Newtype wrapper that represents \( \mathbb{Z}/n\mathbb{Z} \). ModN is a Ring i.e. supports addition, subtraction, and multiplication.

When constructing a ModN n a we must verify that the type a is large enough to accommodate n, hence the possible failure.

Examples

>>> import Data.Text.Display (display)
>>> display $ unsafeModN @7 10
"3 (mod 7)"

Since: 0.1

Constructor for ModN.

Examples

>>> mkModN @5 7
Right (MkModN 2 (mod 5))

>>> mkModN @10 7
Right (MkModN 7 (mod 10))

>>> mkModN @128 (9 :: Int8)
Left "Type 'Int8' has a maximum size of 127. This is not large enough to safely implement mod 128."

Since: 0.1

Template haskell for creating a ModN at compile-time.

Examples

>>> $$(mkModNTH @11 7)
MkModN 7 (mod 11)

Since: 0.1

Variant of mkModN that throws an error when type a is not large enough to fit n.

WARNING: Partial

Examples

>>> unsafeModN @7 12
MkModN 5 (mod 7)

Since: 0.1

This function reduces the argument modulo p but does not check that n fits within a. Note that correct behavior requires this, so this is dangerous. This is intended only for when we absolutely know n fits in a and the check is undesirable for performance reasons. Exercise extreme caution.

Since: 0.1

Since: 0.1

ReversedPrism' that enables total elimination and partial construction.

Examples

>>> import Optics.Core (view)
>>> n = $$(mkModNTH @7 9)
>>> view _MkModN n
2

>>> rmatching (_MkModN @7) 9
Right (MkModN 2 (mod 7))

>>> rmatching (_MkModN @128) (9 :: Int8)
Left 9

Since: 0.1

Reversed matching. Useful with smart-constructor optics.

Since: 0.1