A partially applied score of type s. Comes in four variants, depending on whether the score is fully applied or needs to be combined on either or both sides. Values that need to be combined are lists that represent scores with holes. Each variant carries IDs of type i that determine which objects fit on either of its sides. Only score objects with matching IDs can be combined.

As a shorthand notation, we use a-b to indicate a value that depends on a on its left and on b on its right. If the value does not depend on anything on either side, we use (), i.e. ()-a stands for SLeft _ a and ()-() stands for SVal _.

A type alias for the holes in a Score.

Creates a simple value score of type ()-().

Newtype for the left ID of a partial score.

Newtype for the right ID of a partial score.

Returns the ID on the left side of an Score, or Nothing for SVal and SLeft.

a-b -> a

Returns the ID on the right side of an Score, or Nothing for SVal and SRight.

a-b -> b

Returns a string representation of a Score (more compact than it's Show instance).

Combines two partially applied Scores by applying them to each other and/or multiplying the underlying semiring values. Shapes and IDs at the adjacent sides must match, otherwise Nothing is returned.

a-b × b-c -> a-c

Adds two partially applied Scores by adding their underlying (or resulting) semiring values. This operation is only admitted if the two scores are of the same shape and have matching IDs. Otherwise, Nothing is returned.

a-b + a-b -> a-b

Combines the Scores of two edges with a split operation into the score of the parent edge. This is expected to be called on compatible scores and will throw an error otherwise to indicate parser bugs.

a-b   b-c
--------- unsplit
   a-c

Creates the Score of a left parent edge from a left child edge of an unspread. Will throw an error if called on invalid input to indicate parser bugs.

Creates the Score of a right parent edge from the middle and right child edges of an unspread and a spread operation.

Adds two Scores that are alternative derivations of the same transition. This is expected to be called on compatible scores and will throw an error otherwise to indicate parser bugs.

a-b   a-b
--------- add
   a-b

Extracts the value from a fully applied Score. This function is intended to be used to extract the final score of the parser. If the score is not fully applied, throws an exception to indicate parser bugs.