COP-4620/CIS-6930 PROGRAMMING LANGUAGE TRANSLATORS Instructor: Manuel Bermudez FALL 2015

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1 COP-4620/CIS-6930 PROGRAMMING LANGUAGE TRANSLATORS Instructor: Manuel Bermudez FALL 2015 FINAL EXAM Take-home, Drop-dead deadline: 12 noon Wednesday, Dec. 16 Problem 1 Problem 2 Problem 3 Problem 4 SCORE (30p.) (30p.) (20p.) (20p.) (100p.) NAME

2 Fall 2015 COP-4620/CIS-6930 Final Page 2 of 7 PROBLEM 1. (30 points) The following string-to-tree transduction grammar describes the language of regular expressions over alphabet {a, b, c}. E0 -> E0 E1 => -> E1 E1 -> E2 E1 => cat -> E2 E2 -> E2 list E3 => list -> E3 E3 -> E4 + => + -> E4 * => * -> E4? =>? -> E4 E4 -> ( E0 ) -> a => a -> b => b This language consists of regular expressions. Here is a sample regular expression: (a* b)* list b a+ The language has the following operator precedence hierarchy. Level Operator Type of Op. Associativity Least binding Binary Infix Left Binary Infix Right list Binary Infix Left +, *,? Unary Postfix None Most binding ( ) Embedding None

3 Fall 2015 COP-4620/CIS-6930 Final Page 3 of 7 a) Show that the above grammar is not LL(1). b) Transform the grammar to make it LL(1), calculate Select sets and show the modified grammar is LL(1). c) Show the parse table for the modified grammar. d) Show a step-by-step parse for the sample regular expression shown above, using your parse table from part (c). In each step, show the stack, the remaining input, and the table lookup value, if any. e) Write a recursive descent parser (in pseudo-code) for this language, adding BuildTree statements to build the Abstract Syntax Tree for the original grammar. Hint: Use the "Notes on Parsing" Powerpoint, slides

4 Fall 2015 COP-4620/CIS-6930 Final Page 4 of 7 PROBLEM 2. (30 points) Consider the same grammar as in Problem 1. a) Construct the LR(0) item sets, and build the ACTION and GOTO tables of the LR(0) parser. b) Show that the grammar is NOT LR(0). c) Is the grammar SLR(1)? Show the necessary analysis. d) Is the grammar LALR(1)? Show the necessary analysis. e) Using your ACTION and GOTO tables, show astep-by-step LR parse for the sample regular expression shown in Problem 1. In each step, show the stack, the remaining input, and the action taken (shift or reduce). Then take the sequence of reductions performed by the parser, and use them to build (bottom-up) the Abstract Syntax tree for the input string.

5 Fall 2015 COP-4620/CIS-6930 Final Page 5 of 7 PROBLEM 3. (20 points) You are about to (partially) write a compiler-interpreter for roman numerals. Below is a (slightly incomplete) grammar that recognizes a list of roman numerals, separated by commas. Each numeral is between 1 and In case you don t remember how roman numerals work, the following rules should refresh your memory: 1) Roman numerals are composed of symbols I (one), V (five), X (ten), L (fifty), C(one hundred), D (five hundred), and M (one thousand). 2) A smaller number placed in front of a larger number is subtracted from it. (e.g. IV means four). Only one such smaller number can be subtracted at a time (e.g. IIV does not mean 3). Other restrictions apply (see the grammar). 3) A number placed after a greater or equal number is added to it (e.g. DC means 600, XIII means 13, and MMM means 3000). Again, other restrictions apply. Romans Roman (, Roman)* => romans Roman Thous Hunds Tens Ones => Thous M? M? M? => Hunds CC?C? => C(D M) => DC?C?C? => Tens XX?X? => X(L C) => LX?X?X? => Ones II?I? => I(V X) => VI?I?I? => M M => 1000 D D => 500 C C => 100 L L => 50 X X => 10 V V => 5 I I => 1 a) Some of the tree transduction parts are blank. Each one should be either "+" or "-". YOU FILL THEM IN. Now, assume someone has already undertaken the task of developing a recursive descent parser for this grammar.

6 Fall 2015 COP-4620/CIS-6930 Final Page 6 of 7 b) Show the derivation tree and the abstract syntax tree for the following input: DLVII, MI, MCMXCIV, MMXIII c) Below is a(slightly incomplete) roman compiler back-end program, written in pseudo code. The code for cases "Plus" and "Minus" is missing. YOU FILL THEM IN. program RomanBackEnd(input,output); const One = 1 ; Five = 5 ; Ten = 10 ; Fifty = 50 ; Hundr = 100 ; { These are Node Names } FiveH = 500 ; Thous = 1000 ; Plus = + ; Minus = - ; var i : integer; function Traverse (T:TreeNode): integer; var N,i: integer; begin case NodeName(T) of end end; begin {main} end. Plus: Minus: One : Traverse := 1; Five : Traverse := 5; Ten : Traverse := 10; Fifty : Traverse := 50; Hundr : Traverse := 100; FiveH : Traverse := 500; Thous : Traverse := 1000; ReadTree; for i := 1 to Rank(RootOfTree(1)) do writeln( Value Is,Traverse (Child(Root,i))); d) Annotate each "+" and "-" in your AST with the value returned by function "Traverse", when applied to that node. Show the output of the roman compiler back-end.

7 Fall 2015 COP-4620/CIS-6930 Final Page 7 of 7 PROBLEM 4. (20 points) Now, it s time to fully implement the language of Roman numerals, using the TWS. a) Start with a freshly installed (compiled) copy ofthe original tws and tiny. b) Rename tiny asromans. c) In the romans directory, get rid of everything related to the code generator, and the tests directory. Get rid all "tc" files except "tc". Rename "tc" as "rc". Edit "rc" so it parses and then runs "Romans", instead of Constrain. Don t forget to change the YAHOO! banner :-) d) In the parser directory, rename lex.tiny and parse.tiny to lex.romans and parse.romans. Modify these files to scan and parse Roman numerals. Modify the Makefile accordingly. Note: the TWS seems to have problems with regular expresions such as M M? M?. Decompose them: Thous -> M -> M M -> M M M e) Rename Constrainer.c as Romans.c. Remove Constrain. Edit the Makefile so it compiles Romans.c (into Romans) instead of Constrainer.c. Remove all references to the code generator. f) Now, edit Romans.c. Remove AddIntrinsics and any calls to it. Change the list of node names. In ProcessNode, handle the "romans" tree node, calling Expression on each child, and printing the results. In Expression, handle all the other tree nodes, each returning an integer. g) Send me lex.romans, parse.romans, and Romans.c. along with the rest of your solved exam.

CSE 401 Midterm Exam 11/5/10

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