A transition during greedy parsing. Augments transition data with a flag that indicates whether the transition is a transitive right (2nd) parent of a spread.

The state of the greedy parse between steps. Generally, the current reduction consists of frozen transitions between the ⋊ and the current location and open transitions between the current location and ⋉.

⋊==[1]==[2]==[3]——[4]——[5]——⋉
  └ frozen  ┘  | └   open  ┘
            midSlice (current position)

frozen:   ==[2]==[1]==
midSlice: [3]
open:     ——[4]——[5]——

This is the GSSemiOpen case: The slice at the current pointer ([3]) is represented as an individual slice (midSlice). The frozen part is represented by a Path of frozen transitions (tr') and slices (slc). in reverse direction, i.e. from midslice back to ⋊ (excluding ⋊). The open part is a Path of open transitions (tr) and slices (slc) in forward direction from midSlice up to ⋉.

There are two special cases. All transitions can be frozen (GSFrozen), in which case state only contains the backward Path of frozen transitions (excluding ⋊ and ⋉):

⋊==[1]==[2]==[3]==⋉
                   └ current position
represented as: ==[3]==[2]==[1]==

Or all transitions can be open (GSOpen), in which case the state is just the forward path of open transitions:

⋊——[1]——[2]——[3]——⋉
└ current position
represented as: ——[1]——[2]——[3]——

The open and semiopen case additionally have a list of operations in generative order.

Helper function for showing the frozen part of a piece.

Helper function for showing the open part of a piece.

A parsing action (reduction step) with a single parent transition. Combines the parent elements with a single-transition derivation operation.

A parsing action (reduction step) with two parent transitions. Combines the parent elements with a double-transition derivation operation.

An alias that combines ActionSingle and ActionDouble, representing all possible reduction steps.

Parse a piece in a greedy fashion. At each step, a policy chooses from the possible reduction actions, the reduction is applied, and parsing continues until the piece is fully reduced or no more reduction operations are available. Returns the full derivation from the top (⋊——⋉) or an error message.

A policy that picks the next action at random. Must be partially applied with a random generator before passing to parseGreedy.

Parse a piece randomly using a fresh random number generator.

Parse a piece randomly using an existing random number generator.