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1. data Partition a

   elynx-tree	ELynx.Tree.Partition

   A partition of a tree is a grouping of the leaves of the tree into non-overlapping, non-empty sub sets. For unrooted trees:

   • For example, each branch of an unrooted tree partitions the leaves of the tree into two subsets (see Bipartition).
   For rooted trees:
   • In a similar way, each bifurcating internal node (excluding the root node) partitions the leaves into three subsets called a Partition. If the tree is multifurcating, and a specific node has more than two children, the number of subsets induced by this node is larger than three. Partitions are interesting in that we can use them for calculating incompatible splits, see Distance.
   The order of the subsets of a Partition is meaningless. We ensure by construction that the subsets are ordered, and hence, that equality checks are meaningful.

2. module ELynx.Tree.Phylogeny

   Creation date: Thu Jan 17 16:08:54 2019. The purpose of this module is to facilitate usage of Trees in phylogenetic analyses. A phylogeny is a Tree with unique leaf labels, and unordered sub-forest. Using the Tree data type has some disadvantages.

   1. All trees are rooted. Unrooted trees can be treated with a rooted data structure, as it is used here. However, some functions may be meaningless.
   2. Changing branch labels, node labels, or the topology of the tree is slow, especially when the changes are close to the leaves of the tree.
   3. Internally, the underlying Tree data structure stores the sub-forest as an ordered list. Hence, we have to do some tricks when comparing phylogenies (see equal), and comparison is slow.
   4. Uniqueness of the leaves is not ensured by the data type, but has to be checked at runtime. Functions relying on the tree to have unique leaves do perform this check, and return Left with a message, if the tree has duplicate leaves.
   NOTE: Trees are rooted. NOTE: Trees encoded in Newick format correspond to rooted trees. By convention only, a tree parsed from Newick format is usually thought to be unrooted, when the root node is multifurcating and has three or more children. This convention is not used here. Newick trees are just parsed as they are, and a rooted tree is returned.

3. data Phylo

   elynx-tree	ELynx.Tree.Phylogeny

   Branch label for phylogenetic trees. Branches may have a length and a support value. Especially useful to export trees to Newick format; see toNewick.

4. Phylo :: Maybe Length -> Maybe Support -> Phylo

   elynx-tree	ELynx.Tree.Phylogeny

   No documentation available.

5. data PhyloExplicit

   elynx-tree	ELynx.Tree.Phylogeny

   Explicit branch label with branch length and branch support value.

6. PhyloExplicit :: Length -> Support -> PhyloExplicit

   elynx-tree	ELynx.Tree.Phylogeny

   No documentation available.

7. module ELynx.Tree.Simulate.PointProcess

   Creation date: Tue Feb 13 13:16:18 2018. See Gernhard, T. (2008). The conditioned reconstructed process. Journal of Theoretical Biology, 253(4), 769–778. http://doi.org/10.1016/j.jtbi.2008.04.005. The point process can be used to simulate reconstructed trees under the birth and death process.

8. data PointProcess a b

   elynx-tree	ELynx.Tree.Simulate.PointProcess

   A point process for <math> points and of age <math> is defined as follows. Draw $n$ points on the horizontal axis at <math>. Pick <math> points at locations <math>, <math>; <math>. There is a bijection between (ranked) oriented trees and the point process. Usually, a will be String (or Int) and b will be Double.

9. PointProcess :: [a] -> [b] -> b -> PointProcess a b

   elynx-tree	ELynx.Tree.Simulate.PointProcess

   No documentation available.

10. type Path = [Int]

    elynx-tree	ELynx.Tree.Zipper

    Path from the root of a tree to the node of the tree. The position is specific to a tree topology. If the topology changes, the position becomes invalid.

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