# tower

A heirarchy of classes for numbers and algebras that combine them: a numeric tower.

Performance testing, notes and examples can be found in tower-dev.

The tower looks something like:

To use the library:

{-# OPTIONS_GHC -fno-warn-type-defaults #-}
{-# LANGUAGE NoImplicitPrelude #-}
import Tower.Prelude

Tower.Prelude is a drop-in replacement for Prelude. Behind the scenes, it wraps Protolude. Monoid and Semigroup do not exist in the tower, to avoid trampling on base.


main :: IO ()
main = do

To use literal numbers with tower without a type annotation somewhere, type defaulting as per Num needs to be applied to Additive.

:t 1 + 1
1 + 1 :: (Additive a, Num a) => a

tower awaits OverloadedNums to be practical...

  putStrLn $"1 + 1 = " ++ show (1 + 1 :: Int) putStrLn$ "1.0 + 1.0  = " ++ show (1.0 + 1.0 :: Float)

- as a unary function, and a minus literal eg -1 is treated specially by ghc, and also differently to one another.

:t - 1
- 1 :: Num a => a
:t -1
-1 :: Num t => t

The upshot of this, is that the unary function - is not yet hooking into tower, despite (-) and negate being hidden in the import of protolude.

  putStrLn $"-1 = " ++ show (- 1) The binary function - is ok.  putStrLn$ "1 - 1      = " ++ show (1 - 1 :: Int)
putStrLn $"1.0 - 1.0 = " ++ show (1.0 - 1.0 :: Float) putStrLn$ "1 * 1      = " ++ show (1 * 1 :: Int)
putStrLn $"1.0 * 1.0 = " ++ show (1.0 * 1.0 :: Float) putStrLn$ ("1 / 1 is a type error" :: Text)
putStrLn $"1.0 / 1.0 = " ++ show (1.0 / 1.0 :: Float) Using zero and one rather than magical 0s and 1s in code is great practice.  putStrLn$ "zero       = " ++ show (zero :: Float)
putStrLn $"one = " ++ show (one :: Float) BoundedField ensures that divide by zero works. Having said this, actually printing one/zero as Infinity and -one/zero as -Infinity ain't coming from tower.  putStrLn$ "one / zero = " ++ show (one / zero :: Float)
putStrLn \$ "(zero / zero) + one = " ++ show (zero / zero + one :: Float)

## footnotes

stack build --test --exec "pandoc -f markdown+lhs -i examples/examples.lhs -t html -o index.html --filter pandoc-include --mathjax" --exec "pandoc -f markdown+lhs -i examples/examples.lhs -t markdown -o readme.md --filter pandoc-include --mathjax" --exec "echo Yah, it succeeded" --file-watch