Visualize a tree: Difference between revisions

'''Solution'''

Fōrmulæ is a homoiconic language using expression trees as its fundamental structure, so managing trees is very natural.

'''Creating trees from expressions'''

The ToTree expression creates a tree from a given expression. see the following examples:

[[File:Fōrmulæ - Visualize a tree 01.png]]

[[File:Fōrmulæ - Visualize a tree 02.png]]

Be aware the the expression will be first reduced, like the following:

[[File:Fōrmulæ - Visualize a tree 03.png]]

[[File:Fōrmulæ - Visualize a tree 04.png]]

It order to avoid the reduction, the use of the Protect expression is recommended:

[[File:Fōrmulæ - Visualize a tree 05.png]]

[[File:Fōrmulæ - Visualize a tree 06.png]]

In the following example, it is shown that a matrix is a list containing (same cardinality) sublists:

[[File:Fōrmulæ - Visualize a tree 07.png]]

[[File:Fōrmulæ - Visualize a tree 08.png]]

In the following example, it is shown that, according to the Fōrmulæ arithmetic canon, a negative number is a Negative expression containing a Number expression:

[[File:Fōrmulæ - Visualize a tree 09.png]]

[[File:Fōrmulæ - Visualize a tree 10.png]]

'''Creating trees programatically'''

The tree, like any other expression in Fōrmulæ is a first-class citizen of the language. Fōrmulæ also supports high-order functions, so trees can be set as parameters of functions, or retrieved from functions.

The following example shows a function that produces a Fibonacci tree, a tree that shows the calls of a function that recursively calculates Fibonacci numbers:

[[File:Fōrmulæ - Fibonacci sequence 03.png]]

[[File:Fōrmulæ - Fibonacci sequence 04.png]]

[[File:Fōrmulæ - Fibonacci sequence 05.png]]