that, in mkAddress, we have
-reversed the order of the constituents. The type of mkAddress
-in the abstract syntax takes its arguments in a "logical" order,
-with increasing precision. (This order is sometimes even used in the
-concrete syntax of addresses, e.g. in Russia).
-
-Both existing and non-existing addresses are recognized by this -grammar. The non-existing ones in the following randomly generated -list have afterwards been marked by *: -
-
- > gr -cat=Address -number=7 | l
+ ;GSL2.0
+ ; Nuance speech recognition grammar for SmartEng
+ ; Generated by GF
- * Oxford Street , Paris , France
- * Shaftesbury Avenue , Grenoble , U.K.
- boulevard Raspail , Paris , France
- * rue Blondel , Grenoble , U.K.
- * Shaftesbury Avenue , Grenoble , France
- * Oxford Street , London , France
- * Shaftesbury Avenue , Grenoble , France
+ .MAIN SmartEng_2
+
+ SmartEng_0 [("switch" "off") ("switch" "on")]
+ SmartEng_1 ["dim" ("switch" "off")
+ ("switch" "on")]
+ SmartEng_2 [(SmartEng_0 SmartEng_3)
+ (SmartEng_1 SmartEng_4)]
+ SmartEng_3 ("the" SmartEng_5)
+ SmartEng_4 ("the" SmartEng_6)
+ SmartEng_5 "fan"
+ SmartEng_6 "light"
-Dependent types provide a way to guarantee that addresses are
-well-formed. What we do is to include contexts in
-cat judgements:
+Now, GSL is a context-free format, so how does it cope with dependent types?
+In general, dependent types can give rise to infinitely many basic types
+(exercise!), whereas a context-free grammar can by definition only have
+finitely many nonterminals.
+
+This is where the flag -conversion=finite is needed in the import
+command. Its effect is to convert a GF grammar with dependent types to
+one without, so that each instance of a dependent type is replaced by
+an atomic type. This can then be used as a nonterminal in a context-free
+grammar. The finite conversion presupposes that every
+dependent type has only finitely many instances, which is in fact
+the case in the Smart grammar.
+
+Exercise. If you have access to the Nuance speech recognizer,
+test it with GF-generated language models for SmartEng. Do this
+both with and without -conversion=finite.
+
+Exercise. Construct an abstract syntax with infinitely many instances +of dependent types. +
+ ++An alternative to grammar-based language models are +statistical language models (SLMs). An SLM is +built from a corpus, i.e. a set of utterances. It specifies the +probability of each n-gram, i.e. sequence of n words. The +typical value of n is 2 (bigrams) or 3 (trigrams). +
++One advantage of SLMs over grammar-based models is that they are +robust, i.e. they can be used to recognize sequences that would +be out of the grammar or the corpus. Another advantage is that +an SLM can be built "for free" if a corpus is available. +
+
+However, collecting a corpus can require a lot of work, and writing
+a grammar can be less demanding, especially with tools such as GF or
+Regulus. This advantage of grammars can be combined with robustness
+by creating a back-up SLM from a synthesized corpus. This means
+simply that the grammar is used for generating such a corpus.
+In GF, this can be done with the generate_trees command.
+As with grammar-based models, the quality of the SLM is better
+if meaningless utterances are excluded from the corpus. Thus
+a good way to generate an SLM from a GF grammar is by using
+dependent types and filter the results through the type checker:
- cat - Address ; - Country ; - City Country ; - Street (x : Country)(City x) ; + > generate_trees | put_trees -transform=solve | linearize+
-The first two judgements are as before, but the third one makes
-City dependent on Country: there are no longer just cities,
-but cities of the U.K. and cities of France. The fourth judgement
-makes Street dependent on City; but since
-City is itself dependent on Country, we must
-include them both in the context, moreover guaranteeing that
-the city is one of the given country. Since the context itself
-is built by using a dependent type, we have to use variables
-to indicate the dependencies. The judgement we used for City
-is actually shorthand for
+Exercise. Measure the size of the corpus generated from
+SmartEng, with and without type checker filtering.
+
+A dependent function type needs to introduce a variable for +its argument type, as in
- cat City (x : Country) + switchOff : (k : Kind) -> Action k
-which is only possible if the subsequent context does not depend on x.
-
-The fun judgements of the grammar are modified accordingly:
-
- fun - mkAddress : (x : Country) -> (y : City x) -> Street x y -> Address ; - - UK : Country ; - France : Country ; - Paris : City France ; - London : City UK ; - Grenoble : City France ; - OxfordSt : Street UK London ; - ShaftesburyAve : Street UK London ; - BdRaspail : Street France Paris ; - RueBlondel : Street France Paris ; - AvAlsaceLorraine : Street France Grenoble ; --
-Since the type of mkAddress now has dependencies among
-its argument types, we have to use variables just like we used in
-the context of Street above. What we claimed to be the
-"logical" order of the arguments is now forced by the type system
-of GF: a variable must be declared (=bound) before it can be
-referenced (=used).
-
-The effect of dependent types is that the *-marked addresses above are -no longer well-formed. What the GF parser actually does is that it -initially accepts them (by using a context-free parsing algorithm) -and then rejects them (by type checking). The random generator does not produce -illegal addresses (this could be useful in bulk mailing!). -The linearization algorithm does not care about type dependencies; -actually, since the categories (ignoring their arguments) -are the same in both abstract syntaxes, -we use the same concrete syntax -for both of them. -
--Remark. Function types without +Function types without variables are actually a shorthand notation: writing
- fun PredV1 : NP -> V1 -> S + fun PredVP : NP -> VP -> S
is shorthand for
- fun PredV1 : (x : NP) -> (y : V1) -> S + fun PredVP : (x : NP) -> (y : VP) -> S
or any other naming of the variables. Actually the use of variables -sometimes shortens the code, since we can write e.g. +sometimes shortens the code, since they can share a type:
- oper triple : (x,y,z : Str) -> Str = ... + octuple : (x,y,z,u,v,w,s,t : Str) -> Str
-If a bound variable is not used, it can here, as elswhere in GF, be replaced by +If a bound variable is not used, it can here, as elsewhere in GF, be replaced by a wildcard:
- oper triple : (_,_,_ : Str) -> Str = ... + octuple : (_,_,_,_,_,_,_,_ : Str) -> Str ++
+A good practice for functions with many arguments of the same type +is to indicate the number of arguments: +
++ octuple : (x1,_,_,_,_,_,_,x8 : Str) -> Str ++
+One can also use the variables to document what each argument is expected +to provide, as is done in inflection paradigms in the resource grammar. +
++ mkV : (drink,drank,drunk : Str) -> V- -
The functional fragment of GF terms and types comprises function types, applications, lambda @@ -2629,241 +3802,8 @@ When the operations are used, the type checker requires them to be equipped with all their arguments; this may be a nuisance for a Haskell or ML programmer.
- --This section introduces a way of using dependent types to -formalize a notion known as selectional restrictions -in linguistics. We first present a mathematical model -of the notion, and then integrate it in a linguistically -motivated syntax. -
--In linguistics, a -grammar is usually thought of as being about syntactic well-formedness -in a rather liberal sense: an expression can be well-formed without -being meaningful, in other words, without being -semantically well-formed. -For instance, the sentence -
-- the number 2 is equilateral --
-is syntactically well-formed but semantically ill-formed. -It is well-formed because it combines a well-formed -noun phrase ("the number 2") with a well-formed -verb phrase ("is equilateral") and satisfies the agreement -rule saying that the verb phrase is inflected in the -number of the noun phrase: -
-
- fun PredVP : NP -> VP -> S ;
- lin PredVP np v = {s = np.s ++ vp.s ! np.n} ;
-
--It is ill-formed because the predicate "is equilateral" -is only defined for triangles, not for numbers. -
--In a straightforward type-theoretical formalization of -mathematics, domains of mathematical objects -are defined as types. In GF, we could write -
-- cat Nat ; - cat Triangle ; - cat Prop ; --
-for the types of natural numbers, triangles, and propositions,
-respectively.
-Noun phrases are typed as objects of basic types other than
-Prop, whereas verb phrases are functions from basic types
-to Prop. For instance,
-
- fun two : Nat ; - fun Even : Nat -> Prop ; - fun Equilateral : Triangle -> Prop ; --
-With these judgements, and the linearization rules -
-- lin two = ss ["the number 2"] ; - lin Even x = ss (x.s ++ ["is even"]) ; - lin Equilateral x = ss (x.s ++ ["is equilateral"]) ; --
-we can form the proposition Even two
-
- the number 2 is even --
-but no proposition linearized to -
-- the number 2 is equilateral --
-since Equilateral two is not a well-formed type-theoretical object.
-It is not even accepted by the context-free parser.
-
-When formalizing mathematics, e.g. in the purpose of -computer-assisted theorem proving, we are certainly interested -in semantic well-formedness: we want to be sure that a proposition makes -sense before we make the effort of proving it. The straightforward typing -of nouns and predicates shown above is the way in which this -is guaranteed in various proof systems based on type theory. -(Notice that it is still possible to form false propositions, -e.g. "the number 3 is even". -False and meaningless are different things.) -
-
-As shown by the linearization rules for two, Even,
-etc, it is possible to use straightforward mathematical typings
-as the abstract syntax of a grammar. However, this syntax is not very
-expressive linguistically: for instance, there is no distinction between
-adjectives and verbs. It is hard to give rules for structures like
-adjectival modification ("even number") and conjunction of predicates
-("even or odd").
-
-By using dependent types, it is simple to combine a linguistically -motivated system of categories with mathematically motivated -type restrictions. What we need is a category of domains of -individual objects, -
-- cat Dom --
-and dependencies of other categories on this: -
-- cat - S ; -- sentence - V1 Dom ; -- one-place verb with specific subject type - V2 Dom Dom ; -- two-place verb with specific subject and object types - A1 Dom ; -- one-place adjective - A2 Dom Dom ; -- two-place adjective - NP Dom ; -- noun phrase for an object of specific type - Conj ; -- conjunction - Det ; -- determiner --
-Having thus parametrized categories on domains, we have to reformulate -the rules of predication, etc, accordingly. This is straightforward: -
-- fun - PredV1 : (A : Dom) -> NP A -> V1 A -> S ; - ComplV2 : (A,B : Dom) -> V2 A B -> NP B -> V1 A ; - DetCN : Det -> (A : Dom) -> NP A ; - ModA1 : (A : Dom) -> A1 A -> Dom ; - ConjS : Conj -> S -> S -> S ; - ConjV1 : (A : Dom) -> Conj -> V1 A -> V1 A -> V1 A ; --
-In linearization rules, -we use wildcards for the domain arguments, -because they don't affect linearization: -
-- lin - PredV1 _ np vp = ss (np.s ++ vp.s) ; - ComplV2 _ _ v2 np = ss (v2.s ++ np.s) ; - DetCN det cn = ss (det.s ++ cn.s) ; - ModA1 cn a1 = ss (a1.s ++ cn.s) ; - ConjS conj s1 s2 = ss (s1.s ++ conj.s ++ s2.s) ; - ConjV1 _ conj v1 v2 = ss (v1.s ++ conj.s ++ v2.s) ; --
-The domain arguments thus get suppressed in linearization. -Parsing initially returns metavariables for them, -but type checking can usually restore them -by inference from those arguments that are not suppressed. -
--One traditional linguistic example of domain restrictions -(= selectional restrictions) is the contrast between the two sentences -
-- John plays golf - golf plays John --
-To explain the contrast, we introduce the functions -
-- human : Dom ; - game : Dom ; - play : V2 human game ; - John : NP human ; - Golf : NP game ; --
-Both sentences still pass the context-free parser,
-returning trees with lots of metavariables of type Dom:
-
- PredV1 ?0 John (ComplV2 ?1 ?2 play Golf) - PredV1 ?0 Golf (ComplV2 ?1 ?2 play John) --
-But only the former sentence passes the type checker, which moreover -infers the domain arguments: -
-- PredV1 human John (ComplV2 human game play Golf) --
-To try this out in GF, use pt = put_term with the tree transformation
-that solves the metavariables by type checking:
-
- > p -tr "John plays golf" | pt -transform=solve - > p -tr "golf plays John" | pt -transform=solve --
-In the latter case, no solutions are found. -
--A known problem with selectional restrictions is that they can be more -or less liberal. For instance, -
-- John loves Mary - John loves golf --
-should both make sense, even though Mary and golf
-are of different types. A natural solution in this case is to
-formalize love as a polymorphic verb, which takes
-a human as its first argument but an object of any type as its second
-argument:
-
- fun love : (A : Dom) -> V2 human A ; - lin love _ = ss "loves" ; --
-In other words, it is possible for a human to love anything. -
-
-A problem related to polymorphism is subtyping: what
-is meaningful for a human is also meaningful for
-a man and a woman, but not the other way round.
-One solution to this is coercions: functions that
-"lift" objects from subtypes to supertypes.
-
Perhaps the most well-known idea in constructive type theory is the Curry-Howard isomorphism, also known as the @@ -2892,12 +3832,12 @@ a number y. Our definition is based on two axioms:
Zero is less than Succ y for any y.
-Succ x is less than Succ y.
+Succ x is less than Succ y.
The most straightforward way of expressing these axioms in type theory
-is as typing judgements that introduce objects of a type Less //x y //:
+is as typing judgements that introduce objects of a type Less x y:
cat Less Nat Nat ;
@@ -2927,8 +3867,7 @@ which is the formalization of the proposition that 2 is less than 4.
GF grammars can be used to provide a semantic control of
well-formedness of expressions. We have already seen examples of this:
-the grammar of well-formed addresses and the grammar with
-selectional restrictions above. By introducing proof objects
+the grammar of well-formed actions on household devices. By introducing proof objects
we have now added a very powerful technique of expressing semantic conditions.
@@ -2953,8 +3892,21 @@ by using the Less predicate:
cat Span ;
fun span : (m,n : Nat) -> Less m n -> Span ;
+
-A possible practical application of this idea is proof-carrying documents: +Exercise. Write an abstract and concrete syntax with the +concepts of this section, and experiment with it in GF. +
++Exercise. Define the notions of "even" and "odd" in terms +of proof objects. Hint. You need one function for proving +that 0 is even, and two other functions for propagating the +properties. +
+ ++Another possible application of proof objects is proof-carrying documents: to be semantically well-formed, the abstract syntax of a document must contain a proof of some property, although the proof is not shown in the concrete document. Think, for instance, of small documents describing flight connections: @@ -2975,9 +3927,12 @@ The well-formedness of this text is partly expressible by dependent typing: OK0537 : Flight Frankfurt Prague ;
-This rules out texts saying take OK0537 from Gothenburg to Prague. However, there is a -further condition saying that it must be possible to change from LH3043 to OK0537 in Frankfurt. -This can be modelled as a proof object of a suitable type, which is required by the constructor +This rules out texts saying take OK0537 from Gothenburg to Prague. +However, there is a +further condition saying that it must be possible to +change from LH3043 to OK0537 in Frankfurt. +This can be modelled as a proof object of a suitable type, +which is required by the constructor that connects flights.
@@ -2989,10 +3944,65 @@ that connects flights.
IsPossible x y z u v -> Flight x z ;
-
-
-Mathematical notation and programming languages have lots of
+In the first version of the smart house grammar Smart,
+all Actions were either of
+
+To make this scale up for new Kinds, we can refine this to +restricted polymorphism: defined for Kinds of a certain class +
++The notion of class can be expressed in abstract syntax +by using the Curry-Howard isomorphism as follows: +
+
+Here is an example with switching and dimming. The classes are called
+switchable and dimmable.
+
+ cat + Switchable Kind ; + Dimmable Kind ; + fun + switchable_light : Switchable light ; + switchable_fan : Switchable fan ; + dimmable_light : Dimmable light ; + + switchOn : (k : Kind) -> Switchable k -> Action k ; + dim : (k : Kind) -> Dimmable k -> Action k ; ++
+One advantage of this formalization is that classes for new +actions can be added incrementally. +
+
+Exercise. Write a new version of the Smart grammar with
+classes, and test it in GF.
+
+Exercise. Add some actions, kinds, and classes to the grammar. +Try to port the grammar to a new language. You will probably find +out that restricted polymorphism works differently in different languages. +For instance, in Finnish not only doors but also TVs and radios +can be "opened", which means switching them on. +
+ ++Mathematical notation and programming languages have expressions that bind variables. For instance, a universally quantifier proposition
@@ -3013,6 +4023,8 @@ instance, the function that for any numbers x and y returns the maximum of x+y and x*y + + Let x be a natural number. Assume that x is even. Then x + 3 is odd.In type theory, variable-binding expression forms can be formalized @@ -3041,7 +4053,6 @@ which corresponds to the ordinary notation
(All x)(x = x).
-
An abstract syntax where trees have functions as arguments, as in the two examples above, has turned out to be precisely the right @@ -3135,7 +4146,6 @@ Thus we can compute the linearization of the formula,
All (\x -> Eq x x) --> {s = "[( All x ) ( x = x )]"}.
-
How did we get the linearization of the variable x
into the string "x"? GF grammars have no rules for
@@ -3157,8 +4167,22 @@ is defined in the lexical analysis part of GF parsing
(see more details on lexers below). If several variables are bound in the
same argument, the labels are $0, $1, $2, etc.
+Exercise. Write an abstract syntax of the whole +predicate calculus, with the +connectives "and", "or", "implies", and "not", and the +quantifiers "exists" and "for all". Use higher-order functions +to guarantee that unbounded variables do not occur. +
++Exercise. Write a concrete syntax for your favourite +notation of predicate calculus. Use Latex as target language +if you want nice output. You can also try producing Haskell boolean +expressions. Use as many parenthesis as you need to +guarantee non-ambiguity. +
+ +We have seen that, just like functional programming languages, GF has declarations @@ -3323,79 +4347,55 @@ which is equivalent to the two judgements data Nat = Succ ;
- -
-Transfer means noncompositional tree-transforming operations.
-The command apply_transfer = at is typically used in a pipe:
-
- > p "John walks and John runs" | apply_transfer aggregate | l - John walks and runs --
-See the -sources of this example. +Exercise. Implement an interpreter of a small functional programming +language with natural numbers, lists, pairs, lambdas, etc. Use higher-order +abstract syntax with semantic definitions. As target language, use +your favourite programming language.
-See the -transfer language documentation -for more information. +Exercise. To make your interpreted language look nice, use +precedences instead of putting parentheses everywhere. +You can use the precedence library +of GF to facilitate this.
- -
Lexers and unlexers can be chosen from
a list of predefined ones, using the flags-lexer and `` -unlexer`` either
-in the grammar file or on the GF command line.
-
-Given by help -lexer, help -unlexer:
+in the grammar file or on the GF command line. Here are some often-used lexers
+and unlexers:
- The default is words. - -lexer=words tokens are separated by spaces or newlines - -lexer=literals like words, but GF integer and string literals recognized - -lexer=vars like words, but "x","x_...","$...$" as vars, "?..." as meta - -lexer=chars each character is a token - -lexer=code use Haskell's lex - -lexer=codevars like code, but treat unknown words as variables, ?? as meta - -lexer=text with conventions on punctuation and capital letters - -lexer=codelit like code, but treat unknown words as string literals - -lexer=textlit like text, but treat unknown words as string literals - -lexer=codeC use a C-like lexer - -lexer=ignore like literals, but ignore unknown words - -lexer=subseqs like ignore, but then try all subsequences from longest + The default is words. + -lexer=words tokens are separated by spaces or newlines + -lexer=literals like words, but GF integer and string literals recognized + -lexer=vars like words, but "x","x_...","$...$" as vars, "?..." as meta + -lexer=chars each character is a token + -lexer=code use Haskell's lex + -lexer=codevars like code, but treat unknown words as variables, ?? as meta + -lexer=text with conventions on punctuation and capital letters + -lexer=codelit like code, but treat unknown words as string literals + -lexer=textlit like text, but treat unknown words as string literals - The default is unwords. - -unlexer=unwords space-separated token list (like unwords) - -unlexer=text format as text: punctuation, capitals, paragraph <p> - -unlexer=code format as code (spacing, indentation) - -unlexer=textlit like text, but remove string literal quotes - -unlexer=codelit like code, but remove string literal quotes - -unlexer=concat remove all spaces - -unlexer=bind like identity, but bind at "&+" + The default is unwords. + -unlexer=unwords space-separated token list (like unwords) + -unlexer=text format as text: punctuation, capitals, paragraph <p> + -unlexer=code format as code (spacing, indentation) + -unlexer=textlit like text, but remove string literal quotes + -unlexer=codelit like code, but remove string literal quotes + -unlexer=concat remove all spaces- - -
-Issues:
+More options can be found by help -lexer and help -unlexer:
lincats
-optimize flag
--fcfg vs. others
-
-Thespeak_aloud = sa command sends a string to the speech
+The speak_aloud = sa command sends a string to the speech
synthesizer
Flite.
It is typically used via a pipe:
@@ -3422,8 +4422,8 @@ The method words only for grammars of English.
Both Flite and ATK are freely available through the links
above, but they are not distributed together with GF.
The Editor User Manual @@ -3433,19 +4433,20 @@ describes the use of the editor, which works for any multilingual GF grammar. Here is a snapshot of the editor:
+
+
The grammars of the snapshot are from the Letter grammar package.
- --Forthcoming. -
- -Other processes can communicate with the GF command interpreter, and also with the GF syntax editor. Useful flags when invoking GF are @@ -3453,52 +4454,401 @@ and also with the GF syntax editor. Useful flags when invoking GF are
-batch suppresses the promps and structures the communication with XML tags.
-s suppresses non-output non-error messages and XML tags.
--- -nocpu suppresses CPU time indication.
-
+-nocpu suppresses CPU time indication.
+Thus the most silent way to invoke GF is +
gf -batch -s -nocpu
-
-
-
-GF grammars can be used as parts of programs written in the -following languages. The links give more documentation. +following languages. We will go through a skeleton application in +Haskell, while the next chapter will show how to build an +application in Java. +
++We will show how to build a minimal resource grammar +application whose architecture scales up to much +larger applications. The application is run from the +shell by the command +
++ math ++
+whereafter it reads user input in English and French. +To each input line, it answers by the truth value of +the sentence. +
++ ./math + zéro est pair + True + zero is odd + False + zero is even and zero is odd + False ++
+The source of the application consists of the following +files: +
++ LexEng.gf -- English instance of Lex + LexFre.gf -- French instance of Lex + Lex.gf -- lexicon interface + Makefile -- a makefile + MathEng.gf -- English instantiation of MathI + MathFre.gf -- French instantiation of MathI + Math.gf -- abstract syntax + MathI.gf -- concrete syntax functor for Math + Run.hs -- Haskell Main module ++
+The system was built in 22 steps explained below. +
+ +
+1. Write Math.gf, which defines what you want to say.
+
+ abstract Math = {
+ cat Prop ; Elem ;
+ fun
+ And : Prop -> Prop -> Prop ;
+ Even : Elem -> Prop ;
+ Zero : Elem ;
+ }
+
+
+2. Write Lex.gf, which defines which language-dependent
+parts are needed in the concrete syntax. These are mostly
+words (lexicon), but can in fact be any operations. The definitions
+only use resource abstract syntax, which is opened.
+
+ interface Lex = open Syntax in {
+ oper
+ even_A : A ;
+ zero_PN : PN ;
+ }
+
+
+3. Write LexEng.gf, the English implementation of Lex.gf
+This module uses English resource libraries.
+
+ instance LexEng of Lex = open GrammarEng, ParadigmsEng in {
+ oper
+ even_A = regA "even" ;
+ zero_PN = regPN "zero" ;
+
+ }
+
+
+4. Write MathI.gf, a language-independent concrete syntax of
+Math.gf. It opens interfaces.
+which makes it an incomplete module, aka. parametrized module, aka.
+functor.
+
+ incomplete concrete MathI of Math =
+
+ open Syntax, Lex in {
+
+ flags startcat = Prop ;
+
+ lincat
+ Prop = S ;
+ Elem = NP ;
+ lin
+ And x y = mkS and_Conj x y ;
+ Even x = mkS (mkCl x even_A) ;
+ Zero = mkNP zero_PN ;
+ }
+
+
+5. Write MathEng.gf, which is just an instatiation of MathI.gf,
+replacing the interfaces by their English instances. This is the module
+that will be used as a top module in GF, so it contains a path to
+the libraries.
+
+ instance LexEng of Lex = open SyntaxEng, ParadigmsEng in {
+ oper
+ even_A = mkA "even" ;
+ zero_PN = mkPN "zero" ;
+ }
+
+
+
++6. Test the grammar in GF by random generation and parsing. +
++ $ gf + > i MathEng.gf + > gr -tr | l -tr | p + And (Even Zero) (Even Zero) + zero is evenand zero is even + And (Even Zero) (Even Zero) ++
+When importing the grammar, you will fail if you haven't
GF_LIB_PATH as GF/lib
+make in GF/lib/resource-1.0
-A summary is given in the following chart of GF grammar compiler phases:
-
+7. Now it is time to add a new language. Write a French lexicon LexFre.gf:
+ instance LexFre of Lex = open SyntaxFre, ParadigmsFre in {
+ oper
+ even_A = mkA "pair" ;
+ zero_PN = mkPN "zéro" ;
+ }
+
-Formal and Informal Software Specifications,
-PhD Thesis by
-Kristofer Johannisson, is an extensive example of this.
-The system is based on a multilingual grammar relating the formal language OCL with
-English and German.
+8. You also need a French concrete syntax, MathFre.gf:
+
+ --# -path=.:present:prelude + + concrete MathFre of Math = MathI with + (Syntax = SyntaxFre), + (Lex = LexFre) ; ++
+9. This time, you can test multilingual generation: +
++ > i MathFre.gf + > gr | tb + Even Zero + zéro est pair + zero is even ++ + +
+10. You want to add a predicate saying that a number is odd.
+It is first added to Math.gf:
+
+ fun Odd : Elem -> Prop ; ++
+11. You need a new word in Lex.gf.
+
+ oper odd_A : A ; ++
+12. Then you can give a language-independent concrete syntax in
+MathI.gf:
+
+ lin Odd x = mkS (mkCl x odd_A) ; ++
+13. The new word is implemented in LexEng.gf.
+
+ oper odd_A = mkA "odd" ; ++
+14. The new word is implemented in LexFre.gf.
+
+ oper odd_A = mkA "impair" ; ++
+15. Now you can test with the extended lexicon. First empty +the environment to get rid of the old abstract syntax, then +import the new versions of the grammars. +
++ > e + > i MathEng.gf + > i MathFre.gf + > gr | tb + And (Odd Zero) (Even Zero) + zéro est impair et zéro est pair + zero is odd and zero is even ++ + +
+16. Your grammar is going to be used by persons whMathEng.gfo do not need
+to compile it again. They may not have access to the resource library,
+either. Therefore it is advisable to produce a multilingual grammar
+package in a single file. We call this package math.gfcm and
+produce it, when we have MathEng.gf and
+MathEng.gf in the GF state, by the command
+
+ > pm | wf math.gfcm ++ + +
+17. Write the Haskell main file Run.hs. It uses the EmbeddedAPI
+module defining some basic functionalities such as parsing.
+The answer is produced by an interpreter of trees returned by the parser.
+
+ module Main where + + import GSyntax + import GF.Embed.EmbedAPI + + main :: IO () + main = do + gr <- file2grammar "math.gfcm" + loop gr + + loop :: MultiGrammar -> IO () + loop gr = do + s <- getLine + interpret gr s + loop gr + + interpret :: MultiGrammar -> String -> IO () + interpret gr s = do + let tss = parseAll gr "Prop" s + case (concat tss) of + [] -> putStrLn "no parse" + t:_ -> print $ answer $ fg t + + answer :: GProp -> Bool + answer p = case p of + (GOdd x1) -> odd (value x1) + (GEven x1) -> even (value x1) + (GAnd x1 x2) -> answer x1 && answer x2 + + value :: GElem -> Int + value e = case e of + GZero -> 0 ++ +
+18. The syntax trees manipulated by the interpreter are not raw
+GF trees, but objects of the Haskell datatype GProp.
+From any GF grammar, a file GFSyntax.hs with
+datatypes corresponding to its abstract
+syntax can be produced by the command
+
+ > pg -printer=haskell | wf GSyntax.hs ++
+The module also defines the overloaded functions
+gf and fg for translating from these types to
+raw trees and back.
+
+19. Before compiling Run.hs, you must check that the
+embedded GF modules are found. The easiest way to do this
+is by two symbolic links to your GF source directories:
+
+ $ ln -s /home/aarne/GF/src/GF + $ ln -s /home/aarne/GF/src/Transfer/ ++ +
+20. Now you can run the GHC Haskell compiler to produce the program. +
++ $ ghc --make -o math Run.hs ++
+The program can be tested with the command ./math.
+
+21. For a stand-alone binary-only distribution, only
+the two files math and math.gfcm are needed.
+For a source distribution, the files mentioned in
+the beginning of this documents are needed.
+
+22. As a part of the source distribution, a Makefile is
+essential. The Makefile is also useful when developing the
+application. It should always be possible to build an executable
+from source by typing make. Here is a minimal such Makefile:
+
+ all: + echo "pm | wf math.gfcm" | gf MathEng.gf MathFre.gf + echo "pg -printer=haskell | wf GSyntax.hs" | gf math.gfcm + ghc --make -o math Run.hs ++ + +
+Forthcoming; at the moment, the document
-A simpler example will be explained here.
+ http://www.cs.chalmers.se/~bringert/gf/gf-java.html
-See TALK project deliverables, TALK homepage +by Björn Bringert gives more information on Java. +
+ ++Syntax Editor User Manual: +
+
+http://www.cs.chalmers.se/~aarne/GF2.0/doc/javaGUImanual/javaGUImanual.htm
+
+Resource Grammar Synopsis (on using resource grammars): +
+
+http://www.cs.chalmers.se/~aarne/GF/lib/resource-1.0/synopsis.html
+
+Resource Grammar HOWTO (on writing resource grammars): +
+
+http://www.cs.chalmers.se/~aarne/GF/lib/resource-1.0/synopsis.html
+
+GF Homepage: +
+ - +