GF Quick Reference

Aarne Ranta
April 4, 2006



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).

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,

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 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.

References

GF Homepage

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