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Sections 4.5,4.6. Aggelos Kiayias Computer Science & Engineering Department The University of Connecticut 371 Fairfield Road, Box U-155 Storrs, CT 06269-1155. [email protected] http://www.cse.uconn.edu/~akiayias. Bottom Up Parsing. “Shift-Reduce” Parsing - PowerPoint PPT Presentation
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CH4.1
CSE244
Sections 4.5,4.6Sections 4.5,4.6
Aggelos KiayiasComputer Science & Engineering Department
The University of Connecticut371 Fairfield Road, Box U-155
Storrs, CT [email protected]
http://www.cse.uconn.edu/~akiayias
CH4.2
CSE244
Bottom Up ParsingBottom Up Parsing
““Shift-Reduce” ParsingShift-Reduce” Parsing Reduce a string to the start symbol of the grammar.Reduce a string to the start symbol of the grammar. At every step a particular substring is matched (in At every step a particular substring is matched (in
left-to-right fashion) to the right side of some left-to-right fashion) to the right side of some production and then it is substituted by the non-production and then it is substituted by the non-terminal in the left hand side of the production. terminal in the left hand side of the production.
Consider: S aABe A Abc | b B d
abbcdeaAbcdeaAdeaABeS
Rightmost Derivation:S aABe aAde aAbcde abbcde
CH4.3
CSE244
HandlesHandles
Handle of a string = substring that matches the Handle of a string = substring that matches the RHS of some production AND whose reduction to RHS of some production AND whose reduction to the non-terminal on the LHS is a step along the the non-terminal on the LHS is a step along the reverse of some rightmost derivation.reverse of some rightmost derivation.
Formally: handle of a right sentential form Formally: handle of a right sentential form is <A is <A , location of in > that satisfies the above property.
i.e. i.e. AA is a handle of at the location immediately after the end of , if:
S => A =>
A certain sentential form may have many different handles. Right sentential forms of a non-ambiguous grammar
have one unique handle
*rm rm
CH4.4
CSE244
ExampleExample
S aABe aAde aAbcde abbcde
Consider: S aABe A Abc | b B d
It follows that:S aABe is a handle of aABe in location 1.B d is a handle of aAde in location 3.A Abc is a handle of aAbcde in location 2.A b is a handle of abbcde in location 2.
CH4.5
CSE244
Handle PruningHandle Pruning
A rightmost derivation in reverse can be obtained A rightmost derivation in reverse can be obtained by “handle-pruning.”by “handle-pruning.”
Apply this to the previous example.Apply this to the previous example.S aABeA Abc | bB d
abbcdeFind the handle = b at loc. 2aAbcdeb at loc. 3 is not a handle:aAAcde... blocked.
Also Consider:E E + E | E * E | | ( E ) | id
Derive id+id*idBy two different Rightmost derivations
CH4.6
CSE244
Handle Pruning, IIHandle Pruning, II
Consider the cut of a parse-tree of a certain right Consider the cut of a parse-tree of a certain right sentential form.sentential form.
S
A
Left part Handle (only terminals here)
Viable prefix
CH4.7
CSE244
Shift Reduce Parsing with a StackShift Reduce Parsing with a Stack
Two problems:locate a handle Two problems:locate a handle and decide which production to use (if there are and decide which production to use (if there are more than two candidate productions).more than two candidate productions).
General Construction:General Construction:using a stack: using a stack: 1. “shift” input symbols into the stack until a 1. “shift” input symbols into the stack until a handle is found on top of it.handle is found on top of it.2. “reduce” the handle to the corresponding non-2. “reduce” the handle to the corresponding non-terminal.terminal.(other operations: “accept” when the input is (other operations: “accept” when the input is consumed and only the start symbol is on the stack, consumed and only the start symbol is on the stack, also: “error”).also: “error”).
CH4.8
CSE244
ExampleExample
$$ id $E
id + id * id$
+ id * id$ + id * id$
STACK INPUT Remark
Shift
E E + E | E * E
| ( E ) | idReduce by E id
CH4.9
CSE244
More on Shift-Reduce ParsingMore on Shift-Reduce Parsing
Viable prefix: prefix of a right sentential form that Viable prefix: prefix of a right sentential form that appears on the stack of a Shift-Reduce parser.appears on the stack of a Shift-Reduce parser.
ConflictsConflictseither “shift/reduce” or “reduce/reduce”either “shift/reduce” or “reduce/reduce”
Example:Example:
stmt if expr then stmt
| if expr then stmt else stmt
| other (any other statement)
Stack Inputif … then else … Shift/ Reduce
conflict
CH4.10
CSE244
More ConflictsMore Conflicts
stmt id ( parameter-list )
stmt expr := expr
parameter-list parameter-list , parameter | parameter
parameter id
expr-list expr-list , expr | expr
expr id | id ( expr-list )
Consider the string A(I,J)Corresponding token stream is id(id, id)After three shifts:Stack = id(id Input = , id)
Reduce/Reduce Conflict … what to do?(it really depends on what is A,an array? or a procedure?
CH4.11
CSE244
Operator-Precedence ParsingOperator-Precedence Parsing
Operator Grammars: no production right side is Operator Grammars: no production right side is or has two adjacent non-terminals.or has two adjacent non-terminals.
Consider:E EAE | - E | ( E ) | idA - | + | * | / | ^
Not an operator grammar, but:
E E - E | E + E | E * E | E / E | E ^ E | - E | ( E ) | id
CH4.12
CSE244
Basic TechniqueBasic Technique
For the terminals of the grammar,For the terminals of the grammar,define the relations <. .> and .=.define the relations <. .> and .=.
a <. b means that a yields precedence to ba <. b means that a yields precedence to b a .=. b means that a has the same precedence as b.a .=. b means that a has the same precedence as b. a .> b means hat a takes precedence over ba .> b means hat a takes precedence over b E.g. * .> + or + <. * E.g. * .> + or + <. *
CH4.13
CSE244
Using Operator-Precedence RelationsUsing Operator-Precedence Relations
GOAL: delimit the handle of a right sentential formGOAL: delimit the handle of a right sentential form <. will mark the beginning, .> will mark the end <. will mark the beginning, .> will mark the end
and .=. will be in between.and .=. will be in between. Since no two adjacent non-terminals appear in the Since no two adjacent non-terminals appear in the
RHS of any production, the same is true for any RHS of any production, the same is true for any any sentential form.any sentential form.
So given So given 0 a a1 1 1 aa22 2 … aann n
where each i is either a nonterminal or the empty string. We drop all non-terminals and we write the corresponding
relation between each consecutive pair of terminals. example for $id+id*id$ using standard precedence:
$<.id.>+<.id.>*<.id.>$ Example for $E+E*id$ … $<.+<.*<.id.>$
CH4.14
CSE244
Using Operator-PrecedenceUsing Operator-Precedence
… … ThenThen1. Scan the string to discover the first .>1. Scan the string to discover the first .>2. Scan backwards skipping .=. (if any) until a <. is 2. Scan backwards skipping .=. (if any) until a <. is found.found.3. The handle is the substring delimited by the two 3. The handle is the substring delimited by the two steps above (including any in-between or steps above (including any in-between or surrounding non-terminals).surrounding non-terminals).E.g. E.g. Consider the sentential form E+E*EConsider the sentential form E+E*Ewe obtain $+*$ and from this the stringwe obtain $+*$ and from this the string$<. + <. * .> $$<. + <. * .> $
The handle is E*EThe handle is E*E
CH4.15
CSE244
Operator Precedence ParserOperator Precedence Parser
Set ip to point to the first symbol of w$
Stack=$
Repeat forever:
if $==topofstack and ip==$ then accept
Else { a=topofstack; b=ip;
if a<.b or a.=.b then push(b);advance ip;
if a.>b then repeat pop() until the top stack terminal is related by <.
else error
CH4.16
CSE244
ExampleExample
$$ id $$ + $ + id$ +$ + *$ + * id$ + *$ + $
id + id * id$
+ id * id$ + id * id$
id * id$* id$* id$
id$$$$$$
STACK INPUT Remark
$ <. idid >. +$ <. ++ <. idid .> *+ <. * * <. idid .> $* .> $+ .> $
accept
A sequence of pops corresponds to the
application of some of the productions
CH4.17
CSE244
Operator Precedence Table ConstructionOperator Precedence Table Construction
Basic techniques for operators:Basic techniques for operators: if operator 1 has higher precedence than 2
then set 1.> 2 If the operators are of equal precedence (or the
same operator)set 1.> 2 and 2.> 1 if the operators associate to the leftset 1<. 2 and 2<. 1 if the operators associate to the right
Make <.( and (<. and ).> and .>) id has higher precedence than any other symbol $ has lowest precedence.
CH4.18
CSE244
Unary OperatorsUnary Operators
Unary operators that are not also used as binary Unary operators that are not also used as binary operators are treated as before.operators are treated as before.
Problem: the – sign.Problem: the – sign. Typical solution: have the lexical analyzer return a Typical solution: have the lexical analyzer return a
different token when it sees a unary minus.different token when it sees a unary minus.