Parsing Bottom Up CMPS 450 J. Moloney CMPS 450

We will examine “LR” parsers – Left-to-right, Rightmost derivation Bottom Up Parsing Parse tree build up from leaves We will examine “LR” parsers – Left-to-right, Rightmost derivation Rightmost Parsers Use a stack. Read input from left to right. Create a rightmost derivation. Reads input until entire right-hand side of a rule has been found, then reduce by that rule. Process continues until entire input has been processed. CMPS 450

Simple Expression Grammar Terminals: {id, +, *} Non-Terminals {E, T} Example Stack Input <empty> abd$ a bd$ ab d$ abd $ S $ Simple Grammar Terminals: {a,b,c,d} Non-Terminals {S’, S} (0) S’  S$ S  abc S  abcd Simple Expression Grammar Terminals: {id, +, *} Non-Terminals {E, T} (0) E’  E$ E  E + T E  T T  T * id T  id Example Stack Input <empty> id + id $ id + id $ shift T + id $ R-4 E + id $ R-2 E + id $ shift E + id $ Shift E + T $ R – 4 E $ R – 1 E’ <empty> R - 0 CMPS 450

<empty> id + id * id $ shift id + id * id $ R-4 Example Stack Input <empty> id + id * id $ shift id + id * id $ R-4 T + id * id $ R - 2 E + id * id $ shift E + * id $ shift E + id * id $ R - 4 E + T * id $ shift E + T * id $ shift E + T $ R – 1 E’ $ <empty> shift E’ $ R - 0 Simple Expression Grammar Terminals: {id, +, *} Non-Terminals {E, T} (0) E’  E$ E  E + T E  T T  T * id T  id Rightmost Derivation E’  E$  E + T$  E + T * id  E + id * id$  T + id * id$  id + id * id$ CMPS 450

Shift/ Reduce – LR Parse Tables Use DFA as well as past state to determine shift or reduce. A stack holds terminals, nonterminals and state info. Push State 1 on top of the stack. According to the parse table – row of the state on the top of the stack, column of the next input symbol If there is no entry parsing fails If the entry is “accept” , then accept the string, parsing is successful If entry is a shift – sn – push the next symbol and State n on the stack, and go back to step 2. If the entry is a reduce – r(n) – pop off all the symbols (and associated states) form the stack that match the right-hand side of rule (n), to get a new state according to the parse table (row of the stare on top of the stack, column of the non-terminal on the left-hand side of rule (n)). Push the non-terminal on the left-hand side of the rule and the new state on top of the stack and go to step 2. CMPS 450

num + * $ E T 1 s2 g3 g4 2 r(4) 3 s7 a 4 r(2) s5 5 s6 6 r(3) r(3)`` 7 Parse Table Example num + * $ E T 1 s2 g3 g4 2 r(4) 3 s7 a 4 r(2) s5 5 s6 6 r(3) r(3)`` 7 g8 8 r(1) id + id$ id * id + id $ id id + $ id + * $ CMPS 450