• Motivation
• Concepts
• Key contracts
• API
  • breadthFirstTraverseTree :: Lenses -> TraverseSpecs -> Tree -> A
  • preorderTraverseTree :: Lenses -> TraverseSpecs -> Tree -> A
  • postOrderTraverseTree :: Lenses -> TraverseSpecs -> Tree -> A
  • reduceTree :: Lenses -> TraverseSpecs -> Tree -> A
  • forEachInTree :: Lenses -> TraverseSpecs -> Tree -> A
  • mapOverTree :: Lenses -> MapFn -> Tree -> Tree'
  • pruneWhen :: Lenses -> Predicate -> Tree -> Tree
  • visitTree :: ExtendedTraversalSpecs -> Tree -> A
  • switchTreeDataStructure :: Lenses -> Lenses -> Tree
  • traverseObj :: ExtendedTraversalSpecs -> Tree -> A
• Tests
• Build
• Install
• Examples of lenses

Motivation

There is no shortage of libraries for manipulating trees in javascript. Because we seek to focus on general multi-way trees, we have excluded those libraries focusing on specialized trees (i.e. binary search trees, red-black trees, etc.). Also we did not consider the libraries which look at trees from a visualization perspective (for instance jstree), as we focus here on handling the data structure, and providing a few basic operations on it.

Such libraries include, among the most interesting subjects, in order of interest :

• tree-morph : maintained, API features traversal only, free tree format, tree is immutable, allows partial traversal (node skipping), iterative algorithms, incomplete documentation
• tree-crawl : maintained, API features traversal only, free tree format, tree is mutable, claims to be optimized for performance!, nice API for skipping nodes or canceling a traversal, iterative algorithms, incomplete documentation
• tree-model : maintained and contributed to, imperative object-based API, basic operations (traversal, find) together with utility functions (isRoot, etc.) supporting the imperative portion of the API, recursive algorithms, nice demo site!
• arboreal : ancient, no longer maintained, imperative API, imposed tree format, only basic operations
• t-js : ancient, no longer maintained, semi-functional API,, basic but key functional operations (bfs/dfs/post-order traversals, map, filter, find), an interesting addition (stroll) traversing two trees at the same time, imposed tree format
• DataStructures.Tree ; ancient, undocumented, unmaintained

In practice, it seems that few people use a dedicated tree library for manipulating tree-like data structure. Rather, what I saw in the wild is ad-hoc implementations of traversals, which are adjusted to the particular shape of the data at hand. This is understandable as tree traversal algorithms, specially the recursive ones, are trivial to implement (5-10 lines of code).

However :

• iterative algorithms are almost mandatory to process large trees (to avoid exhausting the stack)
• a generic traversal library fosters reuse (in my particular case, I have various tree formats to handle, and it would not be DRY to write the traversal at hand each time for each format)
• a functional library is also nice to guarantee that there is no destructive update of tree nodes, and at the same time allows natural composition and chaining of tree operations
• a well-designed, tested library enhances readability and maintainability

As a conclusion, these are the design choices made for this library :

• manipulation of tree data structure is based on ADT, i.e. not on a specific or concrete data structure as the aforementioned libraries. Those three possible concrete data structures for a tree should be handled by the library just as easily :
  • [root, [left, [middle, [midright, midleft]], right]], or more commonly
  • {label : 'root', children : [{label:'left'}, {label: 'right'}]}.
  • {key0 : {key0.0 : {}, key0.1 : 'something'}, key1 : 2018}
• immutability of tree nodes
• iterative traversal algorithms
• basic operations available : bfs/dfs/post-order traversals, map/reduce/prune(~filter)/find operations
• advanced operations in a future version : find common ancestor(would involve building a zipper), replace, optional : tree diff(hard), some, every (not so useful), transducers (would be amazing)

At the current state of the library, only the basic operations are implemented.

As a bonus, lenses for object traversal are included and allow traversing and mapping over a javascript object (POJO).

Concepts

In computing, a multi-way tree or rose tree is a tree data structure with a variable and unbounded number of branches per node[^1]. The name rose tree for this structure is prevalent in the functional programming community, so we use it here. For instance, a rose tree can be defined in Haskell as follows : data RoseTree a = RoseTree a [RoseTree a].

There is a distinction between a tree as an abstract data type and as a concrete data structure, analogous to the distinction between a list and a linked list. As a data type, a tree has a value (:: a) and children (:: [RoseTree a]), and the children are themselves trees. A linked tree is an example of specific data structure, implementing the abstract data type and is a group of nodes, where each node has a value and a list of references to other nodes (its children). There is also the requirement that no two "downward" references point to the same node.

As an ADT, the abstract tree type T with values of some type E is defined, using the abstract forest type F (list of trees), by the functions:

• value: T → E
• children: T → F
• nil: () → F
• node: E × F → T

with the axioms:

• value(node(e, f)) = e
• children(node(e, f)) = f

In our API, we will use a parameter lenses which will provide an implementation as necessary of the relevant functions :

• getLabel :: T -> E
• getChildren :: T -> F
• constructTree :: E x F -> T
• nil (the empty forest) will be taken by default to be the empty list ([]). A forest being a list of trees, it is convenient that the empty forest be an empty list.

These functions are gathered into the lenses parameter, as, just like lenses, they allow to focus on a portion of a composite data structure. constructTree can be viewed both as a constructor, and as the setter part of a lens on the tree.

For instance, the tree-like object {label : 'root', children : [{label:'left'}, {label: 'right'}]} can be described by the following lenses :

• getLabel = tree => tree.label
• getChildren = tree => tree.children || []
• constructTree = (label, children) => ({label, children})

[^1]: Bird, Richard (1998). Introduction to Functional Programming using Haskell. Hemel Hempstead, Hertfordshire, UK: Prentice Hall Europe. p. 195. ISBN 0-13-484346-0.

The flexibility offered by the abstract data type comes in handy when interpreting abstract syntax trees, whose format is imposed by the parser, and which may vary widely according to the target language and specific parser. The ADT technique also allows for higher reusability.

NOTE : All functions are provided without currying. We paid attention to the order of parameters to facilitate currying for those who will find it convenient. The ramda functional library can be used easily to curry any relevant provided function. NOTE : This API style could also be called interface-passing style

Key contracts

Key types

• Traversal :: BFS | PRE_ORDER | POST_ORDER
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: HashMap<T, State> (the hashmap exposes get and set methods to read and update itself)
• Reducer<A, T, TraversalState> :: A -> TraversalState -> T -> A (reducer may additionally update the traversal state if necessary to implement a given traversal logic)
• TraverseSpecs :: {{strategy :: Optional<Traversal>, seed : A, visit :: Reducer<A, T, TraversalState> }}

Those types can be slightly modified depending on the specific function executed. The meaning of those types is pretty straight-forward. Let's just notice that TraversalState is a map which associates to each node being traversed the state of the traversal, and possibly any extra state that the API consumer might want to add, while traversing. As a matter of fact, the visit function could mutate TraversalState if that would make sense for the situation at end. That mutation would be invisible from outside of the API, as long as none of the mutated state is exported ("If a tree falls in a forest and no one is around to hear it, does it make a sound?").

No node repetition

It is important to note that no tree can repeat the same nodes with sameness defined by referential equality. It is easy to inadvertently repeat the same node :

const tree1  ...;
const tree2 = {label : ..., children : [tree1, tree1]}

While tree2 is a well-formed tree, our library will bug in that case, for reasons due to our specific implementation (nodes are used as keys to keep the traversal state, and keys must be unique). It gets really tricky if your tree somehow can be a javascript primitive, in which case, this contract would mean that all such primitives should have a different value! Tests so far seems to show that 'normal' tree structures do not have this primitive-value-duplication problem.

API

breadthFirstTraverseTree :: Lenses -> TraverseSpecs -> Tree -> A

Description

Traverse a tree breadth-first, applying a reducer while traversing the tree, and returning the final accumulated reduction.

Types

• Tree :: T
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Reducer<A, T, TraversalState> :: A -> TraversalState -> T -> A
• TraverseSpecs :: {{strategy :: Optional<Traversal>, seed : A, visit :: Reducer<A, T, TraversalState> }}

Other contracts

• a seed must be a JSON object or a function returning a constructor (e.g () => Map) which executed will produce a seed value

Examples

NOTE : for bfs/pre/post-order traversals, we only need the getChildren lens. It is a good habit however to define and pass the fulllenses once and for all.

const tree = {
  label: "root",
  children: [
    { label: "left" },
    {
      label: "middle",
      children: [{ label: "midleft" }, { label: "midright" }]
    },
    { label: "right" }
  ]
};

const lenses = {
  getChildren: tree => tree.children || []
};

const traverse = {
  seed: [],
  visit: (result, traversalState, tree) => {
    result.push(tree.label);
    return result;
  }
};

QUnit.test("main case - breadthFirstTraverseTree", function exec_test(assert) {
  const actual = breadthFirstTraverseTree(lenses, traverse, tree);
  const expected = [
    "root",
    "left",
    "middle",
    "right",
    "midleft",
    "midright"
  ];

  assert.deepEqual(actual, expected, `Works!`);
});

preorderTraverseTree :: Lenses -> TraverseSpecs -> Tree -> A

Description

Traverse a tree pre=order depth-first, applying a reducer while traversing the tree, and returning the final accumulated reduction.

Types

• Tree :: T
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Reducer<A, T, TraversalState> :: A -> TraversalState -> T -> A
• TraverseSpecs :: {{strategy :: Optional<Traversal>, seed : A, visit :: Reducer<A, T, TraversalState> }}

Examples

QUnit.test("main case - preorderTraverseTree", function exec_test(assert) {
  const actual = preorderTraverseTree(lenses, traverse, tree);
  const expected = [
    "root",
    "left",
    "middle",
    "midleft",
    "midright",
    "right"
  ];

  assert.deepEqual(actual, expected, `Works!`);
});

postOrderTraverseTree :: Lenses -> TraverseSpecs -> Tree -> A

Description

Traverse a tree post=order depth-first, applying a reducer while traversing the tree, and returning the final accumulated reduction.

Types

• Tree :: T
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Reducer<A, T, TraversalState> :: A -> TraversalState -> T -> A
• TraverseSpecs :: {{strategy :: Optional<Traversal>, seed : A, visit :: Reducer<A, T, TraversalState> }}

Other contracts

• a seed must be a JSON object or a function returning a constructor (e.g () => Map) which executed will produce a seed value

Examples

QUnit.test("main case - postOrderTraverseTree", function exec_test(assert) {
  const actual = postOrderTraverseTree(lenses, traverse, tree);
  const expected = [
    "left",
    "midleft",
    "midright",
    "middle",
    "right",
    "root"
  ];

  assert.deepEqual(actual, expected, `Works!`);
});

reduceTree :: Lenses -> TraverseSpecs -> Tree -> A

NOTE : the strategy property is this time mandatory as part of the traversal specs.

Description

Traverse a tree according to the parameterized traversal stratgy, applying a reducer while traversing the tree, and returning the final accumulated reduction.

Types

• Tree :: T
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Reducer<A, T, TraversalState> :: A -> TraversalState -> T -> A
• TraverseSpecs :: {{strategy :: Traversal, seed : A, visit :: Reducer<A, T, TraversalState> }}

Other contracts

• a seed must be a JSON object or a function returning a constructor (e.g () => Map) which executed will produce a seed value

Examples

QUnit.test("main case - reduceTree", function exec_test(assert) {
  const reduceTraverse = assoc("strategy", BFS, traverse);
  const actual = reduceTree(lenses, reduceTraverse, tree);
  const expected = [
    "root",
    "left",
    "middle",
    "right",
    "midleft",
    "midright"
  ];

  assert.deepEqual(actual, expected, `Works!`);
});

forEachInTree :: Lenses -> TraverseSpecs -> Tree -> A

Description

Traverse a tree according to the parameterized traversal strategy, applying a reducer while traversing the tree, and returning the final accumulated reduction. Note that, as the action may perform effects, the order of the traversal is particularly relevant.

NOTE : the traversal specs require this time an action property defining the action to execute on each traversed portion of the tree. The same stands for the strategy property.

Types

• Tree :: T
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Action :: T -> traversalState -> ()
• TraverseSpecs :: {{strategy :: Traversal, action :: Action }}

Examples

QUnit.test("main case - forEachInTree", function exec_test(assert) {
  const traces = [];
  const traverse = {
    strategy: POST_ORDER,
    action: (tree, traversalState) => {
      traces.push(traversalState.get(tree))
      traces.push(tree.label)
    }
  }

  forEachInTree(lenses, traverse, tree);
  const actual = traces;
  const expected = [
    {
      "isAdded": true,
      "isVisited": false,
      "path": [
        0,
        0
      ]
    },
    "left",
    {
      "isAdded": true,
      "isVisited": false,
      "path": [
        0,
        1,
        0
      ]
    },
    "midleft",
    {
      "isAdded": true,
      "isVisited": false,
      "path": [
        0,
        1,
        1
      ]
    },
    "midright",
    {
      "isAdded": true,
      "isVisited": true,
      "path": [
        0,
        1
      ]
    },
    "middle",
    {
      "isAdded": true,
      "isVisited": false,
      "path": [
        0,
        2
      ]
    },
    "right",
    {
      "isAdded": true,
      "isVisited": true,
      "path": [
        0
      ]
    },
    "root"
  ];

  assert.deepEqual(actual, expected, `Works!`);
});

mapOverTree :: Lenses -> MapFn -> Tree -> Tree'

Description

Traverse a tree, applying a mapping function, while, and returning a tree with the same structure, containing the mapped nodes. Order of traversal is irrelevant here, as all nodes of the tree are to be traversed, and the mapping function is assumed to be a pure function. Note that the constructTree lens is mandatory here to rebuild the tree from its nodes.

Types

• Tree :: T
• Tree' :: T'
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• MapFn :: E -> E'

Examples

QUnit.test("main case - mapOverTree", function exec_test(assert) {
  const getChildren = tree => tree.children || [];
  const getLabel = tree => tree.label || '';
  const constructTree = (label, trees) => ({label, children : trees});
  const mapFn = label => addPrefix('Map:')(label)
  const lenses = { getChildren, constructTree, getLabel };

  const actual = mapOverTree(lenses, mapFn, tree);
  const expected = {
    "children": [
      {
        "children": [],
        "label": "Map:left"
      },
      {
        "children": [
          {
            "children": [],
            "label": "Map:midleft"
          },
          {
            "children": [],
            "label": "Map:midright"
          }
        ],
        "label": "Map:middle"
      },
      {
        "children": [],
        "label": "Map:right"
      }
    ],
    "label": "Map:root"
  };

  assert.deepEqual(actual, expected, `Works!`);
});

Contracts

• mapFn must be a pure function. In particular, mapFn receives the label (i.e. the structure returned by lenses.getLabel), and canoot modify in-place this label. This ensures the mapOverTree function is also pure.

pruneWhen :: Lenses -> Predicate -> Tree -> Tree

Description

Traverse a tree, applying a predicate, which when failed leads to discarding any descendant nodes of the node failing that predicate. The failing node itself remains in the result tree. Note that the constructTree lens is mandatory here to rebuild the tree from its nodes. Note also that the predicate is passed the traversal state, together with the node. This allows to implement stop conditions by modifying directly the traversal state (adding for instance a isTraversalStopped flag).

Types

• Tree :: T
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Predicate :: T -> TraversalState -> Boolean

Examples

QUnit.test("main case - pruneWhen", function exec_test(assert) {
  const getChildren = tree => tree.children || [];
  const getLabel = tree => tree.label || '';
  const constructTree = (label, trees) => ({label, children : trees});
  const predicate = (tree, traversalState) => traversalState.get(tree).path.length > 1;
  const lenses = { getChildren, constructTree, getLabel };

  const actual = pruneWhen(lenses, predicate, tree);
  const expected = {
    "children": [
      {
        "children": [],
        "label": "left"
      },
      {
        "children": [],
        "label": "middle"
      },
      {
        "children": [],
        "label": "right"
      }
    ],
    "label": "root"
  };

  assert.deepEqual(actual, expected, `Works!`);
});

visitTree :: ExtendedTraversalSpecs -> Tree -> A

Description

This is the generic tree traversal algorithm that all traversals use as their core.

• The tree is traversed starting from the root,
• for each traversed node its children are generating traversal tasks,
• a store is used to keep track of the pending traversal tasks to execute,
• each task involves the application of a visiting function which builds iteratively the result of the traversal, taking inputs from the traversal state, and the traversed node
• the traversal state includes flags (isAdded, isVisited) and relevant information (path) to the traversal
• the traversal state is passed to the getChildren lens, and the visitor function, for those cases where the traversal tasks to generate, or visits to undertake, depend on the traversal state
  • that is for instance the case for iterative post-order traversal, where we traverse a parent node twice, but only visit it once, after its children have been visited)
  • that is also the case for incomplete traversals (pruneWhen), where we discard traversing and visiting some nodes, based on some predicate

Types

• Tree :: T
• Traversal :: BFS | PRE_ORDER | POST_ORDER
• EmptyStore :: *
• Store :: {{empty :: EmptyStore, add :: [T] -> Store -> (), takeAndRemoveOne :: Store -> Maybe<T>, isEmpty :: Store -> Boolean}}
• State :: {{isAdded :: Boolean, isVisited :: Boolean, path :: Array<Number>, ...}} (extensible record)
• TraversalState :: Map<T, State>
• Lenses :: {{getLabel :: T -> E, getChildren :: T -> F, constructTree :: ExF -> T}}
• Reducer<A, T, TraversalState> :: A -> TraversalState -> T -> A
• TraverseSpecs :: {{seed : A, visit :: Reducer<A, T, TraversalState> }}
• ExtendedTraversalSpecs :: {{store :: Store, lenses :: Lenses, traverse :: TraverseSpecs}}

Other contracts

• an empty store must be a JSON object or a function returning a constructor (e.g () => Array) which executed will produce the empty value
• a seed must be a JSON object or a function returning a constructor (e.g () => Map) which executed will produce a seed value

Examples

Breadth-first traversal requires a stack store...

export function breadthFirstTraverseTree(lenses, traverse, tree) {
  const { getChildren } = lenses;
  const traversalSpecs = {
    store: {
      empty: [],
      takeAndRemoveOne: store => store.shift(),
      isEmpty: store => store.length === 0,
      add: (subTrees, store) => store.push.apply(store, subTrees)
    },
    lenses: { getChildren: (traversalState, subTree) => getChildren(subTree) },
    traverse
  };

  return visitTree(traversalSpecs, tree);
}

while a depth-first traversal requires a queue store. Additionally, a custom lens adds children nodes for visit only under some conditions corresponding to post-order traversal (i.e. parent must be visited only after children).

export function postOrderTraverseTree(lenses, traverse, tree) {
  const { getChildren } = lenses;
  const isLeaf = (tree, traversalState) => getChildren(tree, traversalState).length === 0;
  const { seed, visit } = traverse;
  const predicate = (tree, traversalState) => traversalState.get(tree).isVisited || isLeaf(tree, traversalState)
  const decoratedLenses = {
    // For post-order, add the parent at the end of the children, that simulates the stack for the recursive function
    // call in the recursive post-order traversal algorithm
    getChildren: (traversalState, tree) =>
      predicate(tree, traversalState)
        ? []
        : getChildren(tree, traversalState).concat(tree)
  };
  const traversalSpecs = {
    store: {
      empty: [],
      takeAndRemoveOne: store => store.shift(),
      isEmpty: store => store.length === 0,
      add: (subTrees, store) => store.unshift(...subTrees)
    },
    lenses: decoratedLenses,
    traverse: {
      seed: seed,
      visit: (result, traversalState, tree) => {
        // Cases :
        // 1. label has been visited already : visit
        // 2. label has not been visited, and there are no children : visit
        // 3. label has not been visited, and there are children : don't visit, will do it later
        if (predicate(tree, traversalState)) {
          visit(result, traversalState, tree);
        }

        return result;
      }
    }
  };

  return visitTree(traversalSpecs, tree);
}

switchTreeDataStructure :: Lenses -> Lenses -> Tree

Description

Allows to convert between concrete tree data structures. Note that for the conversion to be possible, the lenses must be very well behaved. It is for instance not always possible to convert to an object tree data structure.

Types

The types have been introduced previously.

Other contracts

Good behaviour of the lenses. If you are unsure of your lenses behaviour, try out a few conversions. If it works for a non-trivial tree, then it will always work.

Examples

Cf. tests.

For instance, this tree :

const tree = {
  label: "root",
  children: [
    { label: "left" },
    {
      label: "middle",
      children: [{ label: "midleft" }, { label: "midright" }]
    },
    { label: "right" }
  ]
};

becomes this equivalent tree :

[
    "root",
    [
      "left",
      [
        "middle",
        [
          "midleft",
          "midright"
        ]
      ],
      "right"
    ]
  ]

It is however impossible to convert any of those tree data structure towards an object tree.

traverseObj :: ExtendedTraversalSpecs -> Tree -> A

Description

Allows to traverse an object (POJO), applying a visiting function to every property. Traversal strategy can be specified (pre-order, post-order, or breadth-first).

Types

Types are as introduced previously.

Other contracts

Old same old.

Examples

Cf. tests

Tests

• npm run test

Build

• npm run build
• npm run dist

Install

• npm fp-rosetree

Examples of lenses

Object traversal

An object can be traversed and mapped over with the following lenses :

export const objectTreeLenses = {
  getLabel: tree => {
    if (typeof tree === 'object' && !Array.isArray(tree) && Object.keys(tree).length === 1) {
      return tree;
    }
    else {
      throw `getLabel > unexpected object tree value`
    }
  },
  getChildren: tree => {
    if (typeof tree === 'object' && !Array.isArray(tree) && Object.keys(tree).length === 1) {
      let value = Object.values(tree)[0];
      if (typeof value === 'object' && !Array.isArray(value)) {
        return Object.keys(value).map(prop => ({ [prop]: value[prop] }))
      }
      else {
        return []
      }
    }
    else {
      throw `getChildren > unexpected value`
    }
  },
  constructTree: (label, children) => {
    const labelKey = Object.keys(label)[0];
    return children.length === 0
      ? label
      : {
      [labelKey]: Object.assign.apply(null, children)
    }
  },
};

Cf. tests for examples with mapping over object keys and properties and traversing objects.

Hash-stored tree

We mean by hash-stored tree (by lack of a better name) a tree whose content is mapped to its location path through a hash map. That is the data structure is : Record {cursor :: Cursor, hash :: HashMap<Cursor, Tree>}. The cursor is usually a string which allows to point at a specific subtree.

An example of such concrete data structure is as follows :

  const hash = {
    "0": "root",
    "0.0": "combinatorName",
    "0.1": "componentName",
    "0.2": "emits",
    "0.3": "id",
    "0.2.0": "identifier",
    "0.2.1": "notification",
    "0.2.2": "type",
    "0.2.1.0": "kind",
    "0.2.1.1": "value",
    "0.2.1.1.0": "key"
  };
  const obj  { cursor : "0", hash};

The corresponding lenses would be as follows :

  const sep = '.';

  function makeChildCursor(parentCursor, childIndex, sep) {
    return [parentCursor, childIndex].join(sep)
  }

  const lenses = {
    getLabel: tree => {
      const { cursor, hash } = tree;
      return { label: hash[cursor], hash, cursor }
    },
    getChildren: tree => {
      const { cursor, hash } = tree;
      let childIndex = 0;
      let children = [];

      while ( makeChildCursor(cursor, childIndex, sep) in hash ) {
        children.push({ cursor: makeChildCursor(cursor, childIndex, sep), hash })
        childIndex++;
      }

      return children
    },
    constructTree: (label, children) => {
      const { label: value, hash, cursor } = label;

      return {
        cursor: cursor,
        hash: merge(
          children.reduce((acc, child) => merge(acc, child.hash), {}),
          { [cursor]: value }
        )
      }
    },
  };

Cf. tests for concrete examples.

Array-stored trees

Self-evident from the lenses definitions, a tree is label || [label, children] :

export const arrayTreeLenses = {
  getLabel: tree => {
    return Array.isArray(tree) ? tree[0] : tree
  },
  getChildren: tree => {
    return Array.isArray(tree) ? tree[1] : []
  },
  constructTree: (label, children) => {
    return children && Array.isArray(children) ? [label, children] : label
  },
}

Conversion

TODO