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.
Help on GF commands is obtained on line by the
help command (help), and help on invoking
GF with (gf -help).
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
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.
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
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.
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}
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
-- 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 can appear, with growing priority,
flags and without dash (-)
gf when invoked, 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.
Colon-separated lists of directories searched in the given order:
--# -path=.:../abstract:../common:prelude
This can be (in order of growing preference), as
first line in the top file, as flag to gf
when invoked, or as flag to the i command.
The prefix --# is used only in files.
If the environment variabls GF_LIB_PATH is defined, its
value is automatically prefixed to each directory to
extend the original search path.
Old GF (before GF 2.0):
all judgements in any kinds of modules,
division into files uses includes.
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.
A. Ranta, Grammatical Framework: A Type-Theoretical Grammar Formalism. The Journal of Functional Programming, vol. 14:2. 2004, pp. 145-189.