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--1 Numerals
-- 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.
--
-- *Note* 1. Number 1 as defined
-- in the category $Numeral$ here should not be used in the formation of
-- noun phrases, and should therefore be removed. Instead, one should use
-- [Structural Structural.html]$.one_Quant$. This makes the grammar simpler
-- because we can assume that numbers form plural noun phrases.
--
-- *Note* 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.
abstract Numeral = Cat ** {
cat
Digit ; -- 2..9
Sub10 ; -- 1..9
Sub100 ; -- 1..99
Sub1000 ; -- 1..999
Sub1000000 ; -- 1..999999
fun
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
-- Numerals as sequences of digits have a separate, simpler grammar
cat
Dig ; -- single digit 0..9
fun
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 ;
}
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