# GF Quick Reference

Aarne Ranta
April 4, 2006

- A complete example
- Modules and files
- Judgements
- Types
- Expressions
- Pattern matching
- Sample library functions
- Flags
- File paths
- Alternative grammar formats
- References

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,

- 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 paths

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.

### 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

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