GF Quick Reference Aarne Ranta April 4, 2006 % NOTE: this is a txt2tags file. % Create an html file from this file using: % txt2tags -thtml gf-reference.t2t %!style:../css/style.css %!target:html %!options: --toc %!postproc(html): <meta name = "viewport" content = "width = device-width"><TITLE> %!postproc(html): <H1> <H1><a href="../"><IMG src="../doc/Logos/gf0.png"></a> 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 (``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.