{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install pyparsing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# fourFn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyparsing import (\n",
    "    Literal,\n",
    "    Word,\n",
    "    Group,\n",
    "    Forward,\n",
    "    alphas,\n",
    "    alphanums,\n",
    "    Regex,\n",
    "    ParseException,\n",
    "    CaselessKeyword,\n",
    "    Suppress,\n",
    "    delimitedList,\n",
    ")\n",
    "import math\n",
    "import operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "exprStack = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def push_first(toks):\n",
    "    exprStack.append(toks[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def push_unary_minus(toks):\n",
    "    for t in toks:\n",
    "        if t == \"-\":\n",
    "            exprStack.append(\"unary -\")\n",
    "        else:\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bnf = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BNF():\n",
    "    \"\"\"\n",
    "    expop   :: '^'\n",
    "    multop  :: '*' | '/'\n",
    "    addop   :: '+' | '-'\n",
    "    integer :: ['+' | '-'] '0'..'9'+\n",
    "    atom    :: PI | E | real | fn '(' expr ')' | '(' expr ')'\n",
    "    factor  :: atom [ expop factor ]*\n",
    "    term    :: factor [ multop factor ]*\n",
    "    expr    :: term [ addop term ]*\n",
    "    \"\"\"\n",
    "    global bnf\n",
    "    if not bnf:\n",
    "        # use CaselessKeyword for e and pi, to avoid accidentally matching\n",
    "        # functions that start with 'e' or 'pi' (such as 'exp'); Keyword\n",
    "        # and CaselessKeyword only match whole words\n",
    "        e = CaselessKeyword(\"E\")\n",
    "        pi = CaselessKeyword(\"PI\")\n",
    "        # fnumber = Combine(Word(\"+-\"+nums, nums) +\n",
    "        #                    Optional(\".\" + Optional(Word(nums))) +\n",
    "        #                    Optional(e + Word(\"+-\"+nums, nums)))\n",
    "        # or use provided pyparsing_common.number, but convert back to str:\n",
    "        # fnumber = ppc.number().addParseAction(lambda t: str(t[0]))\n",
    "        fnumber = Regex(r\"[+-]?\\d+(?:\\.\\d*)?(?:[eE][+-]?\\d+)?\")\n",
    "        ident = Word(alphas, alphanums + \"_$\")\n",
    "\n",
    "        plus, minus, mult, div = map(Literal, \"+-*/\")\n",
    "        lpar, rpar = map(Suppress, \"()\")\n",
    "        addop = plus | minus\n",
    "        multop = mult | div\n",
    "        expop = Literal(\"^\")\n",
    "\n",
    "        expr = Forward()\n",
    "        expr_list = delimitedList(Group(expr))\n",
    "        # add parse action that replaces the function identifier with a (name, number of args) tuple\n",
    "        def insert_fn_argcount_tuple(t):\n",
    "            fn = t.pop(0)\n",
    "            num_args = len(t[0])\n",
    "            t.insert(0, (fn, num_args))\n",
    "\n",
    "        fn_call = (ident + lpar - Group(expr_list) + rpar).setParseAction(\n",
    "            insert_fn_argcount_tuple\n",
    "        )\n",
    "        atom = (\n",
    "            addop[...]\n",
    "            + (\n",
    "                (fn_call | pi | e | fnumber | ident).setParseAction(push_first)\n",
    "                | Group(lpar + expr + rpar)\n",
    "            )\n",
    "        ).setParseAction(push_unary_minus)\n",
    "\n",
    "        # by defining exponentiation as \"atom [ ^ factor ]...\" instead of \"atom [ ^ atom ]...\", we get right-to-left\n",
    "        # exponents, instead of left-to-right that is, 2^3^2 = 2^(3^2), not (2^3)^2.\n",
    "        factor = Forward()\n",
    "        factor <<= atom + (expop + factor).setParseAction(push_first)[...]\n",
    "        term = factor + (multop + factor).setParseAction(push_first)[...]\n",
    "        expr <<= term + (addop + term).setParseAction(push_first)[...]\n",
    "        bnf = expr\n",
    "    return bnf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# map operator symbols to corresponding arithmetic operations\n",
    "epsilon = 1e-12\n",
    "opn = {\n",
    "    \"+\": operator.add,\n",
    "    \"-\": operator.sub,\n",
    "    \"*\": operator.mul,\n",
    "    \"/\": operator.truediv,\n",
    "    \"^\": operator.pow,\n",
    "}\n",
    "\n",
    "fn = {\n",
    "    \"sin\": math.sin,\n",
    "    \"cos\": math.cos,\n",
    "    \"tan\": math.tan,\n",
    "    \"exp\": math.exp,\n",
    "    \"abs\": abs,\n",
    "    \"trunc\": int,\n",
    "    \"round\": round,\n",
    "    \"sgn\": lambda a: -1 if a < -epsilon else 1 if a > epsilon else 0,\n",
    "    # functionsl with multiple arguments\n",
    "    \"multiply\": lambda a, b: a * b,\n",
    "    \"hypot\": math.hypot,\n",
    "    # functions with a variable number of arguments\n",
    "    \"all\": lambda *a: all(a),\n",
    "    \"Circle\": lambda x,y,r: f\"center=({x},{y}),radius={r}\"\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_stack(s):\n",
    "    op, num_args = s.pop(), 0\n",
    "    if isinstance(op, tuple):\n",
    "        op, num_args = op\n",
    "    if op == \"unary -\":\n",
    "        return -evaluate_stack(s)\n",
    "    if op in \"+-*/^\":\n",
    "        # note: operands are pushed onto the stack in reverse order\n",
    "        op2 = evaluate_stack(s)\n",
    "        op1 = evaluate_stack(s)\n",
    "        return opn[op](op1, op2)\n",
    "    elif op == \"PI\":\n",
    "        return math.pi  # 3.1415926535\n",
    "    elif op == \"E\":\n",
    "        return math.e  # 2.718281828\n",
    "    elif op in fn:\n",
    "        # note: args are pushed onto the stack in reverse order\n",
    "        args = reversed([evaluate_stack(s) for _ in range(num_args)])\n",
    "        return fn[op](*args)\n",
    "    elif op[0].isalpha():\n",
    "        raise Exception(\"invalid identifier '%s'\" % op)\n",
    "    else:\n",
    "        # try to evaluate as int first, then as float if int fails\n",
    "        try:\n",
    "            return int(op)\n",
    "        except ValueError:\n",
    "            return float(op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(s, expected):\n",
    "    exprStack[:] = []\n",
    "    try:\n",
    "        results = BNF().parseString(s, parseAll=True)\n",
    "        val = evaluate_stack(exprStack[:])\n",
    "    except ParseException as pe:\n",
    "        print(s, \"failed parse:\", str(pe))\n",
    "    except Exception as e:\n",
    "        print(s, \"failed eval:\", str(e), exprStack)\n",
    "    else:\n",
    "        if val == expected:\n",
    "            print(s, \"=\", val, results, \"=>\", exprStack)\n",
    "        else:\n",
    "            print(s + \"!!!\", val, \"!=\", expected, results, \"=>\", exprStack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "test(\"9\", 9)\n",
    "test(\"-9\", -9)\n",
    "test(\"--9\", 9)\n",
    "test(\"-E\", -math.e)\n",
    "test(\"9 + 3 + 6\", 9 + 3 + 6)\n",
    "test(\"9 + 3 / 11\", 9 + 3.0 / 11)\n",
    "test(\"(9 + 3)\", (9 + 3))\n",
    "test(\"(9+3) / 11\", (9 + 3.0) / 11)\n",
    "test(\"9 - 12 - 6\", 9 - 12 - 6)\n",
    "test(\"9 - (12 - 6)\", 9 - (12 - 6))\n",
    "test(\"2*3.14159\", 2 * 3.14159)\n",
    "test(\"3.1415926535*3.1415926535 / 10\", 3.1415926535 * 3.1415926535 / 10)\n",
    "test(\"PI * PI / 10\", math.pi * math.pi / 10)\n",
    "test(\"PI*PI/10\", math.pi * math.pi / 10)\n",
    "test(\"PI^2\", math.pi ** 2)\n",
    "test(\"round(PI^2)\", round(math.pi ** 2))\n",
    "test(\"6.02E23 * 8.048\", 6.02e23 * 8.048)\n",
    "test(\"e / 3\", math.e / 3)\n",
    "test(\"sin(PI/2)\", math.sin(math.pi / 2))\n",
    "test(\"10+sin(PI/4)^2\", 10 + math.sin(math.pi / 4) ** 2)\n",
    "test(\"trunc(E)\", int(math.e))\n",
    "test(\"trunc(-E)\", int(-math.e))\n",
    "test(\"round(E)\", round(math.e))\n",
    "test(\"round(-E)\", round(-math.e))\n",
    "test(\"E^PI\", math.e ** math.pi)\n",
    "test(\"exp(0)\", 1)\n",
    "test(\"exp(1)\", math.e)\n",
    "test(\"2^3^2\", 2 ** 3 ** 2)\n",
    "test(\"(2^3)^2\", (2 ** 3) ** 2)\n",
    "test(\"2^3+2\", 2 ** 3 + 2)\n",
    "test(\"2^3+5\", 2 ** 3 + 5)\n",
    "test(\"2^9\", 2 ** 9)\n",
    "test(\"sgn(-2)\", -1)\n",
    "test(\"sgn(0)\", 0)\n",
    "test(\"sgn(0.1)\", 1)\n",
    "test(\"foo(0.1)\", None)\n",
    "test(\"round(E, 3)\", round(math.e, 3))\n",
    "test(\"round(PI^2, 3)\", round(math.pi ** 2, 3))\n",
    "test(\"sgn(cos(PI/4))\", 1)\n",
    "test(\"sgn(cos(PI/2))\", 0)\n",
    "test(\"sgn(cos(PI*3/4))\", -1)\n",
    "test(\"+(sgn(cos(PI/4)))\", 1)\n",
    "test(\"-(sgn(cos(PI/4)))\", -1)\n",
    "test(\"hypot(3, 4)\", 5)\n",
    "test(\"multiply(3, 7)\", 21)\n",
    "test(\"all(1,1,1)\", True)\n",
    "test(\"all(1,1,1,1,1,0)\", False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "test(\"Circle(0,0,5)\", \"center=(0,0),radius=5\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "test(\"Circle(0,1,3)\", \"center=(0,0),radius=5\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A=3\n",
    "N=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "test(\"N*A/5\",12/5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "body=\"\"\"\\\n",
    "rectangle: \n",
    "    formula: Rectangle(contact, rl, rL)\n",
    "    style:\n",
    "        linecolor: blue\n",
    "        filled_curves: blue\n",
    "    transform: [\"rotate(-theta, contact)\",\n",
    "                \"translate(-rl/2*tangent_vec)\"]\n",
    "N: \n",
    "    formula: Force(contact - rl*normal_vec, contact, r'$N$', text_pos='start')\n",
    "    style:\n",
    "        linecolor: black\n",
    "wheel: \n",
    "    formula: \"Composition({'outer': rectangle})\"   \n",
    "    style:\n",
    "        shadow: 1\n",
    "mc:\n",
    "    formula: Text(r'$c$', c)\n",
    "body: \n",
    "    formula: \"Composition({'wheel': wheel, 'N': N, 'mc': mc})\"\n",
    "    style:\n",
    "        linecolor: black\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ruamel.yaml import YAML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "yaml = YAML()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "gwd = yaml.load(body)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gwd['N'].lc.line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "BNF().parseString(\"Rectangle(contact, rl, rL)\", parseAll=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "BNF().parseString(\"Force(contact - rl*normal_vec, contact, r'$N$', text_pos='start')\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sketchInterpreter(sketch, container):\n",
    "    yaml = YAML()\n",
    "    gwd = yaml.load(sketch)\n",
    "    for _k in list(gwd.keys()):\n",
    "        if _k == \"stop\":\n",
    "            break\n",
    "        _c = gwd[_k]\n",
    "        _t = str(type(_c))\n",
    "        if _k == \"libraries\":\n",
    "            for l in _c:\n",
    "                exec(l,container)\n",
    "        #print(_k, _c, _t)\n",
    "        if _t == \"<class 'ruamel.yaml.scalarfloat.ScalarFloat'>\" or \\\n",
    "        _t == \"<class 'str'>\" or _t == \"<class 'int'>\":\n",
    "            _formula = f\"{_k} = {_c}\".replace(\"<bslash>\",\"\\\\\") \n",
    "            #print(_formula)\n",
    "            exec(_formula,container)\n",
    "        elif _t == \"<class 'ruamel.yaml.comments.CommentedMap'>\":\n",
    "            #print(_c)\n",
    "            _keys = list(_c.keys())\n",
    "            #print(_keys)\n",
    "            if 'formula' in _keys:\n",
    "                _formula = f\"{_k} = {_c['formula']}\".replace(\"<bslash>\",\"\\\\\")\n",
    "                #print(_formula)\n",
    "                exec(_formula,container)\n",
    "            if 'style' in _keys:\n",
    "                for _style in _c[\"style\"]:\n",
    "                    #  x_const.set_linestyle('dotted')\n",
    "                    _param = _c[\"style\"][_style]\n",
    "                    __t = str(type(_param))\n",
    "                    #print(__t)\n",
    "                    if __t == \"<class 'int'>\":\n",
    "                        _style = f\"{_k}.set_{_style}({_param})\"\n",
    "                    else:\n",
    "                        _style = f\"{_k}.set_{_style}('{_param}')\"\n",
    "                    #print(_style)\n",
    "                    exec(_style,container)\n",
    "            if 'transform' in _keys:\n",
    "                #print(_c['transform'])\n",
    "                if str(type(_c['transform'])) == \"<class 'str'>\":\n",
    "                    _t = f\"{_k}.{_c['transform']}\"\n",
    "                    #print(_t)\n",
    "                    exec(_t,container)\n",
    "                else:\n",
    "                    for _transform in _c[\"transform\"]:\n",
    "                    #  x_const.rotate(-theta, contact)\n",
    "                        _t = f\"{_k}.{_transform}\"\n",
    "                        #print(_t)\n",
    "                        exec(_t,container)\n",
    "            if \"action\" in _keys:\n",
    "                _action = _c[\"action\"]\n",
    "                #print(_action)\n",
    "                exec(_action,container)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "parser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import parser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp = parser.expr(\"Force(contact - rl*normal_vec, contact, r'$N$', text_pos='start')\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp.isexpr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "parser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pip install showast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install wheel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import showast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"851pt\" height=\"404pt\" viewBox=\"0.00 0.00 850.50 404.00\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 400)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-400 846.5,-400 846.5,4 -4,4\"/>\n",
       "<!-- 0 -->\n",
       "<g id=\"node1\" class=\"node\"><title>0</title>\n",
       "<text text-anchor=\"start\" x=\"432\" y=\"-375.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Expr</text>\n",
       "</g>\n",
       "<!-- 1 -->\n",
       "<g id=\"node2\" class=\"node\"><title>1</title>\n",
       "<text text-anchor=\"start\" x=\"432\" y=\"-303.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Call</text>\n",
       "</g>\n",
       "<!-- 0&#45;&#45;1 -->\n",
       "<g id=\"edge1\" class=\"edge\"><title>0--1</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M449,-359.697C449,-348.846 449,-334.917 449,-324.104\"/>\n",
       "</g>\n",
       "<!-- 2 -->\n",
       "<g id=\"node3\" class=\"node\"><title>2</title>\n",
       "<text text-anchor=\"start\" x=\"102\" y=\"-231.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Name</text>\n",
       "</g>\n",
       "<!-- 1&#45;&#45;2 -->\n",
       "<g id=\"edge2\" class=\"edge\"><title>1--2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M448,-287C448,-287 225.028,-251.758 146.203,-239.3\"/>\n",
       "</g>\n",
       "<!-- 5 -->\n",
       "<g id=\"node6\" class=\"node\"><title>5</title>\n",
       "<text text-anchor=\"start\" x=\"279\" y=\"-231.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">BinOp</text>\n",
       "</g>\n",
       "<!-- 1&#45;&#45;5 -->\n",
       "<g id=\"edge5\" class=\"edge\"><title>1--5</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M448,-287C448,-287 372.372,-260.428 329.24,-245.274\"/>\n",
       "</g>\n",
       "<!-- 18 -->\n",
       "<g id=\"node19\" class=\"node\"><title>18</title>\n",
       "<text text-anchor=\"start\" x=\"432\" y=\"-231.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Name</text>\n",
       "</g>\n",
       "<!-- 1&#45;&#45;18 -->\n",
       "<g id=\"edge18\" class=\"edge\"><title>1--18</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M448,-287C448,-287 448.381,-267.192 448.673,-252.027\"/>\n",
       "</g>\n",
       "<!-- 21 -->\n",
       "<g id=\"node22\" class=\"node\"><title>21</title>\n",
       "<text text-anchor=\"start\" x=\"522.5\" y=\"-231.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Constant</text>\n",
       "</g>\n",
       "<!-- 1&#45;&#45;21 -->\n",
       "<g id=\"edge21\" class=\"edge\"><title>1--21</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M448,-287C448,-287 489.139,-267.192 520.637,-252.027\"/>\n",
       "</g>\n",
       "<!-- 23 -->\n",
       "<g id=\"node24\" class=\"node\"><title>23</title>\n",
       "<text text-anchor=\"start\" x=\"663\" y=\"-231.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">keyword</text>\n",
       "</g>\n",
       "<!-- 1&#45;&#45;23 -->\n",
       "<g id=\"edge23\" class=\"edge\"><title>1--23</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M448,-287C448,-287 586.683,-257.445 654.942,-242.898\"/>\n",
       "</g>\n",
       "<!-- 3 -->\n",
       "<g id=\"node4\" class=\"node\"><title>3</title>\n",
       "<text text-anchor=\"middle\" x=\"37\" y=\"-158.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">&quot;Force&quot;</text>\n",
       "</g>\n",
       "<!-- 2&#45;&#45;3 -->\n",
       "<g id=\"edge3\" class=\"edge\"><title>2--3</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M111,-215C111,-215 82.8119,-195.192 61.2304,-180.027\"/>\n",
       "</g>\n",
       "<!-- 4 -->\n",
       "<g id=\"node5\" class=\"node\"><title>4</title>\n",
       "<text text-anchor=\"middle\" x=\"119\" y=\"-158.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">Load</text>\n",
       "</g>\n",
       "<!-- 2&#45;&#45;4 -->\n",
       "<g id=\"edge4\" class=\"edge\"><title>2--4</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M111,-215C111,-215 114.047,-195.192 116.381,-180.027\"/>\n",
       "</g>\n",
       "<!-- 6 -->\n",
       "<g id=\"node7\" class=\"node\"><title>6</title>\n",
       "<text text-anchor=\"start\" x=\"174\" y=\"-159.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Name</text>\n",
       "</g>\n",
       "<!-- 5&#45;&#45;6 -->\n",
       "<g id=\"edge6\" class=\"edge\"><title>5--6</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M294,-215C294,-215 248.579,-192.069 218.062,-176.662\"/>\n",
       "</g>\n",
       "<!-- 9 -->\n",
       "<g id=\"node10\" class=\"node\"><title>9</title>\n",
       "<text text-anchor=\"middle\" x=\"263\" y=\"-158.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">Sub</text>\n",
       "</g>\n",
       "<!-- 5&#45;&#45;9 -->\n",
       "<g id=\"edge9\" class=\"edge\"><title>5--9</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M294,-215C294,-215 282.191,-195.192 273.151,-180.027\"/>\n",
       "</g>\n",
       "<!-- 10 -->\n",
       "<g id=\"node11\" class=\"node\"><title>10</title>\n",
       "<text text-anchor=\"start\" x=\"316\" y=\"-159.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">BinOp</text>\n",
       "</g>\n",
       "<!-- 5&#45;&#45;10 -->\n",
       "<g id=\"edge10\" class=\"edge\"><title>5--10</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M294,-215C294,-215 310.38,-195.192 322.92,-180.027\"/>\n",
       "</g>\n",
       "<!-- 7 -->\n",
       "<g id=\"node8\" class=\"node\"><title>7</title>\n",
       "<text text-anchor=\"middle\" x=\"101\" y=\"-86.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">&quot;contact&quot;</text>\n",
       "</g>\n",
       "<!-- 6&#45;&#45;7 -->\n",
       "<g id=\"edge7\" class=\"edge\"><title>6--7</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M182,-143C182,-143 151.145,-123.192 127.522,-108.027\"/>\n",
       "</g>\n",
       "<!-- 8 -->\n",
       "<g id=\"node9\" class=\"node\"><title>8</title>\n",
       "<text text-anchor=\"middle\" x=\"192\" y=\"-86.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">Load</text>\n",
       "</g>\n",
       "<!-- 6&#45;&#45;8 -->\n",
       "<g id=\"edge8\" class=\"edge\"><title>6--8</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M182,-143C182,-143 185.809,-123.192 188.726,-108.027\"/>\n",
       "</g>\n",
       "<!-- 11 -->\n",
       "<g id=\"node12\" class=\"node\"><title>11</title>\n",
       "<text text-anchor=\"start\" x=\"248\" y=\"-87.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Name</text>\n",
       "</g>\n",
       "<!-- 10&#45;&#45;11 -->\n",
       "<g id=\"edge11\" class=\"edge\"><title>10--11</title>\n",
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       "</g>\n",
       "<!-- 14 -->\n",
       "<g id=\"node15\" class=\"node\"><title>14</title>\n",
       "<text text-anchor=\"middle\" x=\"337\" y=\"-86.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">Mult</text>\n",
       "</g>\n",
       "<!-- 10&#45;&#45;14 -->\n",
       "<g id=\"edge14\" class=\"edge\"><title>10--14</title>\n",
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       "<!-- 15 -->\n",
       "<g id=\"node16\" class=\"node\"><title>15</title>\n",
       "<text text-anchor=\"start\" x=\"392\" y=\"-87.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Name</text>\n",
       "</g>\n",
       "<!-- 10&#45;&#45;15 -->\n",
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       "</g>\n",
       "<!-- 12 -->\n",
       "<g id=\"node13\" class=\"node\"><title>12</title>\n",
       "<text text-anchor=\"middle\" x=\"203\" y=\"-14.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">&quot;rl&quot;</text>\n",
       "</g>\n",
       "<!-- 11&#45;&#45;12 -->\n",
       "<g id=\"edge12\" class=\"edge\"><title>11--12</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M260,-71C260,-71 238.288,-51.1921 221.664,-36.0267\"/>\n",
       "</g>\n",
       "<!-- 13 -->\n",
       "<g id=\"node14\" class=\"node\"><title>13</title>\n",
       "<text text-anchor=\"middle\" x=\"275\" y=\"-14.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">Load</text>\n",
       "</g>\n",
       "<!-- 11&#45;&#45;13 -->\n",
       "<g id=\"edge13\" class=\"edge\"><title>11--13</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M260,-71C260,-71 265.714,-51.1921 270.088,-36.0267\"/>\n",
       "</g>\n",
       "<!-- 16 -->\n",
       "<g id=\"node17\" class=\"node\"><title>16</title>\n",
       "<text text-anchor=\"middle\" x=\"398\" y=\"-14.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">&quot;normal_vec&quot;</text>\n",
       "</g>\n",
       "<!-- 15&#45;&#45;16 -->\n",
       "<g id=\"edge16\" class=\"edge\"><title>15--16</title>\n",
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       "<!-- 17 -->\n",
       "<g id=\"node18\" class=\"node\"><title>17</title>\n",
       "<text text-anchor=\"middle\" x=\"501\" y=\"-14.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">Load</text>\n",
       "</g>\n",
       "<!-- 15&#45;&#45;17 -->\n",
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       "<!-- 19 -->\n",
       "<g id=\"node20\" class=\"node\"><title>19</title>\n",
       "<text text-anchor=\"middle\" x=\"430\" y=\"-158.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">&quot;contact&quot;</text>\n",
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       "<g id=\"node21\" class=\"node\"><title>20</title>\n",
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       "<!-- 22 -->\n",
       "<g id=\"node23\" class=\"node\"><title>22</title>\n",
       "<text text-anchor=\"middle\" x=\"595\" y=\"-158.3\" font-family=\"Courier,monospace\" font-size=\"14.00\" fill=\"#008040\">&quot;$N$&quot;</text>\n",
       "</g>\n",
       "<!-- 21&#45;&#45;22 -->\n",
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       "<text text-anchor=\"start\" x=\"767.5\" y=\"-159.3\" font-family=\"Courier,monospace\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#004080\">Constant</text>\n",
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       "<!-- 23&#45;&#45;25 -->\n",
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       "</g>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%showast\n",
    "Force(contact - rl*normal_vec, contact, r'$N$', text_pos='start')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ast\n",
    "\n",
    "root = ast.parse(\"Force(contact - rl*normal_vec, contact, r'$N$', text_pos='start')\")\n",
    "names = sorted({node.id for node in ast.walk(root) if isinstance(node, ast.Name)})\n",
    "constants = sorted({node.value for node in ast.walk(root) if isinstance(node, ast.Constant)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Force', 'contact', 'normal_vec', 'rl']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['$N$', 'start']"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "head = \"\"\"\\\n",
    "libraries: [\"from math import tan, radians, sin, cos\",\"from pysketcher import *\"]\n",
    "fontsize: 18\n",
    "g: 9.81              # constant gravity\n",
    "theta: 30.0          # inclined plane angle\n",
    "L: 10.0              # sketch sizing parameter\n",
    "a: 1.0               #\n",
    "xmin: 0.0            # sketech min Abscissa\n",
    "ymin: -3.0           # sketech min Ordinate     \n",
    "rl: 2.0              # rectangle width\n",
    "rL: 1.0              # rectangle length\n",
    "setframe:            # sketch setup\n",
    "    action: \"drawing_tool.set_coordinate_system(xmin=xmin-L/5, xmax=xmin+1.5*L,ymin=ymin, ymax=ymin+1.5*L,instruction_file='tmp_mpl_friction.py')\"\n",
    "setblackline:        # default frame values and actions\n",
    "    action: \"drawing_tool.set_linecolor('black')\"\n",
    "B: point(a+L,0)                      # wall right end\n",
    "A: point(a,tan(radians(theta))*L)    # wall left end\n",
    "normal_vec: point(sin(radians(theta)),cos(radians(theta)))     # Vector normal to wall\n",
    "tangent_vec: point(cos(radians(theta)),-sin(radians(theta)))   # Vector tangent to wall\n",
    "help_line: Line(A,B)                 # wall line\n",
    "x: a + 3*L/10.\n",
    "y: help_line(x=x)    \n",
    "contact: point(x, y)    \n",
    "c: contact + rL/2*normal_vec\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "myfig={}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pysketcher import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "sketchParse(head,myfig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'g' in myfig"
   ]
  }
 ],
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