CMSC 330 Fall 2007 Homework 2: Grammars and OCaml, Assignments of Programming Languages

Download CMSC 330 Fall 2007 Homework 2: Grammars and OCaml and more Assignments Programming Languages in PDF only on Docsity! CMSC 330 Fall 2007 Homework 2: Grammars, OCAML Posted on: Saturday, Oct. 20, 2007 Due: Tuesday, Oct. 30 9:20AM, 2007 Homework should be submitted in my office (4115 AVW) BEFORE 9:20AM (slip them under my door if it is closed). Homework will not be accepted after 9:20AM as the homework problems may be reviewed in class that day. No late homework is accepted. Late home- work will receive no credit. Be sure to label the problem you are solving clearly with the problem number and subsection. Typing your homework is not required, but homework should be legible. Illegible solutions will receive no credit. Be sure to put your name on the homework. Remember, you must do this homework on your own, without any external sources. If you are unsure what is allowed, please contact the instructor. 1. Creating Grammars Write unambiguous grammars for the following languages: (a) {anbn|n ≥ 0 and n is odd} (b) All valid OCaml lists created using ::. Make sure your construction correctly shows the right association of this operator. Use v(′a) to indicate a value of type ′a. Examples of valid strings in this language: 1 :: [], [], “hi” :: “there” :: [] (c) All valid OCaml guards for if statements in the abbreviated language containing terminals: (, ), ||, &&, <, >, =. Parenthesis must be appropriately matched with every open- ing left parenthesis followed by a closing right parenthesis. ( and ) have the highest precedence, followed by && and || and the lowest precedence is given to <, >, = etc. Use v(′a) to indicate a value of type of type ′a. Note: You don’t need to worry about type compatibility. Assume that this is done separately. 2. Ambiguity Proofs Prove that the following grammar is ambiguous. Note: In class, we did not construct formal “proofs” for unambiguous grammars; however, for ambiguous grammars, we used example strings and the definition of ambiguity. 1