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-- This file:
-- http://anggtwu.net/LUA/ELpeg-cme1.lua.html
-- http://anggtwu.net/LUA/ELpeg-cme1.lua
-- (find-angg "LUA/ELpeg-cme1.lua")
-- Author: Eduardo Ochs <eduardoochs@gmail.com>
--
-- A parser and LaTeXer for expressions like these ones:
-- http://anggtwu.net/mathologer-calculus-easy.html#17:12
-- http://www.youtube.com/watch?v=kuOxDh3egN0#t=17m12s
-- (find-calceasyvideo "17:12" " ")
-- with several weird extensions... for example:
-- "a // b" yields "\frac{a}{b}", and // binds more slowly than +
-- "a m b" yields "a b" - it's multiplication by concatenation
--
-- Superseded by:
-- (find-angg "LUA/CME2.lua")
--
-- (defun e1 () (interactive) (find-angg "LUA/ELpeg1.lua"))
-- (defun ec () (interactive) (find-angg "LUA/ELpeg-cme1.lua"))
-- (defun el () (interactive) (find-angg "LUA/ELpeg-lambda1.lua"))
-- (defun so () (interactive) (find-fline "~/LUA/Show2-outer.tex"))
-- (defun si () (interactive) (find-fline "~/LUA/Show2-inner.tex"))
--
-- (find-cp-LUA-links "ELpeg-cme1 ELpeg1 Globals1 PCall1 Show2 Subst1 Tree1")
--
-- «.how-it-should-look» (to "how-it-should-look")
-- «.Vlast» (to "Vlast")
-- «.fmts-and-funs» (to "fmts-and-funs")
-- «.Freeze» (to "Freeze")
require "ELpeg1" -- (find-angg "LUA/ELpeg1.lua")
gr,V,VA,VE,PE = Gram.new()
_ = S(" ")^0
-- «Vlast» (to ".Vlast")
-- (find-angg "LUA/ELpeg1.lua" "Gram-Vlast")
Gram.set = function (entries, name, pat)
Vlast = pat
entries[name] = pat
end
AST.alttags = {
eq="=", plus="+", minus="-", Mul="*",
div="/", Div="//", pow="^",
paren="()", plic="'"
}
-- ____ _ _
-- | _ \ _ __ ___ | |_ ___ | |_ _ _ _ __ ___
-- | |_) | '__/ _ \| __/ _ \| __| | | | '_ \ / _ \
-- | __/| | | (_) | || (_) | |_| |_| | |_) | __/
-- |_| |_| \___/ \__\___/ \__|\__, | .__/ \___|
-- |___/|_|
--
-- «how-it-should-look» (to ".how-it-should-look")
fun = function (name) return mkast("fun", name) end
var = function (name) return mkast("var", name) end
num = function (str) return mkast("num", str) end
bin = function (a, op, b) return mkast(op, a, b) end
unary = function (op, a) return mkast(op, a) end
paren = function (a) return unary("()", a) end
plic = function (a) return unary("'", a) end
ap = function (a, b) return bin(a, "ap", b) end
eq = function (a, b) return bin(a, "=", b) end
plus = function (a, b) return bin(a, "+", b) end
minus = function (a, b) return bin(a, "-", b) end
mul = function (a, b) return bin(a, "mul", b) end
Mul = function (a, b) return bin(a, "*", b) end
div = function (a, b) return bin(a, "/", b) end
Div = function (a, b) return bin(a, "//", b) end
pow = function (a, b) return bin(a, "^", b) end
E[ "x" ] = var"x"
E[ "ln x" ] = ap(fun"ln", E"x")
E["(ln x)" ] = paren(E"ln x")
E[ "3" ] = num("3")
E["(ln x)^3" ] = pow(E"(ln x)", E"3")
E["(ln x)^3" ] = pow(E"(ln x)", E"3")
E[ "5" ] = num("5")
E[ "sin x"] = ap(fun"sin", E"x")
E[ "5 + sin x"] = plus(E"5", E"sin x")
E["(ln x)^3 // 5 + sin x"] = Div(E"(ln x)^3", E"5 + sin x")
E[ "f" ] = fun"f"
E[ "(x)" ] = paren(E"x")
E[ "f(x)" ] = ap(E"f", E"(x)")
E[ "g" ] = fun"g"
E[ "g(x)" ] = ap(E"g", E"(x)")
E[ "f(x)g(x)" ] = mul(E"f(x)", E"g(x)")
E["(f(x)g(x))" ] = paren(E"f(x)g(x)")
E["(f(x)g(x))'" ] = plic(E"(f(x)g(x))")
E[ "f'" ] = fun"f'"
E[ "f'(x)" ] = ap(E"f'", E"(x)")
E[ "f'(x)g(x)" ] = mul(E"f'(x)", E"g(x)")
E[ "g'" ] = fun"g'"
E[ "g'(x)"] = ap(E"g'", E"(x)")
E[ "f(x)g'(x)"] = mul(E"f(x)", E"g'(x)")
E[ "f'(x)g(x) + f(x)g'(x)"] = plus(E"f'(x)g(x)", E"f(x)g'(x)")
E["(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"] = eq(E"(f(x)g(x))'", E"f'(x)g(x) + f(x)g'(x)")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "ELpeg-cme1.lua"
= E["(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"]
= E["(ln x)^3 // 5 + sin x"]
--]]
-- (find-angg "LUA/ELpeg1.lua" "assocs")
-- (find-LATEXfile "edrxgac2.tex" "\\def\\bsm")
-- (find-angg "LUA/Show2.lua" "texbody")
usepackages = [[
\usepackage{amsmath}
]]
defs = [[
\def\sm #1{\begin{smallmatrix}#1\end{smallmatrix}}
\def\mat #1{\begin{matrix}#1\end{matrix}}
\def\psm #1{\left (\sm {#1}\right )}
\def\bsm #1{\left [\sm {#1}\right ]}
\def\pmat#1{\left (\mat{#1}\right )}
\def\bmat#1{\left [\mat{#1}\right ]}
]]
foldplic = function (A)
local o = A[1]
for i=2,#A do o = plic(o) end
return o
end
assocplic = function (pe, po) return Ct(pe*(_*po)^0) / foldplic end
VA.num = Cs(P"-"^-1 * R"09"^1)
VA.var = anyof "x y a b e"
VA.fun = anyof "f'' f' f g' g ln sin sqrt"
VA.call = P"!" * (R("AZ", "az")^1):Cs()
VA.ap = V.fun *_* V.exprbasic
V.exprbasic = Cparen( "(", ")", V.expr)
+ Cparen(".(", ")", V.expr)
+ Cparen( "{", "}", V.expr)
+ Cparen( "[", "]", V.expr)
+ Cparen(".[", "]", V.expr)
+ V.call + V.ap + V.num + V.fun + V.var
V.exprplic = assocplic(Vlast, Cs"'" )
V.exprsubst = assocl(Vlast, Cs"s" )
V.exprpow = assocr(Vlast, Cs"^" )
V.exprmul = assocl(Vlast, anyof("mul m"))
V.exprMul = assocl(Vlast, Cs"*" )
V.exprdiv = assocl(Vlast, Cs"/" )
V.exprplus = assocl(Vlast, anyof("+ -"))
V.exprDiv = assocl(Vlast, Cs"//" )
V.expreq = assocl(Vlast, Cs"=" )
V.exprceq = assocl(Vlast, Cs":=" )
V.exprnl = assocl(Vlast, Cs";;" )
V.expr = _* V.exprnl
-- __ _ _ __
-- / _|_ __ ___ | |_ ___ __ _ _ __ __| | / _|_ _ _ __ ___
-- | |_| '_ ` _ \| __/ __| / _` | '_ \ / _` | | |_| | | | '_ \/ __|
-- | _| | | | | | |_\__ \ | (_| | | | | (_| | | _| |_| | | | \__ \
-- |_| |_| |_| |_|\__|___/ \__,_|_| |_|\__,_| |_| \__,_|_| |_|___/
--
-- «fmts-and-funs» (to ".fmts-and-funs")
fmts = VTable {}
funs = VTable {}
-- totex00 = ToTeX0 {fmts=fmts, funs=funs}
fmts[ "()"] = "(<1>)"
fmts[".()"] = "\\left(<1>\\right)"
fmts[ "[]"] = "\\bmat{<1>}"
fmts[".[]"] = "\\bsm{<1>}"
fmts[ "{}"] = "{<1>}"
fmts["'"] = "{<1>}'"
fmts["s"] = "<1> <2>"
fmts["+"] = "<1> + <2>"
fmts["-"] = "<1> - <2>"
fmts["*"] = "<1> \\cdot <2>"
fmts["/"] = "<1> / <2>"
fmts["//"] = "\\frac{<1>}{<2>}"
fmts[ "="] = "<1> = <2>"
fmts[":="] = "<1> \\,:=\\, <2>"
fmts[";;"] = "<1> \\\\{} <2>"
fmts["^"] = "{<1>}^{<2>}"
fmts["ap"] = "<1> <2>"
fmts["."] = "<1> <2>"
fmts["m"] = "<1> <2>"
fmts["mul"] = "<1> <2>"
fmts["num"] = "<1>"
fmts["var"] = "<1>"
fmts["call"] = "\\<1> "
fmts["fun"] = "<funs[o[1]] or o[1]>"
funs["ln"] = "\\ln "
funs["sin"] = "\\sin "
funs["sqrt"] = "\\sqrt "
-- V.exprbasic = paren("{", "}", V.expr) + V.word
-- V.exprund = assocl(Vlast, V.opund)
-- V.expradd = assocl(Vlast, V.opadd)
-- «Freeze» (to ".Freeze")
parse_cme = Parser.freeze("expr")
CME = Parser.freeze("expr")
--[[
* (code-etv2 "SHOW2DIR" "/tmp/" "Show2")
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "ELpeg-cme1.lua"
= CME "g(x)"
= CME "g(x)" :totex()
= funs
= funs["g"]
= CME "g(x) := 200*x"
= CME "g(x) := 200*x" :totex()
= CME "x mul y"
= CME "!foo mul y"
= CME "!foo mul y" :totex()
= CME "x mul y" :totex()
= CME "x . y" :totex()
= CME "sqrt{2+3}" :totex()
= CME "sqrt{2+3}" :show()
* (etv)
str = ".(f(g(x))) s .[ f(y):=e^y ;; g(x):=4x]"
str = ".(f(g(x))) s .[ f(y):=e^y ;; g(x):=4x] = (e^{4 x})"
o = gr:cm0("expr", str)
= o
= o:totex()
= o:show()
= Show.log
* (etv)
CME = Parser.freeze("expr")
= CME(".(x^2 * f(g(x))) s .[ f(x):=e^{3x} ;; f'(x):=3e^{3x}]")
= CME(".(x^2 * f(g(x))) s .[ f(x):=e^{3x} ;; f'(x):=3e^{3x}]"):totex()
= CME(".(x^2 mul f(g(x))) s .[ f(x):=e^{3x} ;; f'(x):=3e^{3x}]"):totex()
= CME("[f(x):=x^2 ;; a:=4]")
= CME(" [f(x):=x^2 ;; a:=4]"):totex()
= CME(" [f(x):=x^2 ;; a:=4]"):show()
* (etv)
CME(".[f(x):=x^2 ;; a:=4]"):show()
* (etv)
RC = CME("(f(g(x)))' = f'(g(x))g'(x)")
= RC
= RC:show(2)
* (etv)
str = ".[ f(x):=x^2 ;; a:=3]"
str = "2 s 4"
str = "2 s .[ 4 ]"
str = ".[ f(y):=e^y ;; g(x):=4x]"
str = "2 ;; .[ 4 ]"
= paren("(", ")", V.expr)
= E["(ln x)^3 // 5 + sin x"]
= CME "(ln x)^3 // 5 + sin x"
= E["(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"]
= CME "(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"
= CME "f(x):=x^2 ;; a:=3"
= CME "[ f(x):=x^2 ;; a:=3]"
= CME ".[ f(x):=x^2 ;; a:=3]"
= Show.log
= Show.bigstr
--]]
-- Local Variables:
-- coding: utf-8-unix
-- End: