{-

Print out a list of small semiprimes.

Copyright 2021 Ken Takusagawa

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.

-}
{-# LANGUAGE ScopedTypeVariables, LambdaCase #-}
module Main where {
import System.Environment(getArgs);
import Control.Exception(assert);
import Debug.Trace(trace);
import Data.Function((&));
import Control.Category((>>>));
import Prelude hiding((.),(>>));
--import System.IO(hSetBuffering,stdout,BufferMode(LineBuffering));
import Data.List;
--import Control.Monad;
--import Data.Maybe;
--import qualified Data.Map as Map; import Data.Map(Map);
--import qualified Data.Set as Set; import Data.Set(Set);
--import qualified Data.Bifunctor as Bifunctor;
import Primality2(primes);
import qualified Data.List.Ordered as Ordered;


-- to avoid the redundancy warning
trace_placeholder :: ();
trace_placeholder = (trace,assert) & (id >>> error) "trace_placeholder";

main :: IO();
main = getArgs >>= \case{
[] -> semiprimes & take 1000 & out;
[n] -> semiprimes & take (read n) & out;
_ -> undefined;
};

trim_list :: [Integer] -> [Integer];
trim_list l = takeWhile (\x -> x < 2*head l) l;

form_products :: [Integer] -> [Prod];
form_products l = map (\x -> Prod (head l) x) l;

data Prod = Prod Integer Integer;

val :: Prod -> Integer;
val (Prod x y) = x*y;

instance Eq Prod where{
(==) x y = val x == val y;
};

instance Ord Prod where{
compare x y = compare (val x)(val y);
};

instance Show Prod where{
showsPrec _precedence p@(Prod x y) rest = show (val p) ++ "=" ++ show x ++ "*" ++ show y ++ rest;
};

semiprimelists :: [[Integer]];
semiprimelists = primes () & tails & map trim_list;

semiprimes :: [Prod];
semiprimes = semiprimelists & map form_products & Ordered.mergeAll;

out :: [Prod] -> IO ();
--out = map show >>> unwords >>> putStrLn;
out = mapM_ print;
} --end