GF Quick Reference
Aarne Ranta
April 4, 2006

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This is a quick reference on GF grammars. It aims to
cover all forms of expression available when writing
grammars. It assumes basic knowledge of GF, which
can be acquired from the
[GF Tutorial http://www.grammaticalframework.org/doc/tutorial/gf-tutorial.html].
Help on GF commands is obtained on line by the
help command with ``help``, and help on invoking
GF with ``gf -help``.


===A complete example===

This is a complete example of a GF grammar divided
into three modules in files. The grammar recognizes the
phrases //one pizza// and //two pizzas//.

File ``Order.gf``:
```
abstract Order = {
cat
  Order ;
  Item ;
fun
  One, Two : Item -> Order ;
  Pizza : Item ;
}
```
File ``OrderEng.gf`` (the top file):
```
--# -path=.:prelude
concrete OrderEng of Order =
 open Res, Prelude in {
flags startcat=Order ;
lincat
  Order = SS ;
  Item  = {s : Num => Str} ;
lin
  One it = ss ("one" ++ it.s ! Sg) ;
  Two it = ss ("two" ++ it.s ! Pl) ;
  Pizza  = regNoun "pizza" ;
}
```
File ``Res.gf``:
```
resource Res = open Prelude in {
param Num = Sg | Pl ;
oper regNoun : Str -> {s : Num => Str} =
  \dog -> {s = table {
    Sg => dog ;
    _  => dog + "s"
    }
  } ;
}
```
To use this example, do
```
  % gf             -- in shell: start GF
  > i OrderEng.gf  -- in GF: import grammar
  > p "one pizza"  --        parse string
  > l Two Pizza    --        linearize tree
```



===Modules and files===

One module per file.
File named ``Foo.gf`` contains module named
``Foo``.

Each module has the structure
```
moduletypename =
  Inherits **        -- optional
  open Opens in      -- optional
  { Judgements }
```
Inherits are names of modules of the same type.
Inheritance can be restricted:
```
  Mo[f,g],  -- inherit only f,g from Mo
  Lo-[f,g]  -- inheris all but f,g from Lo
```
Opens are possible in ``concrete`` and ``resource``.
They are names of modules of these two types, possibly
qualified:
```
  (M = Mo), -- refer to f as M.f or Mo.f
  (Lo = Lo) -- refer to f as Lo.f
```
Module types and judgements in them:
```
abstract A          -- cat, fun, def, data
concrete C of A     -- lincat, lin, lindef, printname
resource R          -- param, oper

interface I         -- like resource, but can have
                       oper f : T without definition
instance J of I     -- like resource, defines opers
                       that I leaves undefined
incomplete          -- functor: concrete that opens
 concrete CI of A =    one or more interfaces
  open I in ...
concrete CJ of A =  -- completion: concrete that
  CI with              instantiates a functor by
    (I = J)            instances of open interfaces
```
The forms
``param``, ``oper``
may appear in ``concrete`` as well, but are then
not inherited to extensions.

All modules can moreover have ``flags`` and comments.
Comments have the forms
```
-- till the end of line
{- any number of lines between -}
--# used for compiler pragmas
```
A ``concrete`` can be opened like a ``resource``.
It is translated as follows:
```
cat C          --->  oper C : Type =
lincat C = T           T ** {lock_C : {}}

fun f : G -> C --->  oper f : A* -> C* = \g ->
lin f = t              t g ** {lock_C = <>}
```
An ``abstract`` can be opened like an ``interface``.
Any ``concrete`` of it then works as an ``instance``.



===Judgements===

```
cat C               -- declare category C
cat C (x:A)(y:B x)  -- dependent category C
cat C A B           -- same as C (x : A)(y : B)
fun f : T           -- declare function f of type T
def f = t           -- define f as t
def f p q = t       -- define f by pattern matching
data C = f | g      -- set f,g as constructors of C
data f : A -> C     -- same as
                       fun f : A -> C; data C=f

lincat C = T        -- define lin.type of cat C
lin f = t           -- define lin. of fun f
lin f x y = t       -- same as lin f = \x y -> t
lindef C = \s -> t  -- default lin. of cat C
printname fun f = s -- printname shown in menus
printname cat C = s -- printname shown in menus
printname f = s     -- same as printname fun f = s

param P = C | D Q R -- define parameter type P
                       with constructors
                       C : P, D : Q -> R -> P
oper h : T = t      -- define oper h of type T
oper h = t          -- omit type, if inferrable

flags p=v           -- set value of flag p
```
Judgements are terminated by semicolons (``;``).
Subsequent judgments of the same form may share the
keyword:
```
cat C ; D ;         -- same as cat C ; cat D ;
```
Judgements can also share RHS:
```
fun f,g : A         -- same as fun f : A ; g : A
```


===Types===

Abstract syntax (in ``fun``):
```
C                -- basic type, if cat C
C a b            -- basic type for dep. category
(x : A) -> B     -- dep. functions from A to B
(_ : A) -> B     -- nondep. functions from A to B
(p,q : A) -> B   -- same as (p : A)-> (q : A) -> B
A -> B           -- same as (_ : A) -> B
Int              -- predefined integer type
Float            -- predefined float type
String           -- predefined string type
```
Concrete syntax (in ``lincat``):
```
Str              -- token lists
P                -- parameter type, if param P
P => B           -- table type, if P param. type
{s : Str ; p : P}-- record type
{s,t : Str}      -- same as {s : Str ; t : Str}
{a : A} **{b : B}-- record type extension, same as
                    {a : A ; b : B}
A * B * C        -- tuple type, same as
                    {p1 : A ; p2 : B ; p3 : C}
Ints n           -- type of n first integers
```
Resource (in ``oper``): all those of concrete, plus
```
Tok              -- tokens (subtype of Str)
A -> B           -- functions from A to B
Int              -- integers
Strs             -- list of prefixes (for pre)
PType            -- parameter type
Type             -- any type
```
As parameter types, one can use any finite type:
``P`` defined in ``param P``,
``Ints n``, and record types of parameter types.



===Expressions===

Syntax trees = full function applications
```
f a b              -- : C if fun f : A -> B -> C
1977               -- : Int
3.14               -- : Float
"foo"              -- : String
```
Higher-Order Abstract syntax (HOAS): functions as arguments:
```
F a (\x -> c)      -- : C if a : A, c : C (x : B),
                      fun F : A -> (B -> C) -> C
```
Tokens and token lists
```
"hello"            -- : Tok, singleton Str
"hello" ++ "world" -- : Str
["hello world"]    -- : Str, same as "hello" ++ "world"
"hello" + "world"  -- : Tok, computes to "helloworld"
[]                 -- : Str, empty list
```
Parameters
```
Sg                   -- atomic constructor
VPres Sg P2          -- applied constructor
{n = Sg ; p = P3}    -- record of parameters
```
Tables
```
table {              -- by full branches
  Sg => "mouse" ;
  Pl => "mice"
  }
table {              -- by pattern matching
  Pl => "mice" ;
  _  => "mouse"      -- wildcard pattern
  }
table {
  n => regn n "cat"  -- variable pattern
  }
table Num {...}      -- table given with arg. type
table ["ox"; "oxen"] -- table as course of values
\\_ => "fish"        -- same as table {_ => "fish"}
\\p,q => t           -- same as \\p => \\q => t

t ! p                -- select p from table t
case e of {...}      -- same as table {...} ! e
```
Records
```
{s = "Liz"; g = Fem} -- record in full form
{s,t = "et"}         -- same as {s = "et";t= "et"}
{s = "Liz"} **       -- record extension: same as
  {g = Fem}             {s = "Liz" ; g = Fem}

<a,b,c>        -- tuple, same as {p1=a;p2=b;p3=c}
```
Functions
```
\x -> t            -- lambda abstract
\x,y -> t          -- same as \x -> \y -> t
\x,_ -> t          -- binding not in t
```
Local definitions
```
let x : A = d in t -- let definition
let x = d in t     -- let defin, type inferred
let x=d ; y=e in t -- same as
                      let x=d in let y=e in t
let {...} in t     -- same as let ... in t

t where {...}      -- same as let ... in t
```
Free variation
```
variants {x ; y}     -- both x and y possible
variants {}          -- nothing possible
```
Prefix-dependent choices
```
pre {"a" ; "an" / v} -- "an" before v, "a" otherw.
strs {"a" ; "i" ;"o"}-- list of condition prefixes
```
Typed expression
```
<t:T>                -- same as t, to help type inference
```
Accessing bound variables in ``lin``: use fields ``$1, $2, $3,...``.
Example:
```
fun F : (A : Set) -> (El A -> Prop) -> Prop ;
lin F A B = {s = ["for all"] ++ A.s ++ B.$1 ++ B.s}
```


===Pattern matching===

These patterns can be used in branches of ``table`` and
``case`` expressions. Patterns are matched in the order in
which they appear in the grammar.
```
C                 -- atomic param constructor
C p q             -- param constr. applied to patterns
x                 -- variable, matches anything
_                 -- wildcard, matches anything
"foo"             -- string
56                -- integer
{s = p ; y = q}   -- record, matches extensions too
<p,q>             -- tuple, same as {p1=p ; p2=q}
p | q             -- disjunction, binds to first match
x@p               -- binds x to what p matches
- p               -- negation
p + "s"           -- sequence of two string patterns
p*                -- repetition of a string pattern
```

===Sample library functions===

```
-- lib/prelude/Predef.gf
drop   : Int -> Tok -> Tok   -- drop prefix of length
take   : Int -> Tok -> Tok   -- take prefix of length
tk     : Int -> Tok -> Tok   -- drop suffix of length
dp     : Int -> Tok -> Tok   -- take suffix of length
occur  : Tok -> Tok -> PBool -- test if substring
occurs : Tok -> Tok -> PBool -- test if any char occurs
show   : (P:Type) -> P ->Tok -- param to string
read   : (P:Type) -> Tok-> P -- string to param
toStr  : (L:Type) -> L ->Str -- find "first" string

-- lib/prelude/Prelude.gf
param Bool = True | False
oper
  SS  : Type                   -- the type {s : Str}
  ss  : Str -> SS              -- construct SS
  cc2 : (_,_ : SS) -> SS       -- concat SS's
  optStr : Str -> Str          -- string or empty
  strOpt : Str -> Str          -- empty or string
  bothWays : Str -> Str -> Str -- X++Y or Y++X
  init : Tok -> Tok            -- all but last char
  last : Tok -> Tok            -- last char
  prefixSS : Str -> SS -> SS
  postfixSS : Str -> SS -> SS
  infixSS : Str -> SS -> SS -> SS
  if_then_else : (A : Type) -> Bool -> A -> A -> A
  if_then_Str : Bool -> Str -> Str -> Str
```


===Flags===

Flags can appear, with growing priority,
- in files, judgement ``flags`` and without dash (``-``)
- as flags to ``gf`` when invoked, with dash
- as flags to various GF commands, with dash


Some common flags used in grammars:
```
startcat=cat    use this category as default

lexer=literals  int and string literals recognized
lexer=code      like program code
lexer=text      like text: spacing, capitals
lexer=textlit   text, unknowns as string lits

unlexer=code    like program code
unlexer=codelit code, remove string lit quotes
unlexer=text    like text: punctuation, capitals
unlexer=textlit text, remove string lit quotes
unlexer=concat  remove all spaces
unlexer=bind    remove spaces around "&+"

optimize=all_subs  best for almost any concrete
optimize=values    good for lexicon concrete
optimize=all       usually good for resource
optimize=noexpand  for resource, if =all too big
```
For the full set of values for ``FLAG``,
use on-line ``h -FLAG``.



===File import search paths===

Colon-separated list of directories searched in the
given order:
```
--# -path=.:../abstract:../common:prelude
```
This can be (in order of increasing priority), as
first line in the file, as flag to ``gf``
when invoked, or as flag to the ``i`` command.
The prefix ``--#`` is used only in files.

GF attempts to satisfy an ``import`` command by searching for the
import filename in the above search paths, initially qualified
relative to the current working directory. If the file is not found in
that initial expansion, the search paths are re-qualified relative to
the directories given in the ``GF_LIB_PATH`` environment variable. If
``GF_LIB_PATH`` is not defined, its default value is
``/usr/local/share/gf-3.9/lib`` (assuming you have GF version 3.9).

If your GF resource grammar libraries are installed somewhere else,
you will want to set ``GF_LIB_PATH`` to point there instead. In a
pinch, you can point to the ``GF/lib/src/`` folder in your clone of
the GF source code repository.

Developers of resource grammars may find it useful to define multiple
directories, colon-separated, in ``GF_LIB_PATH``.


===Alternative grammar formats===

**Old GF** (before GF 2.0):
all judgements in any kinds of modules,
division into files uses ``include``s.
A file ``Foo.gf`` is recognized as the old format
if it lacks a module header.

**Context-free** (file ``foo.cf``). The form of rules is e.g.
```
Fun. S ::= NP "is" AP ;
```
If ``Fun`` is omitted, it is generated automatically.
Rules must be one per line. The RHS can be empty.

**Extended BNF** (file ``foo.ebnf``). The form of rules is e.g.
```
S ::= (NP+ ("is" | "was") AP | V NP*) ;
```
where the RHS is a regular expression of categories
and quoted tokens: ``"foo", CAT, T U, T|U, T*, T+, T?``, or empty.
Rule labels are generated automatically.


**Probabilistic grammars** (not a separate format).
You can set the probability of a function ``f`` (in its value category) by
```
--# prob f 0.009
```
These are put into a file given to GF using the ``probs=File`` flag
on command line. This file can be the grammar file itself.

**Example-based grammars**  (file ``foo.gfe``). Expressions of the form
```
in Cat "example string"
```
are preprocessed by using a parser given by the flag
```
--# -resource=File
```
and the result is written to ``foo.gf``.


===References===

[GF Homepage http://www.grammaticalframework.org/]

A. Ranta, Grammatical Framework: A Type-Theoretical Grammar Formalism.
//The Journal of Functional Programming//, vol. 14:2. 2004, pp. 145-189.
