IN F# language: In this project you write a recursive descent parser for a specific grammar. Find your grammar definition in grammars. md file which corresponds to your ID. Grammar: ``` W → TeU T → Tce | e U → e | def | eTa ``` Sentences: - `ececcea` - `cecececea` - `cea` - `ececeee` - `ecececececa` --- 1. Make appropriate changes to your grammar to convert it to the LL(1) form if necessary No left recursion Pairwise disjoint productions 2.Write a recursive descent parser for your grammar. Your parser should output for every test sentence: A test sentence itself A list the grammar rules required to parse a correct sentence. See a parsing example in rd-parser. ipynb script. 3. Use provided sentences from grammars. md file to test correctness of your parser. You recursive-descent parser must output list of grammar rules required to parse a valid sentence of produced by your grammar. Several sentences are provided to you. If case of the error in parser input, i. e. invalid sentence, your parser need to output error and terminate execution. Solution¶ Place your LL grammar in the following cell: place your LL grammar here Place your recursive descent parser in the following cell: In [ ]: Place your recursive recursive descent parser tests in the following cell: In [ ]:

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."