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Warning: this is an htmlized version!
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-- This file:
-- http://anggtwu.net/LUA/Ast1.lua.html
-- http://anggtwu.net/LUA/Ast1.lua
-- (find-angg "LUA/Ast1.lua")
-- Author: Eduardo Ochs <eduardoochs@gmail.com>
--
-- (defun a () (interactive) (find-angg "LUA/Ast1.lua"))
-- (defun a1 () (interactive) (find-angg "LUA/Ast1.lua"))
-- (defun a2 () (interactive) (find-angg "LUA/Ast2.lua"))
-- (defun c3 () (interactive) (find-angg "LUA/Caepro3.lua"))
-- (defun c4 () (interactive) (find-angg "LUA/Caepro4.lua"))
-- (defun g2 () (interactive) (find-angg "LUA/Gram2.lua"))
-- (defun g3 () (interactive) (find-angg "LUA/Gram3.lua"))
-- Machinery for converting asts to text.
-- (find-angg "LUA/Caepro3.lua" "Abbrevs")
-- (find-angg "LUA/Caepro3.lua" "Abbrevs" "fmts =")
-- expand "LATEX/<ma:yyyy_s()>-<ma:MM()>-tudo.pdf"
-- expand "LATEX/<m:yyyy_s(a)>-<m:MM(a)>-tudo.pdf"
-- expand "LATEX/<:yyyy_s>-<:MM>-tudo.pdf"
-- yyyy_s = function (ma, ...) return ma.m:yyyy_s(ma.a, ...) end
-- «.AST» (to "AST")
-- «.AST-tests» (to "AST-tests")
-- «.E» (to "E")
-- «.E-tests» (to "E-tests")
-- «.ToTeX» (to "ToTeX")
-- «.ToTeX-tests» (to "ToTeX-tests")
require "Gram2" -- (find-angg "LUA/Gram2.lua")
lpeg.ptmatch = function (pat, str) PP(pat:Ct():match(str)) end
lpeg.Copyto = function (pat, tag) return pat:Cg(tag) * Cb(tag) end
-- _ ____ _____
-- / \ / ___|_ _|
-- / _ \ \___ \ | |
-- / ___ \ ___) || |
-- /_/ \_\____/ |_|
--
-- «AST» (to ".AST")
-- Based on: (find-angg "LUA/Gram2.lua" "AST")
--
alttags = {eq="=", plus="+", minus="-", Mul="*",
div="/", Div="//", pow="^",
paren="()", plic="'"}
AST = Class {
type = "AST",
ify = function (o)
if type(o) == "table" and o[0] and alttags[o[0]] then
o[0] = alttags[o[0]]
end
return AST(o)
end,
__tostring = function (o) return tostring(SynTree.from(o)) end,
__index = {
},
}
-- «AST-tests» (to ".AST-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Ast1.lua"
= AST.ify {[0]="Mul", 2, 3}
--]]
-- _____
-- | ____|
-- | _|
-- | |___
-- |_____|
--
-- «E» (to ".E")
entries = {}
E = setmetatable({}, {
__call = function (_,name) return entries[name] end,
__index = function (_,name) return entries[name] end,
__newindex = function (_,name,o) entries[name] = o end,
})
fun = function (name) return AST {[0]="fun", name} end
var = function (name) return AST {[0]="var", name} end
num = function (str) return AST {[0]="num", str} end
bin = function (a, op, b) return AST {[0]=op, a, b} end
unary = function (op, a) return AST {[0]=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)")
-- «E-tests» (to ".E-tests")
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Ast1.lua"
L = Code.L
= E["(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"]
= E["(ln x)^3 // 5 + sin x"]
--]]
-- (find-angg "LUA/Gram3.lua" "expr")
gr,V,VA,VE,PE = Gram.new()
grcm = function (...) print(gr:cm(...)) end
_ = S(" ")^0
VA.num = Cs(R"09"^1)
VA.var = anyof "x"
VA.fun = anyof "f' f g' g ln sin"
VA.ap = V.fun *_* V.exprbasic
VA.paren = "("*_* V.expr *_*")"
V.exprbasic = V.paren + V.ap + V.num + V.fun + V.var
V.exprplic = assocpost(V.exprbasic, Cs"'" )
V.exprpow = assocr(V.exprplic, Cs"^" )
V.exprmul = assocl(V.exprpow, Cc"mul" )
V.exprMul = assocl(V.exprmul, Cs"*" )
V.exprplus = assocl(V.exprMul, Cs"+" )
V.exprDiv = assocl(V.exprplus, Cs"//" )
V.expreq = assocl(V.exprDiv, Cs"=" )
V.expr = V.expreq
foldplic = function (A)
local o = A[1]
for i=2,#A do o = plic(o) end
return o
end
V.exprplic = Ct(V.exprbasic * (_*Cs"'")^0) / foldplic
--[[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Ast1.lua"
-- alttags = {}
= grcm("num", "234")
= grcm("expr", "234")
= grcm("expr", "f'")
= grcm("expr", "f'(x)")
= grcm("expr", "f'(x)")
= grcm("expr", "f'(x) + 5")
= grcm("expr", "f'(x) + 5^6 // 20")
= grcm("expr", "(ln x)^3 // 5 + sin x")
= grcm("expr", "(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)")
= E["(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"]
= E["(ln x)^3 // 5 + sin x"]
--]]
-- _____ _____ __ __
-- |_ _|_|_ _|__\ \/ /
-- | |/ _ \| |/ _ \\ /
-- | | (_) | | __// \
-- |_|\___/|_|\___/_/\_\
--
-- «ToTeX» (to ".ToTeX")
AST.__index.totex = function (o) return totex(o) end
AST.__index.tt = function (o) return ToTeX.new(o) end
totex = function (o)
if type(o) == "string" then return o end
if type(o) == "number" then return tostring(o) end
return ToTeX.fromast(o)
end
ToTeX = Class {
type = "ToTeX",
new = function (o) return ToTeX {o=o} end,
from = function (o)
if type(o) == "string" then return o end
if type(o) == "number" then return tostring(o) end
return ToTeX.new(o):asttotex()
end,
fromast = function (o) return ToTeX.from(o) end,
__index = {
fmts = {
["()"] = "(<1>)",
["//"] = "\\frac{<1>}{<2>}",
["^"] = "{<1>}^{<2>}",
["+"] = "<1> + <2>",
["="] = "<1> = <2>",
ap = "<1> <2>",
mul = "<1> <2>",
Mul = "<1> \\cdot <2>",
["'"] = "<1>'",
--
num = "<1>",
var = "<1>",
fun = "<tt.funs[o[1]] or o[1]>",
},
funs = {
ln = "\\ln ",
sin = "\\sin ",
},
--
eval = function (tt,fmt,a,b,c)
return L("tt,o,a,b,c => "..fmt)(tt, tt.o, a, b, c)
end,
getn = function (tt, n) return tt:eval("o[a+0]", n) end,
totexn = function (tt, n) return tt:eval("totex(o[a+0])", n) end,
tostringn = function (tt, n) return tt:eval("tostring(o[a+0])", n) end,
subst = function (tt, fmt)
local isnum = function (s) return s:match"^[0-9]+$" end
local totexn = function (n) return tt:totexn(n) end
local ev = function (s) return tt:eval(s) end
local f = function (s) return isnum(s) and totexn(s) or ev(s) end
return (fmt:gsub("<(.-)>", f))
end,
--
tag = function (tt) return tt.o[0] end,
fmt = function (tt) return tt:tag() and tt.fmts[tt:tag()] end,
asttotex = function (tt)
if not tt:tag() then return "[notag]" end
if not tt:fmt() then return "[no fmt: "..tt:tag().."]" end
return tt:subst(tt:fmt())
end,
},
}
-- «ToTeX-tests» (to ".ToTeX-tests")
--[==[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "Ast1.lua"
L = Code.L
o = E["(ln x)^3 // 5 + sin x"]
o = E["(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)"]
= o
= o:totex()
= E["(ln x)"]
= E["(ln x)"]:tt()
= E["(ln x)"]:tt():tostringn(1)
= E["(ln x)"]:tt():asttotex()
= totex(23)
= E["(ln x)"]:totex()
= E["x"]:totex()
= E["x"]:totex()
= E["x"]:totex0():fmt()
= E["x"]:totex0():format()
= E["x"]:totex0():eval("mytostring(o)")
= E["x"]:totex0():eval("o[0]")
= E["x"]:totex0():eval("o[1]")
= E["x"]:totex0():eval("o[a]", 1)
= E["x"]:totex0():eval("o[a]", "1")
= E["x"]:totex0():eval("o[a+0]", "1")
= fun"x":totex0()
--]==]
-- Local Variables:
-- coding: utf-8-unix
-- End: