-- FILE: ratDiv.mod
-- COMMENT: examples of subsorts and err sorts

show RAT
select RAT
describe all sorts

-- ...
--  NzNat, NzNat < NzInt Nat
--  Nat, Zero NzNat < Nat < Int
--  Zero, Zero < Nat
--  Int, NzInt Nat < Int < Rat
--  NzInt, NzNat < NzInt < NzRat Int
--  Rat, NzRat Int < Rat
--  NzRat, NzInt < NzRat < Rat
--
--         ?Rat                    
--           |                      
--          Rat                    
--    /              \              
--  NzRat           Int            
--   |          /           \        
--  #0       #0=NzInt       Nat      
--              |       /       \    
--             #1     Zero  #1=NzNat

-- opening RAT
open RAT

-- check arity, co-arity, 
-- and attribute of the operation _/_
-- by opening modules 
-- you can see the precedence of a operator
show op _/_

-- test for _/_

-- erro supper sort
parse  2 / 0 .

parse  4 / 2 .
parse  4/2 .
reduce 4 / 2 .

parse  6 / 4 .
reduce 6 / 4 .

parse  3 / 4 .
parse  3/4 .
reduce 3 / 4 .

-- dynamic type checking

parse  (3 / 2) + (1 / 2) .
reduce (3 / 2) + (1 / 2) .
reduce ((3 / 2) + (1 / 2)) :is Nat .

parse  2 / ((3 / 2) + (1 / 2)) .
reduce 2 / ((3 / 2) + (1 / 2)) .
reduce (2 / ((3 / 2) + (1 / 2))) :is Nat .

close