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IBAF-cbs/Funcons-beta/Values/Composite/Trees/Trees.cbs Normal file
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### Trees
[
Datatype trees
Funcon tree
Funcon tree-root-value
Funcon tree-branch-sequence
Funcon single-branching-sequence
Funcon forest-root-value-sequence
Funcon forest-branch-sequence
Funcon forest-value-sequence
]
Meta-variables
T <: values
Datatype
trees(T) ::= tree( _:T, _:(trees(T))*)
/*
`trees(T)` consists of finitely-branching trees with elements of type `T`.
When `V:T`, `tree(V)` is a leaf, and `tree(V,B1,...,Bn)` is a tree with
branches `B1`, ..., `Bn`.
*/
Funcon
tree-root-value(_:trees(T)) : =>(T)?
Rule
tree-root-value tree(V:T, _*:(trees(T))*) ~> V
Funcon
tree-branch-sequence(_:trees(T)) : =>(trees(T))*
Rule
tree-branch-sequence tree(_:T, B*:(trees(T))*) ~> B*
Funcon
single-branching-sequence(_:trees(T)) : =>T+
/*
`single-branching-sequence B ` extracts the values in `B` starting from
the root, provided that `B` is at most single-branching; otherwise it fails.
*/
Rule
single-branching-sequence tree(V:T) ~> V
Rule
single-branching-sequence tree(V:T, B:trees(T))
~> left-to-right( V, single-branching-sequence B)
Rule
single-branching-sequence tree(_:T, _:trees(T), _+:(trees(T))+) ~> fail
/*
A sequence of trees corresponds to a forest, and the selector funcons
on trees `B` extend to forests `B*`:
*/
Funcon
forest-root-value-sequence(_:(trees(T))*) : =>T*
Rule
forest-root-value-sequence(B:trees(T), B*:(trees(T))*)
~>(tree-root-value B , forest-root-value-sequence B*)
Rule
forest-root-value-sequence( ) ~>( )
Funcon
forest-branch-sequence(_:(trees(T))*) : =>T*
Rule
forest-branch-sequence(B:trees(T), B*:(trees(T))*)
~>(tree-branch-sequence B , forest-branch-sequence B*)
Rule
forest-branch-sequence( ) ~>( )
Funcon
forest-value-sequence(_:(trees(T))*) : =>T*
/*
`forest-value-sequence B*` provides the values from a left-to-right pre-order
depth-first traversal.
*/
Rule
forest-value-sequence(tree(V:T, B1*:(trees(T))*), B2*:(trees(T))*)
~>(V , forest-value-sequence B1*, forest-value-sequence B2*)
Rule
forest-value-sequence( ) ~>( )
/*
Other linearizations of trees can be added: breadth-first, right-to-left,
C3, etc.
*/

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IBAF-cbs/Funcons-beta/Values/Composite/Trees/index.md Normal file
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---
layout: default
title: "Trees"
parent: Composite
ancestor: Funcons-beta
---
[Funcons-beta] : [Trees.cbs]
-----------------------------
### Trees
<div class="highlighter-rouge"><pre class="highlight"><code>[
<i class="keyword">Datatype</i> <span class="name"><a href="#Name_trees">trees</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_tree">tree</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_tree-root-value">tree-root-value</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_tree-branch-sequence">tree-branch-sequence</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_single-branching-sequence">single-branching-sequence</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_forest-root-value-sequence">forest-root-value-sequence</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_forest-branch-sequence">forest-branch-sequence</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_forest-value-sequence">forest-value-sequence</a></span>
]</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Meta-variables</i>
<span id="PartVariable_T"><i class="var">T</i></span> <: <span class="name"><a href="../../Value-Types/index.html#Name_values">values</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Datatype</i>
<span class="name"><span id="Name_trees">trees</span></span>(<span id="Variable60_T"><i class="var">T</i></span>) ::= <span id="Name_tree">tree</span>( _:<span id="Variable76_T"><i class="var">T</i></span>, _:(<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable88_T"><i class="var">T</i></span>))<sup class="sup">*</sup>)</code></pre></div>
<code><span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>)</code> consists of finitely-branching trees with elements of type <code><i class="var">T</i></code>.
When <code><i class="var">V</i>:<i class="var">T</i></code>, <code><span class="name"><a href="#Name_tree">tree</a></span>(<i class="var">V</i>)</code> is a leaf, and <code><span class="name"><a href="#Name_tree">tree</a></span>(<i class="var">V</i>,<i class="var">B<sub class="sub">1</sub></i>,...,<i class="var">Bn</i>)</code> is a tree with
branches <code><i class="var">B<sub class="sub">1</sub></i></code>, ..., <code><i class="var">Bn</i></code>.
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
<span class="name"><span id="Name_tree-root-value">tree-root-value</span></span>(_:<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable269_T"><i class="var">T</i></span>)) : =>(<span id="Variable289_T"><i class="var">T</i></span>)<sup class="sup">?</sup>
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_tree-root-value">tree-root-value</a></span> <span class="name"><a href="#Name_tree">tree</a></span>(<span id="Variable306_V"><i class="var">V</i></span>:<i class="var">T</i>, _*:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">*</sup>) ~> <a href="#Variable306_V"><i class="var">V</i></a></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
<span class="name"><span id="Name_tree-branch-sequence">tree-branch-sequence</span></span>(_:<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable363_T"><i class="var">T</i></span>)) : =>(<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable384_T"><i class="var">T</i></span>))<sup class="sup">*</sup>
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_tree-branch-sequence">tree-branch-sequence</a></span> <span class="name"><a href="#Name_tree">tree</a></span>(_:<i class="var">T</i>, <span id="Variable418_B*"><i class="var">B<sup class="sup">*</sup></i></span>:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">*</sup>) ~> <a href="#Variable418_B*"><i class="var">B<sup class="sup">*</sup></i></a></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
<span class="name"><span id="Name_single-branching-sequence">single-branching-sequence</span></span>(_:<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable465_T"><i class="var">T</i></span>)) : =><span id="Variable486_T+"><i class="var">T<sup class="sup">+</sup></i></span></code></pre></div>
<code><span class="name"><a href="#Name_single-branching-sequence">single-branching-sequence</a></span> <i class="var">B</i></code> extracts the values in <code><i class="var">B</i></code> starting from
the root, provided that <code><i class="var">B</i></code> is at most single-branching; otherwise it fails.
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Rule</i>
<span class="name"><a href="#Name_single-branching-sequence">single-branching-sequence</a></span> <span class="name"><a href="#Name_tree">tree</a></span>(<span id="Variable543_V"><i class="var">V</i></span>:<i class="var">T</i>) ~> <a href="#Variable543_V"><i class="var">V</i></a>
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_single-branching-sequence">single-branching-sequence</a></span> <span class="name"><a href="#Name_tree">tree</a></span>(<span id="Variable571_V"><i class="var">V</i></span>:<i class="var">T</i>, <span id="Variable582_B"><i class="var">B</i></span>:<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))
~> <span class="name"><a href="../../../Computations/Normal/Flowing/index.html#Name_left-to-right">left-to-right</a></span>( <a href="#Variable571_V"><i class="var">V</i></a>, <span class="name"><a href="#Name_single-branching-sequence">single-branching-sequence</a></span> <a href="#Variable582_B"><i class="var">B</i></a>)
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_single-branching-sequence">single-branching-sequence</a></span> <span class="name"><a href="#Name_tree">tree</a></span>(_:<i class="var">T</i>, _:<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>), _+:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">+</sup>) ~> <span class="name"><a href="../../../Computations/Abnormal/Failing/index.html#Name_fail">fail</a></span></code></pre></div>
A sequence of trees corresponds to a forest, and the selector funcons
on trees <code><i class="var">B</i></code> extend to forests <code><i class="var">B<sup class="sup">*</sup></i></code>:
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
<span class="name"><span id="Name_forest-root-value-sequence">forest-root-value-sequence</span></span>(_:(<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable737_T"><i class="var">T</i></span>))<sup class="sup">*</sup>) : =><span id="Variable765_T*"><i class="var">T<sup class="sup">*</sup></i></span>
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_forest-root-value-sequence">forest-root-value-sequence</a></span>(<span id="Variable774_B"><i class="var">B</i></span>:<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>), <span id="Variable793_B*"><i class="var">B<sup class="sup">*</sup></i></span>:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">*</sup>)
~>(<span class="name"><a href="#Name_tree-root-value">tree-root-value</a></span> <a href="#Variable774_B"><i class="var">B</i></a> , <span class="name"><a href="#Name_forest-root-value-sequence">forest-root-value-sequence</a></span> <a href="#Variable793_B*"><i class="var">B<sup class="sup">*</sup></i></a>)
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_forest-root-value-sequence">forest-root-value-sequence</a></span>( ) ~>( )</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
<span class="name"><span id="Name_forest-branch-sequence">forest-branch-sequence</span></span>(_:(<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable867_T"><i class="var">T</i></span>))<sup class="sup">*</sup>) : =><span id="Variable895_T*"><i class="var">T<sup class="sup">*</sup></i></span>
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_forest-branch-sequence">forest-branch-sequence</a></span>(<span id="Variable904_B"><i class="var">B</i></span>:<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>), <span id="Variable923_B*"><i class="var">B<sup class="sup">*</sup></i></span>:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">*</sup>)
~>(<span class="name"><a href="#Name_tree-branch-sequence">tree-branch-sequence</a></span> <a href="#Variable904_B"><i class="var">B</i></a> , <span class="name"><a href="#Name_forest-branch-sequence">forest-branch-sequence</a></span> <a href="#Variable923_B*"><i class="var">B<sup class="sup">*</sup></i></a>)
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_forest-branch-sequence">forest-branch-sequence</a></span>( ) ~>( )</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
<span class="name"><span id="Name_forest-value-sequence">forest-value-sequence</span></span>(_:(<span class="name"><a href="#Name_trees">trees</a></span>(<span id="Variable997_T"><i class="var">T</i></span>))<sup class="sup">*</sup>) : =><span id="Variable1025_T*"><i class="var">T<sup class="sup">*</sup></i></span></code></pre></div>
<code><span class="name"><a href="#Name_forest-value-sequence">forest-value-sequence</a></span> <i class="var">B<sup class="sup">*</sup></i></code> provides the values from a left-to-right pre-order
depth-first traversal.
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Rule</i>
<span class="name"><a href="#Name_forest-value-sequence">forest-value-sequence</a></span>(<span class="name"><a href="#Name_tree">tree</a></span>(<span id="Variable1057_V"><i class="var">V</i></span>:<i class="var">T</i>, <span id="Variable1070_B1*"><i class="var">B<sub class="sub">1</sub><sup class="sup">*</sup></i></span>:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">*</sup>), <span id="Variable1104_B2*"><i class="var">B<sub class="sub">2</sub><sup class="sup">*</sup></i></span>:(<span class="name"><a href="#Name_trees">trees</a></span>(<i class="var">T</i>))<sup class="sup">*</sup>)
~>(<a href="#Variable1057_V"><i class="var">V</i></a> , <span class="name"><a href="#Name_forest-value-sequence">forest-value-sequence</a></span> <a href="#Variable1070_B1*"><i class="var">B<sub class="sub">1</sub><sup class="sup">*</sup></i></a>, <span class="name"><a href="#Name_forest-value-sequence">forest-value-sequence</a></span> <a href="#Variable1104_B2*"><i class="var">B<sub class="sub">2</sub><sup class="sup">*</sup></i></a>)
<i class="keyword">Rule</i>
<span class="name"><a href="#Name_forest-value-sequence">forest-value-sequence</a></span>( ) ~>( )</code></pre></div>
Other linearizations of trees can be added: breadth-first, right-to-left,
C3, etc.
____
From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...]
[Trees.cbs]: Trees.cbs
"CBS SOURCE FILE"
[Funcons-beta]: /CBS-beta/docs/Funcons-beta
"FUNCONS-BETA"
[Unstable-Funcons-beta]: /CBS-beta/docs/Unstable-Funcons-beta
"UNSTABLE-FUNCONS-BETA"
[Languages-beta]: /CBS-beta/docs/Languages-beta
"LANGUAGES-BETA"
[Unstable-Languages-beta]: /CBS-beta/docs/Unstable-Languages-beta
"UNSTABLE-LANGUAGES-BETA"
[CBS-beta]: /CBS-beta "CBS-BETA"
[PLanCompS Project]: https://plancomps.github.io
"PROGRAMMING LANGUAGE COMPONENTS AND SPECIFICATIONS PROJECT HOME PAGE"
[CBS-beta issues...]: https://github.com/plancomps/CBS-beta/issues
"CBS-BETA ISSUE REPORTS ON GITHUB"
[Suggest an improvement...]: mailto:plancomps@gmail.com?Subject=CBS-beta%20-%20comment&Body=Re%3A%20CBS-beta%20specification%20at%20Values/Composite/Trees/Trees.cbs%0A%0AComment/Query/Issue/Suggestion%3A%0A%0A%0ASignature%3A%0A
"GENERATE AN EMAIL TEMPLATE"

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IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/forest-branch-sequence.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print [forest-branch-sequence
(tree(1),
tree(2,tree(3)),
tree(4),
tree(5,tree(6),tree(7)))
]
)
;
}
tests {
result-term: null-value;
standard-out: [
[tree(3),tree(6),tree(7)]
];
}

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IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/forest-root-value-sequence.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print [forest-root-value-sequence
(tree(1),
tree(2,tree(3)),
tree(4),
tree(5,tree(6),tree(7)))
]
)
;
}
tests {
result-term: null-value;
standard-out: [
[1,2,4,5]
];
}

20
IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/forest-value-sequence.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print [forest-value-sequence
(tree(1),
tree(2,tree(3)),
tree(4),
tree(5,tree(6),tree(7)))
]
)
;
}
tests {
result-term: null-value;
standard-out: [
[1,2,3,4,5,6,7]
];
}

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IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/single-branching-sequence.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print [single-branching-sequence tree(1)],
print [single-branching-sequence tree(1,tree(2,tree(3)))],
else(
print [single-branching-sequence tree(1,tree(2),tree(3))],
print [single-branching-sequence tree(1,tree(2,tree(3,tree(4),tree(5))))],
print "OK")
)
;
}
tests {
result-term: null-value;
standard-out: [
[1],
[1,2,3],
"OK"
];
}

16
IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/tree-branch-sequence.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print tree-branch-sequence
tree(1,tree(2,tree(3)),tree(4),tree(5,tree(6),tree(7)))
)
;
}
tests {
result-term: null-value;
standard-out: [
tree(2,tree(3)), tree(4), tree(5,tree(6),tree(7))
];
}

16
IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/tree-root-value.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print tree-root-value
tree(1,tree(2,tree(3)),tree(4),tree(5,tree(6),tree(7)))
)
;
}
tests {
result-term: null-value;
standard-out: [
1
];
}

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IBAF-cbs/Funcons-beta/Values/Composite/Trees/tests/tree.config Normal file
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general {
funcon-term:
initialise-giving finalise-failing
sequential (
print tree(1),
print tree(1,tree(2,tree(3))),
print tree(1,tree(2),tree(3)),
print tree(1,tree(2,tree(3)),tree(4),tree(5,tree(6),tree(7)))
)
;
}
tests {
result-term: null-value;
standard-out: [
tree(1),
tree(1,tree(2,tree(3))),
tree(1,tree(2),tree(3)),
tree(1,tree(2,tree(3)),tree(4),tree(5,tree(6),tree(7)))
];
}