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<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2024-06-25 Tue 19:30 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Diane</title>
<meta name="author" content="Nathan Mull" />
<meta name="generator" content="Org Mode" />
<link rel="stylesheet" type="text/css" href="indexStyle.css" />
<script src="diane.js"></script>
</head>
<body>
<div id="content" class="content">
<h1 class="title">Diane</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orgaa5ccda">The Playground</a>
<ul>
<li><a href="#org333ad0d">Instructions</a></li>
<li><a href="#org4264913">Keyboard Shortcuts</a></li>
</ul>
</li>
<li><a href="#org6c25255">Syntax</a></li>
<li><a href="#orgaf554bf">Semantics</a>
<ul>
<li><a href="#orgf3e6779">Notation for Environments</a></li>
<li><a href="#org0e806ae">Stack Manipulation</a></li>
<li><a href="#orgea6df44">Arithmetic and Comparisons</a></li>
<li><a href="#org8301bf3">Subroutines</a></li>
<li><a href="#org27cdfbd">Variables</a></li>
<li><a href="#org87fb8f8">Conditionals</a></li>
</ul>
</li>
</ul>
</div>
</div>
<p>
<a href="https://github.com/nmmull/Diane">Diane</a> is a <b>toy stack-oriented language with dynamic scoping</b>. It's
not pretty or all that interesting, but it's simple enough to present
the syntax and semantics in a straightforward way (and to build a
reasonable playground for it).
</p>
<p>
Diane was born out of a need to visualize evaluation. During the
spring (2024), I co-taught a course on <a href="https://nmmull.github.io/CS320/landing/Spring-2024/index.html">programming languages</a> in which
we often used stack-oriented languages to motivate and demonstrate
operational semantics. I worked through step-by-step evaluations on
the board often enough to want a process for doing it which is <i>automatic</i> and
<i>interactive</i>, along the same lines as the <a href="https://pythontutor.com/cp/composingprograms.html#mode=edit">Python Tutor</a> for <a href="https://www.composingprograms.com">Composing
Programs</a>.
</p>
<p>
<b>Disclaimer.</b> This page is not a tutorial, just a description of
the language and playground.
</p>
<div id="outline-container-orgaa5ccda" class="outline-2">
<h2 id="orgaa5ccda">The Playground</h2>
<div class="outline-text-2" id="text-orgaa5ccda">
<p>
The primary goal of this project was to build a <a href="playground.html">playground</a> (in <a href="https://elm-lang.org">Elm</a>)
for toying with Diane programs. The playground consists of an editor
window for writing programs, a visualization window for seeing how the
stack and environment change over the course of evaluation, and a
console window for seeing intermediate print statements and error
messages.
</p>
<p>
The playground can also be embedded:
</p>
<div id="embed-example"></div>
<script>
var app = Elm.Main.init({
node: document.getElementById('embed-example'),
flags: {
hasTrace: true,
adjustable: false,
program: `def SUMSQUARES {
dup * swap dup * +
}
2 3 #SUMSQUARES @X
X print`
}});
</script>
<p>
We take advantage of this below to highlight features of the
semantics.
</p>
<p>
Partly out of laziness, partly out of a general bent towards minimal
interfaces, there are no instructions for using the playground
<i>within</i> the playground itself, so I've included them here.
</p>
</div>
<div id="outline-container-org333ad0d" class="outline-3">
<h3 id="org333ad0d">Instructions</h3>
<div class="outline-text-3" id="text-org333ad0d">
<ul class="org-ul">
<li>The <b>step</b> button consumes a single command of the program in the
editor window and updates the stack and environment accordingly.</li>
<li>The <b>run</b> button consumes as much of the program as possible until
<ul class="org-ul">
<li>the entire program is consumed</li>
<li>there is an error</li>
<li>the evaluation times out</li>
</ul></li>
<li>The <b>undo</b> button reverses a step taken by pressing either the
<b>step</b> button or the <b>run</b>.</li>
<li>The <b>reset</b> button resets the program state to its initial state,
clearing the undo history.</li>
<li>The <b>save</b> button sets the program in the editor window to be the
program of the initial state. This also clears the undo
history.<sup><a id="fnr.1" class="footref" href="#fn.1" role="doc-backlink">1</a></sup></li>
<li>The <b>clear</b> button in the console window clears the messages printed
there.<sup><a id="fnr.2" class="footref" href="#fn.2" role="doc-backlink">2</a></sup></li>
</ul>
</div>
</div>
<div id="outline-container-org4264913" class="outline-3">
<h3 id="org4264913">Keyboard Shortcuts</h3>
<div class="outline-text-3" id="text-org4264913">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left">\</td>
<td class="org-left"><b>step</b></td>
</tr>
<tr>
<td class="org-left">ALT</td>
<td class="org-left"><b>run</b></td>
</tr>
<tr>
<td class="org-left">`</td>
<td class="org-left"><b>undo</b></td>
</tr>
</tbody>
</table>
<p>
It's possible to step through a program while writing it using the
above keyboard shortcuts. In most cases you can also hold down the
key to rapidly step through a program, providing a make-shift
animation mechanism.
</p>
</div>
</div>
</div>
<div id="outline-container-org6c25255" class="outline-2">
<h2 id="org6c25255">Syntax</h2>
<div class="outline-text-2" id="text-org6c25255">
<p>
The following is a simple <a href="https://en.wikipedia.org/wiki/Extended_Backus%E2%80%93Naur_form">EBNF Grammar</a> describing a Diane program. In
short, a program is a sequence of whitespace-separated commands.
</p>
<hr />
<pre class="example">
<program> ::= { <command> }
<body> ::= '{' <program> '}'
<command> ::= <int> | 'drop' | 'swap' | 'dup' | 'rot'
| '+' | '-' | '*' | '/' | '%' | '=' | '<'
| 'def' <ident> <body> | '#' <ident>
| '@' <ident> | '[' | ']'
| '?' <body> 'else' <body> | 'while' <body> 'do' <body>
<int> ::= ℤ
<ident> ::= ALL_CAPS_SNAKE
</pre>
<hr />
</div>
</div>
<div id="outline-container-orgaf554bf" class="outline-2">
<h2 id="orgaf554bf">Semantics</h2>
<div class="outline-text-2" id="text-orgaf554bf">
<p>
We take a <b>value</b> (𝕍) to be a integer (ℤ) or a program representing a
subroutine (ℙ).<sup><a id="fnr.3" class="footref" href="#fn.3" role="doc-backlink">3</a></sup> A <b>configuration</b>,
written ( S, E, P ), is made up of a stack of integers (S), an
environment consisting of a list of collections identifier-value
bindings (E), and a program as given by the above
grammar (P). The <a href="https://en.wikipedia.org/wiki/Operational_semantics#Structural_operational_semantics">operational semantics</a> of Diane are given by the
reduction rules below.
</p>
</div>
<div id="outline-container-orgf3e6779" class="outline-3">
<h3 id="orgf3e6779">Notation for Environments</h3>
<div class="outline-text-3" id="text-orgf3e6779">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left">⟨⟩</td>
<td class="org-left">empty collection of bindings</td>
</tr>
<tr>
<td class="org-left">𝒢</td>
<td class="org-left">global bindings</td>
</tr>
<tr>
<td class="org-left">L · E</td>
<td class="org-left">E with (shadowing) local bindings L</td>
</tr>
<tr>
<td class="org-left">E[X ↦ A]</td>
<td class="org-left">E with X bound to the value A (in topmost local bindings)</td>
</tr>
<tr>
<td class="org-left">X ∈ E</td>
<td class="org-left">X is bound in E</td>
</tr>
<tr>
<td class="org-left">E[X]</td>
<td class="org-left">the value to which X is bound in E (searched for top down)</td>
</tr>
<tr>
<td class="org-left">E/X</td>
<td class="org-left">E with any binding of X removed</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org0e806ae" class="outline-3">
<h3 id="org0e806ae">Stack Manipulation</h3>
<div class="outline-text-3" id="text-org0e806ae">
<p>
Several commands are dedicated to manipulating the stack. We can
</p>
<ul class="org-ul">
<li><b>push</b> an integer onto the stack</li>
<li><b>drop</b> the top element off the stack</li>
<li><b>swap</b> the top two elements on the stack</li>
<li><b>dup</b>-licate the top element on the stack</li>
<li><b>rot</b>-ate the top three elements on the stack</li>
</ul>
<p>
In the case that there aren't enough integers on the stack to perform
a given operation, a stack underflow error message is printed to the
console.
</p>
<p>
There is also an unofficial command for <b>print</b>-ing the top element of
the stack and removing it. See the example below.<sup><a id="fnr.4" class="footref" href="#fn.4" role="doc-backlink">4</a></sup>
</p>
<pre class="example">
𝑘 ∈ ℤ
────────────────────────────────── ( push )
( S, E, k P ) ⟶ ( 𝑘 :: S, E, P )
───────────────────────────────────── ( drop )
( 𝑛 :: S, E, drop P ) ⟶ ( S, E, P )
─────────────────────────────────── ( dropErr )
( ⊥, E, drop P ) ⟶ StackUnderflow
──────────────────────────────────────────────────── ( swap )
( 𝑚 :: 𝑛 :: S, E, swap P) ⟶ ( 𝑛 :: 𝑚 :: S, E, P )
──────────────────────────────────────── ( swapErr₁ )
( 𝑛 :: ⊥, E, swap P ) ⟶ StackUnderflow
─────────────────────────────────── ( swapErr₀ )
( ⊥, E, swap P ) ⟶ StackUnderflow
──────────────────────────────────────────────────── ( dup )
( 𝑛 :: S, E, dup P ) ⟶ ( 𝑛 :: 𝑛 :: S, E, P )
─────────────────────────────────── ( dupErr₀ )
( ⊥, E, dup P ) ⟶ StackUnderflow
──────────────────────────────────────────────────────────── ( rot )
( 𝑙 :: 𝑚 :: 𝑛 :: S, E, rot P ) ⟶ ( 𝑚 :: 𝑛 :: 𝑙 :: S, E, P )
──────────────────────────────────────────── ( rotErr₂ )
( 𝑚 :: 𝑛 :: S, E, rot P ) ⟶ StackUnderflow
─────────────────────────────────────── ( rotErr₁ )
( 𝑛 :: ⊥, E, rot P ) ⟶ StackUnderflow
─────────────────────────────────── ( rotErr₀ )
( ⊥, E, rot P ) ⟶ StackUnderflow
</pre>
<p>
The following is a small example program using these commands. Press
the <b>step</b> button to see how the stack changes as each command is
consumed and evaluated. Note that the last command cannot be consumed
because there are no integers on the stack to duplicate. Attempting
to evaluate this command results in a stack underflow error message.
</p>
<div id="push-example"></div>
<script>
var app = Elm.Main.init({
node: document.getElementById('push-example'),
flags: {
hasTrace: true,
adjustable: false,
program: `1 2 3
drop swap dup
rot rot rot
print print print
dup`
}});
</script>
</div>
</div>
<div id="outline-container-orgea6df44" class="outline-3">
<h3 id="orgea6df44">Arithmetic and Comparisons</h3>
<div class="outline-text-3" id="text-orgea6df44">
<p>
The commands in this section are used to operate on the integers on the
stack. We can
</p>
<ul class="org-ul">
<li>(+) add</li>
<li>(-) subtract</li>
<li>(*) multiply</li>
<li>(/) divide</li>
<li>(%) determine the modulus</li>
<li>(=) check for equality</li>
<li>(<) check for less-than</li>
</ul>
<p>
As above, if there aren't enough integers on the stack to perform an
operation, a stack underflow error message is printed. An error may
also occur when trying to divide by zero.
</p>
<pre class="example">
────────────────────────────────────────────────── ( add )
( 𝑚 :: 𝑛 :: S, E, + P ) ⟶ ( 𝑚 ＋ 𝑛 :: S, E, P )
───────────────────────────────────── ( addErr₁ )
( 𝑛 :: ⊥, E, + P ) ⟶ StackUnderflow
──────────────────────────────── ( addErr₀ )
( ⊥, E, - P ) ⟶ StackUnderflow
─────────────────────────────────────────────── ( sub )
( 𝑚 :: 𝑛 :: S, E, - P ) ⟶ ( 𝑚 ─ 𝑛 :: S, E, P )
───────────────────────────────────── ( subErr₁ )
( 𝑛 :: ⊥, E, - P ) ⟶ StackUnderflow
──────────────────────────────── ( subErr₀ )
( ⊥, E, - P ) ⟶ StackUnderflow
───────────────────────────────────────────────── ( mul )
( 𝑚 :: 𝑛 :: S, E, * P ) ⟶ ( 𝑚 × 𝑛 :: S, E, P )
───────────────────────────────────── ( mulErr₁ )
( 𝑛 :: ⊥, E, * P ) ⟶ StackUnderflow
──────────────────────────────── ( mulErr₀ )
( ⊥, E, * P ) ⟶ StackUnderflow
n ≠ 0
────────────────────────────────────────────────── ( div )
( 𝑚 :: 𝑛 :: S, E, / P ) ⟶ ( 𝑚 ／ 𝑛 :: S, E, P )
────────────────────────────────────── ( divErrByZero )
( 𝑚 :: 0 :: S, E, / P ) ⟶ DivByZero
───────────────────────────────────── ( divErr₁ )
( 𝑛 :: ⊥, E, / P ) ⟶ StackUnderflow
──────────────────────────────── ( divErr₀ )
( ⊥, E, / P ) ⟶ StackUnderflow
n ≠ 0
─────────────────────────────────────────────────── ( mod )
( 𝑚 :: 𝑛 :: S, E, % P ) ⟶ ( 𝑚 mod 𝑛 :: S, E, P )
────────────────────────────────────── ( modErrByZero )
( 𝑚 :: 0 :: S, E, % P ) ⟶ DivByZero
───────────────────────────────────── ( modErr₁ )
( 𝑛 :: ⊥, E, % P ) ⟶ StackUnderflow
──────────────────────────────── ( modErr₀ )
( ⊥, E, % P ) ⟶ StackUnderflow
𝑚 ＝ 𝑛
──────────────────────────────────────────── ( eq )
( 𝑚 :: 𝑛 :: S, E, = P ) ⟶ ( 1 :: S, E, P )
𝑚 ≠ 𝑛
──────────────────────────────────────────── ( neq )
( 𝑚 :: 𝑛 :: S, E, = P ) ⟶ ( 0 :: S, E, P )
───────────────────────────────────── ( eqErr₁ )
( 𝑛 :: ⊥, E, = P ) ⟶ StackUnderflow
──────────────────────────────── ( eqErr₀ )
( ⊥, E, = P ) ⟶ StackUnderflow
𝑚 < 𝑛
──────────────────────────────────────────── ( le )
( 𝑚 :: 𝑛 :: S, E, < P ) ⟶ ( 1 :: S, E, P )
𝑚 ≮ 𝑛
──────────────────────────────────────────── ( nle )
( 𝑚 :: 𝑛 :: S, E, = P ) ⟶ ( 0 :: S, E, P )
───────────────────────────────────── ( leErr₁ )
( 𝑛 :: ⊥, E, = P ) ⟶ StackUnderflow
──────────────────────────────── ( leErr₀ )
( ⊥, E, = P ) ⟶ StackUnderflow
</pre>
<div id="arith-example"></div>
<script>
var app = Elm.Main.init({
node: document.getElementById('arith-example'),
flags: {
hasTrace: true,
adjustable: false,
program: `3 4 5 + * 4 swap / 7 < 5 /`
}});
</script>
</div>
</div>
<div id="outline-container-org8301bf3" class="outline-3">
<h3 id="org8301bf3">Subroutines</h3>
<div class="outline-text-3" id="text-org8301bf3">
<p>
A subroutine is just a named program. We can <i>define</i> subroutines and
<i>call</i> them. Defining a subroutine adds a binding in the environment
of its name to the program in the body of its definition. Calling a
subroutine simply prepends its body to the program being
evaluated.<sup><a id="fnr.5" class="footref" href="#fn.5" role="doc-backlink">5</a></sup>
</p>
<pre class="example">
────────────────────────────────────────────── ( def )
( S, E, def F { Q } P ) ⟶ ( S, E[F ↦ Q], P )
F ∈ E E[X] ∈ ℙ
─────────────────────────────────── ( call )
( S, E, #F P ) ⟶ ( S, E, E[F] P )
F ∈ E E[X] ∉ ℙ
────────────────────────────── ( callErr₁ )
( S, E, #F P ) ⟶ InvalidCall
F ∉ E
────────────────────────────────── ( callErr₀ )
( S, E, #F P ) ⟶ UnknownVariable
</pre>
<div id="arith-example"></div>
<script>
var app = Elm.Main.init({
node: document.getElementById('arith-example'),
flags: {
hasTrace: false,
adjustable: false,
program: `def INCR {
1 +
}
2 #INCR
5 #INCR #INCR
def DUPTWO {
swap
dup rot
dup rot
swap
}
#DUPTWO`
}});
</script>
</div>
</div>
<div id="outline-container-org27cdfbd" class="outline-3">
<h3 id="org27cdfbd">Variables</h3>
<div class="outline-text-3" id="text-org27cdfbd">
<p>
A variable is just a named integer. We can
</p>
<ul class="org-ul">
<li><i>assign</i> an integer to a variable, which adds a binding to the environment</li>
<li><i>lookup</i> a variable binding in the environment (by typing the variable itself)</li>
</ul>
<p>
Variables bindings are available within <i>blocks</i> (or globally). Local
blocks can be opened and closed using the delimiters '[' and ']',
respectively.<sup><a id="fnr.6" class="footref" href="#fn.6" role="doc-backlink">6</a></sup>
Bindings created within a local block are available only within the
evaluation of that block. Bindings not created within a local block
are available anywhere in the program after they've been created.
</p>
<pre class="example">
────────────────────────────────────────── ( assign )
( 𝑛 :: S, E, @X P ) ⟶ ( S, E[X ↦ 𝑛], P )
───────────────────────────────── ( assignErr₀ )
( ⊥, E, @X P ) ⟶ StackUnderflow
X ∈ E E[X] ∈ ℤ
───────────────────────────────────── ( lookup )
( S, E, X P ) ⟶ ( E[X] :: S, E, P )
X ∈ E E[X] ∉ ℤ
─────────────────────────────── ( lookupErr₁ )
( S, E, X P ) ⟶ InvalidLookup
X ∉ E
───────────────────────────────── ( lookupErr₂ )
( S, E, X P ) ⟶ UnknownVariable
────────────────────────────────── ( openLocal )
( S, E, [ P ) ⟶ ( S, ⟨⟩ · E, P )
───────────────────────────────── ( closeLocal )
( S, L · E, ] P ) ⟶ ( S, E, P )
───────────────────────────── ( closeLocalErr )
( S, 𝒢, ] P ) ⟶ GlobalClose
</pre>
<div id="arith-example"></div>
<script>
var app = Elm.Main.init({
node: document.getElementById('arith-example'),
flags: {
hasTrace: false,
adjustable: false,
program: `1 @X
X 1 + @Y
[
X Y
10 @X
X 10 + @Y
X Y
]
X Y`
}});
</script>
</div>
</div>
<div id="outline-container-org87fb8f8" class="outline-3">
<h3 id="org87fb8f8">Conditionals</h3>
<div class="outline-text-3" id="text-org87fb8f8">
<p>
Finally, there are if-statements for conditional reasoning. We also
include while-loops with the usual semantics (i.e., defined in terms of if-statements).
</p>
<pre class="example">
𝑛 ≠ 0
─────────────────────────────────────────────────────── ( ifTrue )
( 𝑛 :: S, E, ? { Q₁ } else { Q₂ } P ) ⟶ ( S, E, Q₂ P )
──────────────────────────────────────────────────────── ( ifFalse )
( 0 :: S, E, ? { Q₁ } else { Q₂ } P ) ⟶ ( S, E, Q₁ P )
─────────────────────────────────────────────────── ( ifErr₀ )
( ⊥, E, ? { Q₁ } else { Q₂ } P ) ⟶ StackUnderflow
─────────────────────────────────────────────────────── ( while )
( S, E, while { Q₁ } do { Q₂ } P ) ⟶
( S, E, Q₁ ? { Q₂ while { Q₁ } do { Q₂ } } else { } P )
</pre>
<div id="cond-example"></div>
<script>
var app = Elm.Main.init({
node: document.getElementById('cond-example'),
flags: {
hasTrace: true,
adjustable: false,
program: `0 @N
N 5 = ? {
24 print
} else {
37 print
}
while { 5 N < } do {
N print
1 N + @N
}`
}});
</script>
</div>
</div>
</div>
<div id="footnotes">
<h2 class="footnotes">Footnotes: </h2>
<div id="text-footnotes">
<div class="footdef"><sup><a id="fn.1" class="footnum" href="#fnr.1" role="doc-backlink">1</a></sup> <div class="footpara" role="doc-footnote"><p class="footpara">Note that this only saves the program, not the whole
program state. When reseting, the stack and environment will be
empty, but the inital program will be the most recently saved
program.</p></div></div>
<div class="footdef"><sup><a id="fn.2" class="footnum" href="#fnr.2" role="doc-backlink">2</a></sup> <div class="footpara" role="doc-footnote"><p class="footpara">This cannot be undone.</p></div></div>
<div class="footdef"><sup><a id="fn.3" class="footnum" href="#fnr.3" role="doc-backlink">3</a></sup> <div class="footpara" role="doc-footnote"><p class="footpara">In other word, 𝕍 = ℤ ∪ ℙ.</p></div></div>
<div class="footdef"><sup><a id="fn.4" class="footnum" href="#fnr.4" role="doc-backlink">4</a></sup> <div class="footpara" role="doc-footnote"><p class="footpara">It's
unofficial because printed strings are not a part of the
configuration. Semantically, <b>print</b> is identical to <b>drop</b>.</p></div></div>
<div class="footdef"><sup><a id="fn.5" class="footnum" href="#fnr.5" role="doc-backlink">5</a></sup> <div class="footpara" role="doc-footnote"><p class="footpara">Its truly amazing to me how simple this is.</p></div></div>
<div class="footdef"><sup><a id="fn.6" class="footnum" href="#fnr.6" role="doc-backlink">6</a></sup> <div class="footpara" role="doc-footnote"><p class="footpara">Note that they aren't actually delimiters. It's
possible to write program which opens more blocks than it closes.</p></div></div>
</div>
</div></div>
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</html>