Numeral.html

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<i> Produced by 
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (aarne@cs.chalmers.se) 2002 under GNU GPL.
 </i>
<p>
<h1> Numerals</h1>

This grammar defines numerals from 1 to 999999. 
The implementations are adapted from the
[numerals library http://www.cs.chalmers.se/~aarne/GF/examples/numerals/] 
which defines numerals for 88 languages.
The resource grammar implementations add to this inflection (if needed)
and ordinal numbers.
<p>
<b>Note</b> 1. Number 1 as defined 
in the category <tt>Numeral</tt> here should not be used in the formation of
noun phrases, and should therefore be removed. Instead, one should use
[Structural Structural.html]<tt>.one_Quant</tt>. This makes the grammar simpler
because we can assume that numbers form plural noun phrases.
<p>
<b>Note</b> 2. The implementations introduce spaces between
parts of a numeral, which is often incorrect - more work on
(un)lexing is needed to solve this problem.
<pre>
  abstract Numeral = Cat [Numeral,Digits] ** {
  
  cat 
    Digit ;       -- 2..9
    Sub10 ;       -- 1..9
    Sub100 ;      -- 1..99
    Sub1000 ;     -- 1..999
    Sub1000000 ;  -- 1..999999
  
  data 
    num : Sub1000000 -> Numeral ;
  
    n2, n3, n4, n5, n6, n7, n8, n9 : Digit ;
  
    pot01 : Sub10 ;                               -- 1
    pot0 : Digit -> Sub10 ;                       -- d * 1
    pot110 : Sub100 ;                             -- 10
    pot111 : Sub100 ;                             -- 11
    pot1to19 : Digit -> Sub100 ;                  -- 10 + d
    pot0as1 : Sub10 -> Sub100 ;                   -- coercion of 1..9
    pot1 : Digit -> Sub100 ;                      -- d * 10
    pot1plus : Digit -> Sub10 -> Sub100 ;         -- d * 10 + n
    pot1as2 : Sub100 -> Sub1000 ;                 -- coercion of 1..99
    pot2 : Sub10 -> Sub1000 ;                     -- m * 100
    pot2plus : Sub10 -> Sub100 -> Sub1000 ;       -- m * 100 + n
    pot2as3 : Sub1000 -> Sub1000000 ;             -- coercion of 1..999
    pot3 : Sub1000 -> Sub1000000 ;                -- m * 1000
    pot3plus : Sub1000 -> Sub1000 -> Sub1000000 ; -- m * 1000 + n
</pre>

Numerals as sequences of digits have a separate, simpler grammar
<pre>
  cat 
    Dig ;  -- single digit 0..9
  
  data
    IDig  : Dig -> Digits ;       -- 8
    IIDig : Dig -> Digits -> Digits ; -- 876
  
    D_0, D_1, D_2, D_3, D_4, D_5, D_6, D_7, D_8, D_9 : Dig ;
  
  }
</pre>

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