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<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>
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<li><a href="../examples/test-symbols.lua.html">test-symbols.lua</a></li>
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<h2>Manual</h2>
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<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> unpack = utils.unpack
<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(unpack(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,unpack(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,unpack(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>,unpack(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>,unpack(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 = {unpack(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>
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