aabb S "SS S "asb S "bsa S "# Example: Parser derivation input Plan for Today Finish complexity argument for exhaustive search parsing

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1 Plan for Today Finish complexity argument for exhaustive search parsing FIRT and FOLLOW sets Predictive Parsing table Error messages for MiniVG C453 Lecture Top-Down Predictive Parsers 1 Example: input Parser " "ab "ba "# derivation?

2 Phase 1: Exhaustive earch " ab ba # " " ab " ba " # Find derivation of All possible derivations of length 1 " " ab " ba " #

3 Phase 1 ab Phase 2 ab ba ab ab ab ab " ab ba # ab abab ab Phase 2 " ab ba # ab ab ab ab Phase 3 ab

4 input Final result of exhaustive search (top-down parsing) Parser " " ab " ba " # derivation ab C453 Lecture Top-Down Predictive Parsers 7 Time complexity of exhaustive search uppose there are no productions of the form A "# A B Number of phases for string w : O(2 w ) C453 Lecture Top-Down Predictive Parsers 8

5 For grammar with rules Time for phase 1: possible derivations C453 Lecture Top-Down Predictive Parsers 9 Time for phase 2: 2 2 possible derivations C453 Lecture Top-Down Predictive Parsers 10

6 2 w Time for phase : 2 w 2 w possible derivations C453 Lecture Top-Down Predictive Parsers 11 Total time needed for string w : 2 2 w phase 1 phase 2 phase 2 w Extremely bad C453 Lecture Top-Down Predictive Parsers 12

7 For general context-free grammars: There exists a general parsing algorithm that parses a string in time 3 w w For LL(1) grammars we can use Predictive parsing and parse in w C453 Lecture Top-Down Predictive Parsers 13 Example Predictive Parser (1) start -> mesh EOF (2) mesh -> NUM nodelist NUM elemlist (3a & b) nodelist -> ϵ node nodelist (4) node -> NODE NUM REAL REAL // node_id, x, y (5a & b) elemlist -> ϵ elem elemlist (6a) elem -> TRI NUM NUM NUM NUM // elem_id, 3 node ids (6b) elem -> QR NUM NUM NUM NUM NUM //elem_id,4 node ids void start() { switch(m_looahead) { case NUM: mesh(); match(toen.tag.eof); brea; void mesh() { switch(this.m_looahead) { case NUM: num_nodes = ((Num)m_looahead).value; match(num); nodelist(); num_elem = ((Num)m_looahead).value; match(num); elemlist(); brea; void nodelist() { switch(m_looahead) { case NUM: brea; // nodelist -> epsilon case NODE: node(); nodelist(); brea; // nodelist -> node nodelist C453 Lecture Top-Down Predictive Parsers 14

8 C453 Lecture Top-Down Predictive Parsers 15 MiniVG Grammar and getting started with parser (1) svg -> VG_TART elem_list VG_END EOF (2a & b) elem_list -> elem elem_list epsilon (3) elem -> RECT_TART... ELEM_END (4) elem -> CIRCLE_TART... ELEM_END (5) elem -> LINE_TART... ELEM_END C453 Lecture Top-Down Predictive Parsers 16

9 FIRT and FOLLOW sets nullable(x) X is a nonterminal nullable(x) is true if X can derive the empty string FIRT FIRT(z) = {z}, where z is a terminal FIRT(X) = union of all FIRT( rhs i ), where X is a nonterminal and X -> rhs i FIRT(rhs i ) = union all of FIRT(sym) on rhs up to and including first nonnullable FOLLOW(Y), only relevant when Y is a nonterminal loo for Y in rhs of rules (lhs -> rhs) and union all FIRT sets for symbols after Y up to and including first nonnullable if all symbols after Y are nullable then also union in FOLLOW(lhs) C453 Lecture Top-Down Predictive Parsers 17 Compute FIRT and FOLLOW sets for example (1) start -> mesh EOF (2) mesh -> NUM nodelist NUM elemlist (3a & b) nodelist -> ϵ node nodelist (4) node -> NODE NUM REAL REAL // node_id, x, y (5a & b) elemlist -> ϵ elem elemlist (6a) elem -> TRI NUM NUM NUM NUM // elem_id, 3 node ids (6b) elem -> QR NUM NUM NUM NUM NUM //elem_id,4 node ids C453 Lecture Top-Down Predictive Parsers 18

10 Constructing the Predictive Parser Table Algorithm for each X -> gamma for each T in FIRT(gamma) table[x,t] = X->gamma if gamma is nullable for each T in FOLLOW(X) table[x,t] = X->gamma (1) start -> mesh EOF (2) mesh -> NUM nodelist NUM elemlist (3a & b) nodelist -> ϵ node nodelist (4) node -> NODE NUM REAL REAL // node_id, x, y (5a & b) elemlist -> ϵ elem elemlist (6a) elem -> TRI NUM NUM NUM NUM // elem_id, 3 node ids (6b) elem -> QR NUM NUM NUM NUM NUM //elem_id,4 node ids C453 Lecture Top-Down Predictive Parsers 19 how correspondence of parse table and code (1) start -> mesh EOF (2) mesh -> NUM nodelist NUM elemlist (3a & b) nodelist -> ϵ node nodelist (4) node -> NODE NUM REAL REAL // node_id, x, y (5a & b) elemlist -> ϵ elem elemlist (6a) elem -> TRI NUM NUM NUM NUM // elem_id, 3 node ids (6b) elem -> QR NUM NUM NUM NUM NUM //elem_id,4 node ids void start() { switch(m_looahead) { case NUM: mesh(); match(toen.tag.eof); brea; void mesh() { switch(this.m_looahead) { case NUM: num_nodes = ((Num)m_looahead).value; match(num); nodelist(); num_elem = ((Num)m_looahead).value; match(num); elemlist(); brea; void nodelist() { switch(m_looahead) { case NUM: brea; // nodelist -> epsilon case NODE: node(); nodelist(); brea; // nodelist -> node nodelist C453 Lecture Top-Down Predictive Parsers 20

11 Error recovery for MiniVG Unexpected EOF Reference MiniVG interpreter appears to print out?. Eg, [5,26] Expected character 't' and got '?. You can copy above or do [5,26] Expected character 't' and got EOF. Mismatch exception for whitespace When expect whitespace and don t get it, what should the error message be? Covered in recitation, what was the answer? Unexpected word or Expect number or color in quotes Writeup suggests that Expect only number or colors in quotes has higher precedence than Unexpected word Reference interpreter appears to give precedence to Unexpected word We will accept either C453 Lecture Top-Down Predictive Parsers 21