diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..8dab695
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,3 @@
+a.s
+a.out
+.gitignore
diff --git a/README.md b/README.md
index 08080c8..4ed26d3 100644
--- a/README.md
+++ b/README.md
@@ -15,4 +15,4 @@ to make it executable, please use `gcc`: `gcc ./a.c -o output.out`
 the example `.tc` file is in `./test`
 
 ## Known issues
- - parser for a + b + c .. and a * b * c
\ No newline at end of file
+ - all connected variable are pathized (I don't understand the tricky method to elimitated the path number)
\ No newline at end of file
diff --git a/passesInstrument.md b/passesInstrument.md
index 3c03136..d95fb4c 100644
--- a/passesInstrument.md
+++ b/passesInstrument.md
@@ -14,3 +14,4 @@ assign_homes
  5. **OK**assign homes (register allocation)
  6. **OK**patch instructions
  7. **OK**prelude & conclusion
+ 8. **OK** (vartex coloring)
\ No newline at end of file
diff --git a/src/TComp.jl b/src/TComp.jl
index e18faa1..23aa43c 100644
--- a/src/TComp.jl
+++ b/src/TComp.jl
@@ -1,6 +1,8 @@
 module TComp
 include("./parser.jl")
+include("./vertexcoloring.jl")
 using .Parser
+using .VertexColoring
 using Match
 
 # For pass 2
@@ -15,7 +17,7 @@ prog = read(f, String)
 
 #(prog)
 parsed = Parser.totalParse(prog)
-#print(parsed)
+println("PARSED\n", Parser.prettyStringLisp(parsed))
 tmp_var_no = 0
 
 
@@ -156,6 +158,8 @@ end
 
 ### PASS 3 assign x86 instruction
 function assignInstruction(inp)
+    println("INP", inp)
+
     resList = []
     for i in inp
         @match i begin
@@ -166,7 +170,7 @@ function assignInstruction(inp)
                 push!(resList, ["movq", val, "%rax"])
             end
             [("%let", "id"), [_ty, (id, "id")],
-               [("%prime", "id"), (op, _), [(lhs, lhs_t), (rhs, rhs_t)]]] =>
+                [("%prime", "id"), (op, _), [(lhs, lhs_t), (rhs, rhs_t)]]] =>
             begin
                 instr = ""
                 ops = ["+", "-", "*", "/"]
@@ -205,13 +209,8 @@ function assignInstruction(inp)
                 line = ["movq", val, id]
                 push!(resList, line)
             end
-
-            (c, "int") => begin
-                c_modified = "\$" * c
-                push!(resList, [c_modified])
-            end
-
-            (v, "id") => push!(resList, [v])
+            (c, "int") => push!(resList, ["movq", "\$" * c, "%rax"])
+            (val, "id") => push!(resList, ["movq", val, "%rax"])
             _ => println("Error")
         end
     end
@@ -228,11 +227,78 @@ res2 = explicitControlRemoveComplex(res)
 
 #println("PASS2", Parser.prettyStringLisp(res2))
 res3 = assignInstruction(res2)
-#println("PASS3", res3)
+println("RES3:\n", res3)
+# generate vertex graph for register allocation using vertex-coloring model
+function generateVertexGraph(prog)
+    graph = []
+    progReversed = reverse(prog)
+
+    varRegex = r"(^[^\$].*)"
+
+    out = Set([])
+    in_ = Set([])
+    use = Set([])
+    def = Set([])
+
+    for i in progReversed
+        use = Set([])
+        def = Set([])
+        # only support binary operation(3-term)
+        out = in_ #prev. out-set becomes current in-set
+        @match i begin
+        ["movq", orig, dest] => # dest = orig
+            begin
+                if match(varRegex, orig) != nothing
+                    push!(use, orig)
+                end
+                if match(varRegex, dest) != nothing
+                    push!(def, dest)
+                end
+            end
+        # dest = orig (+-*/) dest
+        [op, orig, dest] where (op in ["addq", "subq", "imulq", "divq"]) =>
+            begin
+                if match(varRegex, orig) != nothing
+                    push!(use, orig)
+                end
+                if match(varRegex, dest) != nothing
+                    push!(use, dest)
+                    push!(def, dest)
+                end
+            end
+        _ => 0
+        end
+
+        in_ = union(use, setdiff(out, def))
+        #println("IN", in_)
+        #println("DEF", def)
+        #println("OUT", out)
+        in_list = collect(in_)
+
+        for j in range(1, length(in_list)-1)
+            for k in range(j+1,length(in_list))
+                path1 = [in_list[j], in_list[k]]
+                path2 = [in_list[k], in_list[j]]
+                if !(path1 in graph) & !(path2 in graph)
+                    push!(graph, path1)
+                end 
+            end
+        end
+    end
+    return graph
+end
+
+vertexGraph = generateVertexGraph(res3)
+println(vertexGraph)
+colorGraphDictWithMaxId = VertexColoring.vertexColoring(vertexGraph)
+colorGraphDict = colorGraphDictWithMaxId[1]
+colorMaxId = colorGraphDictWithMaxId[2]
+
+registerList = ["%rax", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15"]
 
 
 # PASS4 assign home
-function assignHomes(inp)
+function assignHomes(inp, colorGraph, registerList)
     varRegex = r"(^[^\$%].*)"
     res = []
     vars = []
@@ -250,8 +316,6 @@ function assignHomes(inp)
             end
         end 
     end
-    #println("ALL_VAR", vars)
-
 
     varsLength = length(vars)
     for i in inp
@@ -259,18 +323,33 @@ function assignHomes(inp)
         orig = i[2]
         dest = i[3]
 
-        origIdx = findfirst(x -> x == orig,vars)
-        if origIdx != nothing
-            realAddressIdx = varsLength - origIdx + 1
-            realAddress = "-$(realAddressIdx * 8)(%rbp)"
-            orig = realAddress
+
+        if orig in keys(colorGraph)
+            origColorId = colorGraph[orig]
+            if origColorId <= length(registerList)
+                orig = registerList[origColorId]
+            else
+                origIdx = findfirst(x -> x == orig,vars)
+                realAddressIdx = varsLength - origIdx + 1
+                realAddress = "-$(realAddressIdx * 8)(%rbp)"
+                orig = realAddress
+            end 
+        elseif match(r"(^[^\$%].+)", orig) != nothing # isolated (unpathized) variable
+            orig = "%rax"
         end
 
-        destIdx = findfirst(x -> x == dest,vars)
-        if destIdx != nothing
-            realAddressIdx = varsLength - destIdx + 1
-            realAddress = "-$(realAddressIdx * 8)(%rbp)"
-            dest = realAddress
+        if dest in keys(colorGraph)
+            destColorId = colorGraph[dest]
+            if destColorId <= length(registerList)
+                dest = registerList[destColorId]
+            else
+                destIdx = findfirst(x -> x == dest,vars)
+                realAddressIdx = varsLength - destIdx + 1
+                realAddress = "-$(realAddressIdx * 8)(%rbp)"
+                dest = realAddress
+            end  
+        elseif match(r"(^[^\$%].+)", dest) != nothing # isolated (unpathized) variable
+            dest = "%rax"             
         end
 
         push!(res, [instr, orig, dest])
@@ -294,13 +373,20 @@ function patchInstruction(inp)
 
             cmd2 = [inst, "%rax", dest]
             push!(res, cmd2)
-        elseif (inst == "imulq") & (match(r"^%.+", dest) == nothing)
-            cmd1 = ["movq", dest, "%rax"]
-            cmd2 = ["imulq", orig, "%rax"]
-            cmd3 = ["movq", "%rax", dest]
-            push!(res, cmd1)
-            push!(res, cmd2)
-            push!(res, cmd3)
+        elseif (inst == "imulq")
+            if (match(r"^%.+", dest) == nothing)
+                cmd1 = ["movq", dest, "%rax"]
+                cmd2 = ["imulq", orig, "%rax"]
+                cmd3 = ["movq", "%rax", dest]
+                push!(res, cmd1)
+                push!(res, cmd2)
+                push!(res, cmd3)
+            else  #if dest is a %register
+                cmd1 = ["imulq", orig, dest] #result stored in %rax
+                cmd2 = ["movq", "%rax", dest]
+                push!(res, cmd1)
+                push!(res, cmd2)
+            end
 
         else
             push!(res, i)
@@ -309,7 +395,7 @@ function patchInstruction(inp)
     return res
 end
 
-res4 = assignHomes(res3)
+res4 = assignHomes(res3, colorGraphDict, registerList)
 res4_prog = res4[1]
 varNumber = res4[2]
 res5 = patchInstruction(res4_prog)
@@ -317,8 +403,8 @@ res5 = patchInstruction(res4_prog)
 
 
 ## PASS6 add prelude and conclude
-function preludeConclude(prog, varNumber)
-    rspSubqMax = varNumber * 8
+function preludeConclude(prog, colorMaxId, registerList)
+    rspSubqMax = (colorMaxId < length(registerList)) ? 0 : ((colorMaxId - length(registerList)) * 8)
 
     body = "start:\n"
 
@@ -337,13 +423,13 @@ function preludeConclude(prog, varNumber)
     	pushq %rbp
     	movq	 %rsp, %rbp\n""" * "\tsubq	 \$$rspSubqMax, %rsp\n\tjmp start\n\n"
 
-    conclude = """\nconclusion:\n""" * "\taddq	 \$$rspSubqMax, %rsp\n\tpopq	%rbp\n\tretq"
+    conclude = """\nconclusion:\n""" * "\taddq	 \$$rspSubqMax, %rsp\n\tpopq	%rbp\n\tretq\n"
 
     assemblyProg = prelude * body * conclude
     return assemblyProg
 end
 
-res6 = preludeConclude(res5, varNumber)
+res6 = preludeConclude(res5, colorMaxId, registerList)
 # println("PASS6",res6) # emit assembly code
 f2 = open("./a.s", "w")
 write(f2, res6) #write the assembly code
diff --git a/src/parser.jl b/src/parser.jl
index 33b948f..3166113 100644
--- a/src/parser.jl
+++ b/src/parser.jl
@@ -1,4 +1,5 @@
 module Parser
+using Match
 
 struct ParserResult
     matched
@@ -85,7 +86,9 @@ end
 
 
 
-patternList = [("int", "\\d+"),
+patternList = [
+               ("cmt", "[#][^\\r\\n]+"),
+               ("int", "\\d+"),
                ("id", "[_a-zA-Z][_0-9a-zA-Z]*"),
                ("lParen", "[\\(]"),
                ("rParen", "[\\)]"),
@@ -184,8 +187,8 @@ func = "(" fn_args ")" "=>" body
 unit = func | "(" exp ")" | atom
 args = unit ("," unit)*
 factor = unit "(" args ")"
-term = (factor (*|/) factor) | factor
-exp = (term (+|-) term) | term
+term = (factor (*|/) term) | factor
+exp = (term [(+|-) exp]) | term
 
 letexp = ty id "=" exp ";" body
 body = exp | letexp
@@ -233,10 +236,12 @@ function funcAux(input)
 end
 
 function longUnitAux(input)
-    rawFunc = seq([typ("lParen"),  exp, typ("rParen")])
+    rawFunc = seq([typ("lParen"), exp, typ("rParen")])
     rawRes = rawFunc.fun(input)
     if rawRes != nothing
-        matched = rawRes.matched[2]
+        #fix for tree fix problem
+        matched = [("%wrapper", "id"), rawRes.matched[2]]
+        
         res = ParserResult(matched, rawRes.remained)
         return res
     else
@@ -300,10 +305,26 @@ end
 factor = Psr(factorAux)
 
 function longTermAux(input)
-    rawFunc = seq([factor,  (typ("mul") | typ("div")), factor])
+    rawFunc = seq([factor,  (typ("mul") | typ("div")), term])
     rawRes = rawFunc.fun(input)
     if rawRes != nothing
-        matched = [("%prime", "id"), rawRes.matched[2], [rawRes.matched[1], rawRes.matched[3]]]
+        #correct the tree a /(b / c) -> (a / b) / c
+        leftRator = rawRes.matched[2]
+        a = rawRes.matched[1]
+        bc = rawRes.matched[3]
+        matched = @match bc begin
+            [("%prime", "id"), (rightRator, tRightRator), [b, c]] where ((rightRator == "*") || (rightRator == "/")) =>
+            begin
+                [("%prime", "id"), (rightRator, tRightRator), [[("%prime", "id"), leftRator, [a, b]], c]]
+            end
+            _ => begin
+                 [("%prime", "id"), leftRator, [a, bc]]
+
+            end
+
+        end
+
+        #matched = [("%prime", "id"), leftRator, [a, bc]]
         res = ParserResult(matched, rawRes.remained)
         return res
     else
@@ -322,10 +343,26 @@ term = Psr(termAux)
 
 
 function longExpAux(input)
-    rawFunc = seq([term,  (typ("plus") | typ("minus")), term])
+    rawFunc = seq([term,  (typ("plus") | typ("minus")), exp])
     rawRes = rawFunc.fun(input)
     if rawRes != nothing
-        matched = [("%prime", "id"), rawRes.matched[2], [rawRes.matched[1], rawRes.matched[3]]]
+        #correct the tree a -(b - c) -> (a - b) - c
+        leftRator = rawRes.matched[2]
+        a = rawRes.matched[1]
+        bc = rawRes.matched[3]
+        matched = @match bc begin
+            [("%prime", "id"), (rightRator, tRightRator), [b, c]] where ((rightRator == "+") || (rightRator == "-")) =>
+            begin
+                [("%prime", "id"), (rightRator, tRightRator), [[("%prime", "id"), leftRator, [a, b]], c]]
+            end
+            _ => begin
+                 [("%prime", "id"), leftRator, [a, bc]]
+
+            end
+
+        end
+
+        #matched = [("%prime", "id"), leftRator, [a, bc]]
         res = ParserResult(matched, rawRes.remained)
         return res
     else
@@ -426,6 +463,17 @@ letExp = Psr(letExpAux)
 
 body = letExp | exp
 
+
+function fixTree(item)
+    return @match item begin
+        (val, t) => item
+        [("%wrapper", "id"), inner] => fixTree(inner)
+        [vars...] => map(fixTree, item)
+        _ => println("parse Error in fixTree")
+    end
+end
+
+
 function totalParse(prog)
     isEntirelyMatched = match(matchEntirely, prog)
     if isEntirelyMatched == false
@@ -437,10 +485,13 @@ function totalParse(prog)
     groupNameList = map(processKeys, collect(mI))
     zippedTokenList = collect(zip(matchedList, groupNameList))
 
-    withoutSpaces = filter((x)-> x[2] != "sp", zippedTokenList)
-    initWrapped = ParserResult([], withoutSpaces)
+    withoutSpaceCmt = filter((x)-> (x[2] != "sp") & (x[2] != "cmt"), zippedTokenList)
+    initWrapped = ParserResult([], withoutSpaceCmt)
     res = initWrapped >> body
-    return res.matched
+
+    res2 = fixTree(res.matched)
+
+    return res2
 end
 
 
diff --git a/misc/vertexcoloring.jl b/src/vertexcoloring.jl
similarity index 60%
rename from misc/vertexcoloring.jl
rename to src/vertexcoloring.jl
index dab4f04..a4c9e32 100644
--- a/misc/vertexcoloring.jl
+++ b/src/vertexcoloring.jl
@@ -1,4 +1,6 @@
-graph = [['a', 'b'], ['b', 'c'], ['e', 'd'], ['e', 'a'], ['a', 'c'], ['b','e'], ['e','c']]
+module VertexColoring
+
+#graph = [['a', 'b'], ['b', 'c'], ['e', 'd'], ['e', 'a'], ['a', 'c'], ['b','e'], ['e','c']]
 
 
 function vertexColoring(graph)
@@ -30,19 +32,18 @@ function vertexColoring(graph)
 
     color = Dict()
 
-    println(verticesList)
 
 
+    tmpId = -1
     for i in verticesList
         i_adjacents = adjacentNodes[i]
-        println(i_adjacents)
         i_adjacents_color_set = Set(map(x -> getColor(x, color), collect(i_adjacents)))
         i_adjacents_color_list = sort(collect(i_adjacents_color_set))
 
         if i_adjacents_color_list == [notDefined]
-            color[i] = 0
+            color[i] = 2
         else
-            tmpId = 0
+            tmpId = 2
             for i in i_adjacents_color_list
                 if tmpId == i
                     tmpId += 1
@@ -52,8 +53,26 @@ function vertexColoring(graph)
         end
     end
 
-    return color
+    maxColorId = tmpId
+
+    #force gDict["%rax"] = 1
+    color["%rax"] = 1
+    return (color, maxColorId)
 
 end
 
-println(vertexColoring(graph))
\ No newline at end of file
+#println(vertexColoring(graph))
+
+# Disabled = force the color id for %rax set to 1
+"""function correctGraph(gDict)
+    raxOrigId = gDict["%rax"]
+    for node in keys(gDict)
+        if gDict[node] == raxOrigId
+            gDict[node] = 1
+        elseif gDict[node] == 1
+            gDict[node] = raxOrigId
+        end
+    end
+    return gDict
+end"""
+end
\ No newline at end of file
diff --git a/test/prog2.tc b/test/prog2.tc
new file mode 100644
index 0000000..2d6a611
--- /dev/null
+++ b/test/prog2.tc
@@ -0,0 +1,6 @@
+int a = 10;
+int a = 13;
+int b = (12 + (0 - a));
+int c = (14 + b);
+int d = 20;
+a - (b - c)
\ No newline at end of file