1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
<head>
<title>Penlight Documentation</title>
<link rel="stylesheet" href="../ldoc_fixed.css" type="text/css" />
</head>
<body>
<div id="container">
<div id="product">
<div id="product_logo"></div>
<div id="product_name"><big><b></b></big></div>
<div id="product_description"></div>
</div> <!-- id="product" -->
<div id="main">
<!-- Menu -->
<div id="navigation">
<br/>
<h1>Penlight</h1>
<ul>
<li><a href="../index.html">Index</a></li>
</ul>
<h2>Examples</h2>
<ul class="nowrap">
<li><a href="../examples/seesubst.lua.html">seesubst.lua</a></li>
<li><a href="../examples/sipscan.lua.html">sipscan.lua</a></li>
<li><strong>symbols.lua</strong></li>
<li><a href="../examples/test-cmp.lua.html">test-cmp.lua</a></li>
<li><a href="../examples/test-data.lua.html">test-data.lua</a></li>
<li><a href="../examples/test-listcallbacks.lua.html">test-listcallbacks.lua</a></li>
<li><a href="../examples/test-pretty.lua.html">test-pretty.lua</a></li>
<li><a href="../examples/test-symbols.lua.html">test-symbols.lua</a></li>
<li><a href="../examples/testclone.lua.html">testclone.lua</a></li>
<li><a href="../examples/testconfig.lua.html">testconfig.lua</a></li>
<li><a href="../examples/testglobal.lua.html">testglobal.lua</a></li>
<li><a href="../examples/testinputfields.lua.html">testinputfields.lua</a></li>
<li><a href="../examples/testinputfields2.lua.html">testinputfields2.lua</a></li>
<li><a href="../examples/testxml.lua.html">testxml.lua</a></li>
<li><a href="../examples/which.lua.html">which.lua</a></li>
</ul>
<h2>Libraries</h2>
<ul class="nowrap">
<li><a href="../libraries/pl.html">pl</a></li>
<li><a href="../libraries/pl.app.html">pl.app</a></li>
<li><a href="../libraries/pl.array2d.html">pl.array2d</a></li>
<li><a href="../libraries/pl.class.html">pl.class</a></li>
<li><a href="../libraries/pl.compat.html">pl.compat</a></li>
<li><a href="../libraries/pl.comprehension.html">pl.comprehension</a></li>
<li><a href="../libraries/pl.config.html">pl.config</a></li>
<li><a href="../libraries/pl.data.html">pl.data</a></li>
<li><a href="../libraries/pl.dir.html">pl.dir</a></li>
<li><a href="../libraries/pl.file.html">pl.file</a></li>
<li><a href="../libraries/pl.func.html">pl.func</a></li>
<li><a href="../libraries/pl.import_into.html">pl.import_into</a></li>
<li><a href="../libraries/pl.input.html">pl.input</a></li>
<li><a href="../libraries/pl.lapp.html">pl.lapp</a></li>
<li><a href="../libraries/pl.lexer.html">pl.lexer</a></li>
<li><a href="../libraries/pl.luabalanced.html">pl.luabalanced</a></li>
<li><a href="../libraries/pl.operator.html">pl.operator</a></li>
<li><a href="../libraries/pl.path.html">pl.path</a></li>
<li><a href="../libraries/pl.permute.html">pl.permute</a></li>
<li><a href="../libraries/pl.pretty.html">pl.pretty</a></li>
<li><a href="../libraries/pl.seq.html">pl.seq</a></li>
<li><a href="../libraries/pl.sip.html">pl.sip</a></li>
<li><a href="../libraries/pl.strict.html">pl.strict</a></li>
<li><a href="../libraries/pl.stringio.html">pl.stringio</a></li>
<li><a href="../libraries/pl.stringx.html">pl.stringx</a></li>
<li><a href="../libraries/pl.tablex.html">pl.tablex</a></li>
<li><a href="../libraries/pl.template.html">pl.template</a></li>
<li><a href="../libraries/pl.test.html">pl.test</a></li>
<li><a href="../libraries/pl.text.html">pl.text</a></li>
<li><a href="../libraries/pl.types.html">pl.types</a></li>
<li><a href="../libraries/pl.url.html">pl.url</a></li>
<li><a href="../libraries/pl.utils.html">pl.utils</a></li>
<li><a href="../libraries/pl.xml.html">pl.xml</a></li>
</ul>
<h2>Classes</h2>
<ul class="nowrap">
<li><a href="../classes/pl.Date.html">pl.Date</a></li>
<li><a href="../classes/pl.List.html">pl.List</a></li>
<li><a href="../classes/pl.Map.html">pl.Map</a></li>
<li><a href="../classes/pl.MultiMap.html">pl.MultiMap</a></li>
<li><a href="../classes/pl.OrderedMap.html">pl.OrderedMap</a></li>
<li><a href="../classes/pl.Set.html">pl.Set</a></li>
</ul>
<h2>Manual</h2>
<ul class="nowrap">
<li><a href="../manual/01-introduction.md.html">Introduction</a></li>
<li><a href="../manual/02-arrays.md.html">Tables and Arrays</a></li>
<li><a href="../manual/03-strings.md.html">Strings. Higher-level operations on strings.</a></li>
<li><a href="../manual/04-paths.md.html">Paths and Directories</a></li>
<li><a href="../manual/05-dates.md.html">Date and Time</a></li>
<li><a href="../manual/06-data.md.html">Data</a></li>
<li><a href="../manual/07-functional.md.html">Functional Programming</a></li>
<li><a href="../manual/08-additional.md.html">Additional Libraries</a></li>
<li><a href="../manual/09-discussion.md.html">Technical Choices</a></li>
</ul>
</div>
<div id="content">
<h2>symbols.lua</h2>
<pre>
<span class="global">require</span> <span class="string">'pl'</span>
utils.import <span class="string">'pl.func'</span>
<span class="keyword">local</span> ops = <span class="global">require</span> <span class="string">'pl.operator'</span>
<span class="keyword">local</span> List = <span class="global">require</span> <span class="string">'pl.List'</span>
<span class="keyword">local</span> append,concat = <span class="global">table</span>.insert,<span class="global">table</span>.concat
<span class="keyword">local</span> compare,find_if,compare_no_order,imap,reduce,count_map = tablex.compare,tablex.find_if,tablex.compare_no_order,tablex.imap,tablex.reduce,tablex.count_map
<span class="keyword">local</span> <span class="global">unpack</span> = <span class="global">table</span>.<span class="global">unpack</span>
<span class="keyword">function</span> bindval (self,val)
<span class="global">rawset</span>(self,<span class="string">'value'</span>,val)
<span class="keyword">end</span>
<span class="keyword">local</span> optable = ops.optable
<span class="keyword">function</span> sexpr (e)
<span class="keyword">if</span> isPE(e) <span class="keyword">then</span>
<span class="keyword">if</span> e.op ~= <span class="string">'X'</span> <span class="keyword">then</span>
<span class="keyword">local</span> args = tablex.imap(sexpr,e)
<span class="keyword">return</span> <span class="string">'('</span>..e.op..<span class="string">' '</span>..<span class="global">table</span>.concat(args,<span class="string">' '</span>)..<span class="string">')'</span>
<span class="keyword">else</span>
<span class="keyword">return</span> e.repr
<span class="keyword">end</span>
<span class="keyword">else</span>
<span class="keyword">return</span> <span class="global">tostring</span>(e)
<span class="keyword">end</span>
<span class="keyword">end</span>
psexpr = compose(<span class="global">print</span>,sexpr)
<span class="keyword">function</span> equals (e1,e2)
<span class="keyword">local</span> p1,p2 = isPE(e1),isPE(e2)
<span class="keyword">if</span> p1 ~= p2 <span class="keyword">then</span> <span class="keyword">return</span> <span class="keyword">false</span> <span class="keyword">end</span> <span class="comment">-- different kinds of animals!
</span> <span class="keyword">if</span> p1 <span class="keyword">and</span> p2 <span class="keyword">then</span> <span class="comment">-- both PEs
</span> <span class="comment">-- operators must be the same
</span> <span class="keyword">if</span> e1.op ~= e2.op <span class="keyword">then</span> <span class="keyword">return</span> <span class="keyword">false</span> <span class="keyword">end</span>
<span class="comment">-- PHs are equal if their representations are equal
</span> <span class="keyword">if</span> e1.op == <span class="string">'X'</span> <span class="keyword">then</span> <span class="keyword">return</span> e1.repr == e2.repr
<span class="comment">-- commutative operators
</span> <span class="keyword">elseif</span> e1.op == <span class="string">'+'</span> <span class="keyword">or</span> e1.op == <span class="string">'*'</span> <span class="keyword">then</span>
<span class="keyword">return</span> compare_no_order(e1,e2,equals)
<span class="keyword">else</span>
<span class="comment">-- arguments must be the same
</span> <span class="keyword">return</span> compare(e1,e2,equals)
<span class="keyword">end</span>
<span class="keyword">else</span> <span class="comment">-- fall back on simple equality for non PEs
</span> <span class="keyword">return</span> e1 == e2
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="comment">-- run down an unbalanced operator chain (like a+b+c) and return the arguments {a,b,c}
</span><span class="keyword">function</span> tcollect (op,e,ls)
<span class="keyword">if</span> isPE(e) <span class="keyword">and</span> e.op == op <span class="keyword">then</span>
<span class="keyword">for</span> i = <span class="number">1</span>,#e <span class="keyword">do</span>
tcollect(op,e[i],ls)
<span class="keyword">end</span>
<span class="keyword">else</span>
ls:append(e)
<span class="keyword">return</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">function</span> rcollect (e)
<span class="keyword">local</span> res = List()
tcollect(e.op,e,res)
<span class="keyword">return</span> res
<span class="keyword">end</span>
<span class="comment">-- balance ensures that +/* chains are collected together, operates in-place.
</span><span class="comment">-- thus (+(+ a b) c) or (+ a (+ b c)) becomes (+ a b c), order immaterial
</span><span class="keyword">function</span> balance (e)
<span class="keyword">if</span> isPE(e) <span class="keyword">and</span> e.op ~= <span class="string">'X'</span> <span class="keyword">then</span>
<span class="keyword">local</span> op,args = e.op
<span class="keyword">if</span> op == <span class="string">'+'</span> <span class="keyword">or</span> op == <span class="string">'*'</span> <span class="keyword">then</span>
args = rcollect(e)
<span class="keyword">else</span>
args = imap(balance,e)
<span class="keyword">end</span>
<span class="keyword">for</span> i = <span class="number">1</span>,#args <span class="keyword">do</span>
e[i] = args[i]
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">return</span> e
<span class="keyword">end</span>
<span class="comment">-- fold constants in an expression
</span><span class="keyword">function</span> fold (e)
<span class="keyword">if</span> isPE(e) <span class="keyword">then</span>
<span class="keyword">if</span> e.op == <span class="string">'X'</span> <span class="keyword">then</span>
<span class="comment">-- there could be _bound values_!
</span> <span class="keyword">local</span> val = <span class="global">rawget</span>(e,<span class="string">'value'</span>)
<span class="keyword">return</span> val <span class="keyword">and</span> val <span class="keyword">or</span> e
<span class="keyword">else</span>
<span class="keyword">local</span> op = e.op
<span class="keyword">local</span> addmul = op == <span class="string">'*'</span> <span class="keyword">or</span> op == <span class="string">'+'</span>
<span class="comment">-- first fold all arguments
</span> <span class="keyword">local</span> args = imap(fold,e)
<span class="keyword">if</span> <span class="keyword">not</span> addmul <span class="keyword">and</span> <span class="keyword">not</span> find_if(args,isPE) <span class="keyword">then</span>
<span class="comment">-- no placeholders in these args, we can fold the expression.
</span> <span class="keyword">local</span> opfn = optable[op]
<span class="keyword">if</span> opfn <span class="keyword">then</span>
<span class="keyword">return</span> opfn(<span class="global">unpack</span>(args))
<span class="keyword">else</span>
<span class="keyword">return</span> <span class="string">'?'</span>
<span class="keyword">end</span>
<span class="keyword">elseif</span> addmul <span class="keyword">then</span>
<span class="comment">-- enforce a few rules for + and *
</span> <span class="comment">-- split the args into two classes, PE args and non-PE args.
</span> <span class="keyword">local</span> classes = List.partition(args,isPE)
<span class="keyword">local</span> pe,npe = classes[<span class="keyword">true</span>],classes[<span class="keyword">false</span>]
<span class="keyword">if</span> npe <span class="keyword">then</span> <span class="comment">-- there's at least one non PE argument
</span> <span class="comment">-- so fold them
</span> <span class="keyword">if</span> #npe == <span class="number">1</span> <span class="keyword">then</span> npe = npe[<span class="number">1</span>]
<span class="keyword">else</span> npe = npe:reduce(optable[op])
<span class="keyword">end</span>
<span class="comment">-- if the result is a constant, return it
</span> <span class="keyword">if</span> <span class="keyword">not</span> pe <span class="keyword">then</span> <span class="keyword">return</span> npe <span class="keyword">end</span>
<span class="comment">-- either (* 1 x) => x or (* 1 x y ...) => (* x y ...)
</span> <span class="keyword">if</span> op == <span class="string">'*'</span> <span class="keyword">then</span>
<span class="keyword">if</span> npe == <span class="number">0</span> <span class="keyword">then</span> <span class="keyword">return</span> <span class="number">0</span>
<span class="keyword">elseif</span> npe == <span class="number">1</span> <span class="keyword">then</span> <span class="comment">-- identity
</span> <span class="keyword">if</span> #pe == <span class="number">1</span> <span class="keyword">then</span> <span class="keyword">return</span> pe[<span class="number">1</span>] <span class="keyword">else</span> npe = <span class="keyword">nil</span> <span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">else</span> <span class="comment">-- special cases for +
</span> <span class="keyword">if</span> npe == <span class="number">0</span> <span class="keyword">then</span> <span class="comment">-- identity
</span> <span class="keyword">if</span> #pe == <span class="number">1</span> <span class="keyword">then</span> <span class="keyword">return</span> pe[<span class="number">1</span>] <span class="keyword">else</span> npe = <span class="keyword">nil</span> <span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="comment">-- build up the final arguments
</span> <span class="keyword">local</span> res = {}
<span class="keyword">if</span> npe <span class="keyword">then</span> append(res,npe) <span class="keyword">end</span>
<span class="keyword">for</span> val,count <span class="keyword">in</span> <span class="global">pairs</span>(count_map(pe,equals)) <span class="keyword">do</span>
<span class="keyword">if</span> count > <span class="number">1</span> <span class="keyword">then</span>
<span class="keyword">if</span> op == <span class="string">'*'</span> <span class="keyword">then</span> val = val ^ count
<span class="keyword">else</span> val = val * count
<span class="keyword">end</span>
<span class="keyword">end</span>
append(res,val)
<span class="keyword">end</span>
<span class="keyword">if</span> #res == <span class="number">1</span> <span class="keyword">then</span> <span class="keyword">return</span> res[<span class="number">1</span>] <span class="keyword">end</span>
<span class="keyword">return</span> PE{op=op,<span class="global">unpack</span>(res)}
<span class="keyword">elseif</span> op == <span class="string">'^'</span> <span class="keyword">then</span>
<span class="keyword">if</span> args[<span class="number">2</span>] == <span class="number">1</span> <span class="keyword">then</span> <span class="keyword">return</span> args[<span class="number">1</span>] <span class="keyword">end</span> <span class="comment">-- identity
</span> <span class="keyword">if</span> args[<span class="number">2</span>] == <span class="number">0</span> <span class="keyword">then</span> <span class="keyword">return</span> <span class="number">1</span> <span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">return</span> PE{op=op,<span class="global">unpack</span>(args)}
<span class="keyword">end</span>
<span class="keyword">else</span>
<span class="keyword">return</span> e
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">function</span> expand (e)
<span class="keyword">if</span> isPE(e) <span class="keyword">and</span> e.op == <span class="string">'*'</span> <span class="keyword">and</span> isPE(e[<span class="number">2</span>]) <span class="keyword">and</span> e[<span class="number">2</span>].op == <span class="string">'+'</span> <span class="keyword">then</span>
<span class="keyword">local</span> a,b = e[<span class="number">1</span>],e[<span class="number">2</span>]
<span class="keyword">return</span> expand(b[<span class="number">1</span>]*a) + expand(b[<span class="number">2</span>]*a)
<span class="keyword">else</span>
<span class="keyword">return</span> e
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">function</span> isnumber (x)
<span class="keyword">return</span> <span class="global">type</span>(x) == <span class="string">'number'</span>
<span class="keyword">end</span>
<span class="comment">-- does this PE contain a reference to x?
</span><span class="keyword">function</span> references (e,x)
<span class="keyword">if</span> isPE(e) <span class="keyword">then</span>
<span class="keyword">if</span> e.op == <span class="string">'X'</span> <span class="keyword">then</span> <span class="keyword">return</span> x.repr == e.repr
<span class="keyword">else</span>
<span class="keyword">return</span> find_if(e,references,x)
<span class="keyword">end</span>
<span class="keyword">else</span>
<span class="keyword">return</span> <span class="keyword">false</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">local</span> <span class="keyword">function</span> muli (args)
<span class="keyword">return</span> PE{op=<span class="string">'*'</span>,<span class="global">unpack</span>(args)}
<span class="keyword">end</span>
<span class="keyword">local</span> <span class="keyword">function</span> addi (args)
<span class="keyword">return</span> PE{op=<span class="string">'+'</span>,<span class="global">unpack</span>(args)}
<span class="keyword">end</span>
<span class="keyword">function</span> diff (e,x)
<span class="keyword">if</span> isPE(e) <span class="keyword">and</span> references(e,x) <span class="keyword">then</span>
<span class="keyword">local</span> op = e.op
<span class="keyword">if</span> op == <span class="string">'X'</span> <span class="keyword">then</span>
<span class="keyword">return</span> <span class="number">1</span>
<span class="keyword">else</span>
<span class="keyword">local</span> a,b = e[<span class="number">1</span>],e[<span class="number">2</span>]
<span class="keyword">if</span> op == <span class="string">'+'</span> <span class="keyword">then</span> <span class="comment">-- differentiation is linear
</span> <span class="keyword">local</span> args = imap(diff,e,x)
<span class="keyword">return</span> balance(addi(args))
<span class="keyword">elseif</span> op == <span class="string">'*'</span> <span class="keyword">then</span> <span class="comment">-- product rule
</span> <span class="keyword">local</span> res,d,ee = {}
<span class="keyword">for</span> i = <span class="number">1</span>,#e <span class="keyword">do</span>
d = fold(diff(e[i],x))
<span class="keyword">if</span> d ~= <span class="number">0</span> <span class="keyword">then</span>
ee = {<span class="global">unpack</span>(e)}
ee[i] = d
append(res,balance(muli(ee)))
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">if</span> #res > <span class="number">1</span> <span class="keyword">then</span> <span class="keyword">return</span> addi(res)
<span class="keyword">else</span> <span class="keyword">return</span> res[<span class="number">1</span>] <span class="keyword">end</span>
<span class="keyword">elseif</span> op == <span class="string">'^'</span> <span class="keyword">and</span> isnumber(b) <span class="keyword">then</span> <span class="comment">-- power rule
</span> <span class="keyword">return</span> b*x^(b-<span class="number">1</span>)
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">else</span>
<span class="keyword">return</span> <span class="number">0</span>
<span class="keyword">end</span>
<span class="keyword">end</span></pre>
</div> <!-- id="content" -->
</div> <!-- id="main" -->
<div id="about">
<i>generated by <a href="http://github.com/stevedonovan/LDoc">LDoc 1.4.6</a></i>
<i style="float:right;">Last updated 2020-09-22 15:59:54 </i>
</div> <!-- id="about" -->
</div> <!-- id="container" -->
</body>
</html>
|
