Agda.Utils.SemiRing

Documentation

class SemiRing a where

Semirings (https://en.wikipedia.org/wiki/Semiring).

Methods

ozero :: a

oone :: a

oplus :: a -> a -> a

otimes :: a -> a -> a

Instances

SemiRing Weight

SemiRing Occurrence

Occurrence is a complete lattice with least element Mixed and greatest element Unused.

It forms a commutative semiring where oplus is meet (glb) and otimes is composition. Both operations are idempotent.

For oplus, Unused is neutral (zero) and Mixed is dominant. For otimes, StrictPos is neutral (one) and Unused is dominant.

SemiRing Edge

These operations form a semiring if we quotient by the relation "the Occurrence components are equal".

SemiRing a => SemiRing (Maybe a)

class SemiRing a => StarSemiRing a where

Star semirings (https://en.wikipedia.org/wiki/Semiring#Star_semirings).

Methods

ostar :: a -> a

Instances

StarSemiRing Occurrence

StarSemiRing Edge

As OccursWhere does not have an oplus we cannot do something meaningful for the OccursWhere here.

E.g. ostar (Edge JustNeg w) = Edge Mixed (w oplus (w >*< w)) would probably more sense, if we could do it.

StarSemiRing a => StarSemiRing (Maybe a)