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Implementation of Parsers Bottom-Up Syntax Analysis

Bottom-Up Syntax Anaysis

Educational Objectives:• General Principles of Bottom-Up Syntax Analysis• LR(k) Analysis• Resolving Conflicts in Parser Generation• Connection between CFGs and push-down automata

Ina Schaefer Context-Free Analysis 59


Basic Ideas: Bottom-Up Syntax Analysis

• Bottom-Up Analysis is more powerful than top-down analysis,since production is chosen at the end of the analysis while intop-down analysis the production is selected up front.

• LR: Read input from left (L) and search for right derivations (R)



Principles of LR Parsing

1. Reduce from sentence to axiom2. Construct sentential forms from prefixes in (N ! T )! and input

rests in T !. Prefixes are right sentential forms of grammar. Suchprefixes are called viable prefixes. This prefix property has to holdinvariantly to avoid dead ends.

3. Reductions are always made at the left-most possible position.



Viable Prefix

DefinitionLet S "!

rm !Au "rm !"u a right sentential form of !.

Then " is called handle or redex of the right sentential for !"u.

Each prefix of !" is a viable prefix of !.



Regularity of Viable Prefixes

TheoremThe language of viable prefixes of a grammar ! is regular.

Proof.Cf. Wilhelm, Maurer Thm. 8.4.1 and Corrollary 8.4.2.1. (pp. 361, 362),Essential proof steps are illustrated in the following by construction ofLR # DFA(!).



LR Parsing: Examples

• Consider !1! S $ aCD! C $ b! D $ a|b

Analysis of aba can lead to an dead end. (cf. Lecture).

Considering viable prefixes can avoid this.



LR Parsing: Examples (2)

• Consider !2! S $ E#! E $ a|(E)|EE

Analysis of ( ( a ) ) ( a) # (cf. Lecture)

Stack can manage prefixes already read.



LR Parsing: Examples (3)

• Consider !3! S $ E#! E $ E + T |T! T $ ID

Analysis of ID + ID + ID # (cf. Lecture)



LR Parsing: Shift and Reduce

Schematic syntax tree for input xay with a % T , x , y % T ! and startsymbol S:

80© A. Poetzsch-Heffter, TU Kaiserslautern26.04.2007

x a y

!a

Lesezeiger

Schematischer Syntaxbaum zur Eingabe xay mit

a in T, x,y in T* und Startsymbol S:

x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger

Schiebe Schritt (shift): Reduktionsschritt (reduce):

"$=>


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>

Read Pointer

Read Pointer

Read PointerIna Schaefer Context-Free Analysis 67


LR Parsing: Shift and Reduce (2)Shift step:


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>

Read Pointer

Read Pointer

Read Pointer

Reduce step:


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>


x a y

!a

Lesezeiger



x a y

! = "#

Lesezeiger

x a y

!

Lesezeiger


"$=>

Read Pointer

Read Pointer

Read Pointer



LR Parsing: Shift and Reduce (3)

Main Problems:• Reductions can only be performed if remaining prefix is still a

viable prefix.• When to shift? When to reduce? Which production to use?

Solution:For each grammar ! construct LR # DFA(!) automaton (also calledLR(0) automaton), that describes the viable prefixes.



Construction of LR-DFA

Let ! =( T , N,", S) be a CFG.• For each non-terminal n % N, construct Item Automaton• Build union of item automata: Start state is the start state of item

automaton for S, Final states are final states of item automata• Add # transitions from each state which contains the position point

in front for a non-terminal A to the starting state of the itemautomaton of A

If all states of the LR-DFA automaton are considered as final states,the accepted language is the language of viable prefixes.



Construction of LR-DFA: Example

!3: S $ E#, E $ E + T |T , T $ ID


!5 : S E # , E E + T | T , T ID

Beispiel: (Konstruktion eines LR-DEA)

Konstruktion des LR-DEA für

[S .E #] [S E.# ] [S E#.]

[E .E+T]

[E .T ]

[T .ID ]

[E E+.T] [E E+T.]

[E T.]

[T ID.]

E #

E + T

ID

[E E.+T]

T

"

" "

"

Deterministisch machen liefert folgenden Automaten:Ina Schaefer Context-Free Analysis 71


Construction of LR-DFA: Example (2)

Determinisation:


[S .E #]

[S E.# ][S E#.]

[E .E+T]

[E .T ]

[T .ID ]

[E E+.T]

[E E+T.][E T.] [T ID.]

E #

+

T

IDFehlerT

[E E.+T]

bezeichnet Fehlerkanten

q0

q1 q2

q3

q4q5

q6

Die zuverlässigen Präfixe maximaler Länge:

E# , T , ID , E+ID , E+T

[T .ID ]

ID

Bemerkungen:

• Im Beispiel enthält jeder Endzustand genau eine

vollständig gelesene Produktion. Dies ist im Allg.

nicht so.

• Enthält ein Endzustand mehrere vollständig gelesene

Produktionen spricht man von einem reduce/reduce-

Konflikt.

• Enthält ein Endzustand eine vollständig gelesene

und eine unvollständig gelesene Produktion

mit einem Terminal nach dem Positionspunkt,

spricht man von einem shift/reduce-Konflikt.

q7

Error

Error Transitions

Viable prefixes of maximal length: E#, T , ID, E + ID, E + T



Construction of LR-DFA: Example (3)

Remarks:• In the example, each final state contains one completely read

production, this is in general not the case.• If a final state contains more than one completely read

productions, we have a reduce/reduce conflict.• If a final state contains a completely read and an uncompletely

read production with a terminal after the position point, we have ashift/reduce conflict.



Analysis with LR-DFA

Analysis of ID + ID + ID # with LR-DFA(the viable prefix is underlined)


Analyse von ID + ID + ID # mit dem LR-DEA,

unterstrichen ist jeweils der zuverlässige Präfix:

ID + ID + ID # <=

T + ID + ID # <=

E + ID + ID # <=

E + T + ID # <=

E + ID # <=

E + T # <=

E # <=

S

Beispiel: (Analyse mit LR-DEA)

Beachte:

• Die Satzformen bestehen immer aus einem

zuverlässigen Präfix und der Resteingabe.

• Verwendet man nur den LR-DEA

zur Analyse muss man nach jeder Reduktion

die Satzform von Anfang an lesen.

deshalb: verwende Kellerautomaten zur Analyse



Analysis with LR-DFA (2)

Note:• The sentential forms always consist of a viable prefix and a

remaining input.• If an LR-DFA is used, after each reduction the sentential form has

to be read from the beginning.

Thus: Use pushdown automaton for analysis.



LR pushdown automaton

DefinitionLet ! =( N, T ,", S) be a CFG. The LR-DFA pushdown automaton for !contains:

• a finite set of state Q (the states of the LR-DFA(!))• a set of actions Act = {shift , accept , error} ! red("), where

red(") contains an action reduce(A $ ") for each productionA $ ".

• an action table at : Q $ Act .• a successor table succ : P & (N ! T ) $ Q with

P = {q % Q |at(q) = shift}



LR pushdown automaton (2)

Remarks:• The LR-DFA pushdown automaton is a variant of pushdown

automata particularly designed for LR parsing.• States encode the read left context.• If there are no conflicts, the action table can be directly

constructed from the LR-DFA:! accept: final state of item automaton of start symbol! reduce: all other final states! error: error state! shift: all other states



Execution of Pushdown Automaton

• Configuration: Q! & T ! where variable stack denotes thesequence of states and variable inr denotes the remaining input

• Start configuration: (q0, input), where q0 is the start state of theLR-DFA

• Interpretation Procedure:

(stack, inr) := (q0,input);do {

step(stack,inr);} while ( at(top(stack)) != accept

and at(top(stack)) ! = error );if (( at (top(stack)) == error) return error;

with



Execution of Push-Down Automaton (2)

void step ( var StateSeq stack, var SymbolSeq inr) {State tk: = top(stack);switch ( at(tk) ) {case shift:

stack: = push ( succ (tk,top(inr)), keller);inr := tail(inr);break;

case reduce A -> a:stack := mpop( length(a) ,stack);stack := push (succ(top(stack), A), stack);break;

}}



LR push down automaton: Example

LR-DFA with states q0, . . . , q7 for grammar !3

Action Table


Beispiel: (LR-Kellerautomat zu !5 )

Aktionstabelle:

q0 schieben

q1 schieben

q2 akzeptieren

q3 schieben

q4 reduzieren E E+T

q5 reduzieren E T

q6 reduzieren T ID

q7 fehler

Nachfolgertabelle:

ID + # E T

q0 q6 q7 q7 q1 q5

q1 q7 q3 q2 q7 q7

q2

q3 q6 q7 q7 q7 q4

q4

q5

q6

q7

LR-DEA mit Zuständen q0 – q7 (siehe Beipiel oben)

Rechnung zu Eingabe ID + ID + ID # :

Keller Eingaberest Aktion

q0

q0 q6

q0 q5

q0 q1

q0 q1 q3

q0 q1 q3 q6

q0 q1 q3 q4

q0 q1

q0 q1 q3

q0 q1 q3 q6

q0 q1 q3 q4

q0 q1

q0 q1 q2

ID + ID + ID # schieben

+ ID + ID # reduzieren T ID

+ ID + ID # reduzieren E T

+ ID + ID # schieben

ID + ID # schieben

+ ID # reduzieren T ID

+ ID # reduzieren E E+T

+ ID # schieben

ID # schieben

# reduzieren T ID

# reduzieren E E+T

# schieben

akzeptieren

shift

accept

error

reduce

shift

shift

reduce

reduce

Successor Table



Aktionstabelle:

q0 schieben

q1 schieben

q2 akzeptieren

q3 schieben

q4 reduzieren E E+T

q5 reduzieren E T

q6 reduzieren T ID

q7 fehler

Nachfolgertabelle:

ID + # E T

q0 q6 q7 q7 q1 q5

q1 q7 q3 q2 q7 q7

q2

q3 q6 q7 q7 q7 q4

q4

q5

q6

q7




q0

q0 q6

q0 q5

q0 q1

q0 q1 q3

q0 q1 q3 q6

q0 q1 q3 q4

q0 q1

q0 q1 q3

q0 q1 q3 q6

q0 q1 q3 q4

q0 q1

q0 q1 q2





ID + ID # schieben



+ ID # schieben

ID # schieben

# reduzieren T ID

# reduzieren E E+T

# schieben

akzeptieren



LR push down automaton: Example (2)Computation for Input ID + ID + ID #



Aktionstabelle:

q0 schieben

q1 schieben

q2 akzeptieren

q3 schieben

q4 reduzieren E E+T

q5 reduzieren E T

q6 reduzieren T ID

q7 fehler

Nachfolgertabelle:

ID + # E T

q0 q6 q7 q7 q1 q5

q1 q7 q3 q2 q7 q7

q2

q3 q6 q7 q7 q7 q4

q4

q5

q6

q7




q0

q0 q6

q0 q5

q0 q1

q0 q1 q3

q0 q1 q3 q6

q0 q1 q3 q4

q0 q1

q0 q1 q3

q0 q1 q3 q6

q0 q1 q3 q4

q0 q1

q0 q1 q2





ID + ID # schieben



+ ID # schieben

ID # schieben

# reduzieren T ID

# reduzieren E E+T

# schieben

akzeptieren

Stack Input Rest Action

shiftshift

shift

shiftshift

shiftaccept

reduce

reduce

reducereduce

reducereduce



LR-DFA Construction

Questions:• Does LR-DFA construction work for all unambiguous grammars?• For which grammars does the construction work?• How can the construction be generalized / made more

expressive?



Example LR-DFALR-DFA for !6: S $ E#, E $ T + E |T , T $ ID|N(), N $ ID


Fragen:

• Funktioniert die obige Konstruktion für alle

eindeutigen Grammatiken?

• Für welche Grammatiken funktioniert sie?

• Wie kann man sie verallgemeinern/mächtiger machen?

Beispiel:

LR-DEA für !6 :

S E # , E T+E | T , T ID | N( ) , N ID

[S .E #]

[S E.# ] [S E#.]

[E .T+E]

[E .T ]

[T .ID ]

[ T N(.) ]

E

#

+

T

ID

Fehler

T

bezeichnet Fehlerkanten

q0

q1 q2 q3

q4

q5

q6

ID[T .N( ) ]

[N .ID ]

[E T.+E]

[E T. ][E T+.E]

[E .T ]

[E .T+E]

[T .N( ) ]

[N .ID ]

[T .ID ]

[E T+E.]

E

[T ID.]

q10

[N ID.]

N

[ T N.( ) ] [ T N( ). ]

N

( )q8q7 q9

error

Error Transitions



LR Parsing Conflicts

2 Kinds of Conflicts:• Shift/Reduce Conflicts (q4 in example)• Reduce/Reduce Conflicts (q6 in example)



LR Parsing Theory

DefinitionLet ! =( N, T ,", S) be a CFG and k % N. ! is an LR(k) grammar if forany two right derivations

S "!rm "Au "rm "!u

S "!rm $Bv "rm "!w

it holds that:If prefix(k , u) = prefix(k , w) then " = $, A = B and v = w



LR Parsing Theory (2)

Remarks:

• While for LL grammars the selection of the production depends onthe non-terminal to be derived, for LR grammars it depends on thecomplete left context.

• For LL grammars, the look ahead considers the language to begenerated from the non-terminal. For LR grammars, the lookahead considers the language generated from not yet readnon-terminals.



Characterization of LR(0)

TheoremA reduced CFG ! is LR(0) if-and-only-if the LR-DFA(!) contains noconflicts.

Proof.cf. Lecture



Characterization of LR(0) (2)

Example: Application of LR(0)-ChracterizationShow (using the above theorem) that !5 is LR(0).!5:

• S $ A|B• A $ aAb|0• B $ aBbb|1



Expressiveness of LR(k)

• For each context-free language L with prefix property(i.e. 'v , w % L: v is no prefix of w), there exists an LR(0) grammar.

• Grammar !5 is not LL(k), but LR(0).• Methods for LR(1) can be generalized to LR(k), SLR(k) and

LALR(k).



Resolving Conflicts by Look Ahead

• Compute look ahead sets from (N ! T )"k for items. The lookahead set of an item approximates the set of prefixes of length kwith which the input rest at this item can start.

• If the look ahead sets at an item are disjoint, then the action to beexecuted (shift, reduce) can be determined by k symbols lookahead.

• For an item, select the action whose look ahead set contains theprefix of the input rest. Action table has to be extended.

• For computation of look ahead sets, there are different methods.



Common Methods for Look Ahead Computation

• SLR(k) uses LR-DFA and FOLLOWk of conflicting items for lookahead

• LALR(k) - look ahead LR - uses LR-DFA with state-dependentlook ahead sets

• LR(k) integrates computation of look ahead sets in automataconstruction (LR(k) automaton)



SLR Grammars

Definition (SLR(1) grammar)Let ! =( N, T ,", S) be a CFG and LA([A $ ".]) = FOLLOW1(A).

A state LR-DEA(!) has an SLR(1) conflict if there exists two differentreduce items with LA([A $ ".]) ( LA([B $ !.]) )= * or two items[A $ ".] and [B $ ".a!] with a % LA([A $ a]).

! is SLR(1) if there is no SLR(1) conflict.



SLR Grammars (2)

Example: !6 is an SLR(1) grammar• S $ E#

• E $ T + E |T• T $ ID|N()

• N $ IDConsider the conflicts between [E $ T .] and [E $ T . + E ] andbetween [T $ ID.] and [N $ ID.]

FOLLOW1(E) ( {+} = {#} ({ +} = *FOLLOW1(T ) ( FOLLOW1(N) = {#,+} ({ (} = *



SLR Grammars (3)

Example: !7 (simplifed C expressions) is not an SLR(1) grammar

• S $ E#

• E $ L = R|R• L $ +R|ID• R $ L



SLR Grammars (4)LR-DFA for !7


Beispiel: (nicht SLR(1)-Sprache)

Betrachte folgende Grammatik für vereinfachte

C-Ausdrücke:

!7 : S E # , E L = R | R , L *R | ID , R L

Der zugehörige LR-DEA:

[S .E# ]

[S E.# ] [S E#. ]

[E .L=R]

[E .R]

[E L .=R]

[E L= .R]

[E L=R.]

[E R.]

[R .L]

[R L .]

[L .*R]

[L .ID]

[L * .R][L *R.]

[L ID.]

[R .L]

[L .*R]

[L .ID]

[R .L]

[L .*R]

[L .ID]

[R L .]

ER

L

*

=

ID

#

R

* LID

ID

R

L

*

Der einzige Zustand mit einem Konflikt enthält die

Items [E L .=R] und [R L .] mit

FOLLOW1(R) { = } = { =, # } { = } = { =} = { }

U U

/

Only conflict in items [E $ L. = R] and [R $ L.] with

FOLLOW1(R) ( {=} = {=,#} ({ =} )= *



Construction of LR(1) Automata

LR(1) automaton contains items [A $ ".!, V ] with V , T where• " is on top of the stack• the input rest is derivable from !c with c % V , i.e.

V , FOLLOW1(A).



Construction of LR(1) Automata (2)

LR(1) automaton for !7. Conflict is resolved, as {=} ({ #} = *.


Konstruktion von LR(1)-Automaten:

Items der Form [ A !.", V ] mit V T

und der Bedeutung, dass ! auf dem Keller liegt und

der Anfang des Eingaberests aus "c ableitbar ist mitc in V. D.h. V FOLLOW1(A) .

U

U

S .E#

S E.#

S E#.

E .L=R #

E .R #

E L .=R # E L= .R #

E L=R. #

E R. #

R .L #

R L . #

L .*R #,=

L .ID #,=

L * .R #,=

L *R. #,=

L ID. #

R .L #

L .*R #

L .ID #

R .L #,=

L .*R #,=

L .ID #,=

R L . #

E R

L

*

=

ID

#

R

*

L

ID

ID

R

L

*

L * .R #

R .L #

L .*R #

L .ID #

L *R. #

*L ID. #,=

R L . #,=

R

L

Konflikt kann behoben werden, da {=} {#} = {}U



LALR(1) Automata

• LALR(1) Automata are constructed from LR(1) automata bymerging states in which items only differ in look ahead sets. Lookahead sets for equal items are conjoint. The resulting automatonhas the same states as the LR-DFA.

• However, LALR(1) automata can be generated more efficiently.



LALR(1) Automata (2)LR(1) automaton for !7.


LALR(1)-Automaten:

Aus dem LR(1)-Automaten erhält man den LALR(1)-

Automaten durch Zusammenlegen der Zustände, in

denen sich die Items nur in der Vorausschaumenge

unterscheiden. Die Vorausschaumengen zu gleichen

Items werden dabei vereinigt. Der resultierende Automat

hat die gleichen Zustände wie der LR-DEA..

S .E#

S E.#

S E#.

E .L=R #

E .R #

E L .=R # E L= .R #

E L=R. #

E R. #

R .L #

R L . #

L .*R #,=

L .ID #,=

L * .R #,=

L *R. #,=

R .L #

L .*R #

L .ID #

R .L #,=

L .*R #,=

L .ID #,=

E R

L

*

=

ID

#

*

ID

ID

R

L

*

L ID. #,=

R L . #,=

R

L

Der LALR(1)-Automat lässt sich allerdings effizienter

direkt konstruieren.

q0

q1

q2

q3

q4

q5

q6

q7

q8

q9



Grammar Classes


Zusammenhang der Grammatikklassen:

Lesen Sie zu Unterabschnitt 2.2.2.2:

Wilhelm, Maurer:

• aus Kap. 8, Abschnitt 8.4.1 bis einschl. 8.4.5,

S. 353 – 383.

mehrdeutige Grammatiken

eindeutige Grammatiken

LR(k)

LR(1)

LALR(1)

SLR(1)

LR(0)

LL(k)

LL(1)

LL(0)

unambiguous grammars

ambiguous grammars



Literature

Recommended Reading for Bottom-Up Analysis:• Wilhelm, Maurer: Chapter 8, Sections 8.4.1 - 8.4.5, pp. 353 - 383



Parser Generators

Educational Objectives

• Usage of Parser Generators• Characteristics of Parser Generators



JavaCUP Parser Generator

• CUP - Constructor of Useful Parsershttp://www2.cs.tum.edu/projects/cup/

• Java-based Generator for LALR-Parsers

• JFlex can be used to generate according scanner.

• Running JavaCUP:

java -jar java-cup-11a.jar options inputfile



Structure of JavaCUP Specification

package JavaPackageName;import java_cup.runtime.*;

/* User supplied code for scanner, actions, ... */

/* Terminals (tokens returned by the scanner). */terminal TerminalDecls;

/* Non-terminals */non terminal NonTerminalDecls;

/* Precedences */precedence [left | right | nonassoc ] TerminalList;

/* Grammar */start with non-terminalName;

non_terminalName :: = prod_1 | ... | prod_n ;Ina Schaefer Context-Free Analysis 104


Example: JavaCUP Specification for !7

import java_cup.runtime.*;

/* Terminals (tokens returned by the scanner). */terminal ID, EQ, MULT;

/* Non terminals */non terminal S, E, L, R;

/* The grammar */

start with S;

S ::= E;E ::= L EQ R | R;L ::= MULT R | ID;R ::= L;



Structure of Generated Parser Code

• Output Files parser.java and sym.java

• Tables for LALR Automaton! Production table: provides the symbol number of the left hand side

non-terminal, along with the length of the right hand side, for eachproduction in the grammar,

! Action table: indicates what action (shift, reduce, or error) is to betaken on each lookahead symbol when encountered in each state

! Reduce-goto table: indicates which state to shift to after reduce



Usage of Generated Parser

• Parser calls scanner with scan() method when a new terminal isneeded

• Initialising Parser with new Scanner

parser parser_obj = new parser(new my_scanner());

• Usage of Parser:

Symbol parse_tree = parser_obj.parse();


Error Handling

Error Handling

Educational Objectives:

• Problems and Principles of Error Handling• Techniques of Error Handling for Context-Free Analysis


Error Handling

Principles of Error Handling

Error handling is required in all analysis phases and at runtime. Onedistinguishes

• lexical errors• parse errors (in context-free analysis)• errors in name and type analysis• runtime errors (cannot be avoided in most cases)• logical errors (behavioural errors)

First 2 (3) kinds of errors are syntactic errors. We only consider errorhandling in context-free analysis.

Specification of error handling results basically from languagespecification.


Error Handling

Requirements for error handling

• Errors should be localized as exactly as possible.(Problem: Error is not detected at error position.)

• As many errors at possible should be detected at once, but onlyreal errors and no errors as consequences.

• Errors are not always unique, i.e. it is not clear in general how tocorrect an error: class int { Int a; .... } or int a = 1-;

• Error handling should not slow down analysis of correct programs.

Therefore, error handling is non-trivial and depends on the sourcelanguage to be analysed.


Error Handling

Error Handling in Context-Free Analysis

1. Panic Error HandlingMark synchronizing terminal symbols, e.g. end or ;

If parser reaches error state, all symbols up to next synchronizingsymbol are skipped and the stack is corrected as if the productionwith the synchronizing symbol was read correctly.

! Pros: easy to implement, termination guaranteed! Cons: large parts of the program can be skipped or misinterpreted! Example: Incorrect Input a : = b *** c;

Read until ; correct stack and reuse as if statement has beenaccepted


Error Handling

Error Handling in Context-Free Analysis (2)

2. Error ProductionsExtend grammar with productions describing typical errorsituations, so called error productions. Error messages can bedirectly associated with error productions.

! Pros: easy to implement, termination guaranteed! Cons: extended grammar can belong to more general grammar

class, knowledge of typical error situations is necessary! Example: Typical error in PASCAL

if ... then A := E; else ...Error Production:Stmt $ if Expr then Stmt! ; else Stmt!


Error Handling


3. Production-Local Error CorrectionGoal is local correction of input such that analysis can beresumed. Local means that it is tried to correct the input for thecurrent production.

! Pros: flexible and powerful technique! Cons: problematic if errors occur earlier than they can be detected,

operations for corrections can lead to nonterminating analysis


Error Handling


4. Global Error CorrectionAttempt to get a correction that is as good as possible by alteringthe read input or the look ahead input.

Idea: Define distance or quality measure on inputs. For eachincorrect input, look for a syntactically correct input that is bestaccording to the used measure.

! Pros: very powerful technique! Cons: analysis effort can be rather high, implementation is complex

and poses risk of non-termination.


Error Handling


5. Interactive Error CorrectionIn modern programming languages, syntactic analysis is oftenalready supported by editors. In this case, editor marks errorpositions.

! Pros: quick feedback, possible error positions are shown directly,interaction with programmer possible

! Cons: editing can be disturbed, analysis must be able to handleincomplete programs

The presented techniques can also be combined. For selection oftechnique, programming language syntax is important. Errorhandling also depends on grammar class and implementationtechniques used for parser.


Error Handling

Burke-Fischer Error Handling

Example of global error correction technique

• Procedure: Use correction window of n symbols before symbol atwhich error was detected. Check all possible variations of symbolsequence in correction window that can be obtained by insertion,exchange or modification of a symbol at any position.

• Quality Measure: Choose variation that allows longestcontinuation of parsing procedure

• Implementation: Work with two stack automata, one representsthe configuration at the beginning of the correction window, theother one the configuration at the end of the correction window. Inan error case, the automaton running behind can be used toresume at the old position and to test the computed variations.


Error Handling

Literature

Recommended Reading: Wilhelm, Maurer: Chapter 8,Sections 8.3.6 and 8.4.6 (general understanding sufficient)


Concrete and Abstract Syntax


Educational Objectives

• Connection of parsing to other phases of program processing andtranslation

• Differences between abstract and concrete syntax• Language concepts for describing syntax trees• Syntax tree construction



Connection of Parsers to other Phases

1. Parser directly controls following phases2. Concrete Syntax Tree as Interface3. Abstract Syntax Tree as Interface



Direct Control by Parser

• Example: Recursive Descent: Parser calls other actions aftereach derivation/reduction step

• Pros:! simple (if realisable)! flexible! efficient (especially memory efficient)

• Cons:! non-modular, no clear interfaces! not suitable for global aspects of translation! following phases depend on parsing! cannot be used with every parser generator



Abstract Syntax vs. Concrete Syntax

Definition (Concrete Syntax)The concrete syntax of a programming languages determines theactual text representation of the programs (incl. key words,separators).If ! is the CFG used for parsing a program P in a certain language, thesyntax tree of P according to ! is the concrete syntax tree of P.

Definition (Abstract Syntax)The abstract syntax of a programming language describes the treestructure of programs in a form that is sufficient and suitable for furtherprocessing.A tree for representing a program P according to the abstract syntax ofa language is called abstract syntax tree of P.



Abstract Syntax

• abstraction from keywords and separators• operator precedences are represented in tree structure (different

non-terminals are not necessary)• better incorporation of symbol information• simplifying transformations

Remarks:• The abstract syntax of a language is often not specified in the

language report.• The abstract syntax usually also comprises information about

source code positions.



Example: Concrete vs. Abstract Syntax

Concrete Syntax: !2

• S $ E#

• E $ T + E |T• T $ F + T |F• F $ (E) |ID

Abstract Syntax• Exp = Add | Mult Ident• Add (Exp left, Exp right)• Mult (Exp left, Exp right)



Example: Concrete vs. Abstract Syntax (2)Text: (a + b) + c

Concrete Syntax Tree

Textrepräsentation: ( a + b ) * c

Konkreter Syntaxbaum: Abstrakter Syntaxbaum:

S Mult

T

E #

Mult

Add c

F

F

T

a b

E

E T

FF

T

( ID ID ) * ID( ID + ID ) * IDa b c


Abstract Syntax Tree

Textrepräsentation: ( a + b ) * c

Konkreter Syntaxbaum: Abstrakter Syntaxbaum:

S Mult

T

E #

Mult

Add c

F

F

T

a b

E

E T

FF

T

( ID ID ) * ID( ID + ID ) * IDa b c




Concrete Syntax Tree as Interface

Token Stream

Parser (with Tree Construction)

Concrete Syntax Tree

Further LanguageProcessing

• Counters disadvantages of direct control by parser• Advantages over Abstract Syntax

! No additional specification of abstract syntax required! Tree construction does not have to be described.! Tree construction can be done automatically by parser generators.



Abstract Syntax Tree as Interface

Token Stream

Parser (with Transforming Tree Construction)

Abstract Syntax Tree

Further LanguageProcessing

• Advantages over Concrete Syntax! Simpler, more compact tree representation! Simplifies later phases! Often implemented by programming or specification language as

mutable data structure



Abstract Syntax: Specification and Tree Construction

• For representing abstract syntax trees, we use order-sorted terms.• The sets and types of these terms are described by type

declarations.



Order-sorted Data Types

DefinitionOder-sorted Data Types are specified by declarations of the followingform:

• Variant Type Declarations V = V0|V1| . . . |Vm

• Tuple Type Declaration T (T1sel1, . . . , Tnseln)• List Type Declarations L + S

Example:• Exp = Add | Mult | Ident• Add (Exp left, Exp right)• Mult (Exp left, Exp right)

where Ident is a predefined type.



Order-sorted Data Types (2)

Definition (Order-sorted Types - contd.)Order-sorted Terms are recursively defined as

• If t is a term of type Vi , then it is also of type V.• If ti is a term of type Ti for each i, then T (t1, . . . , tn) is of type T ,

T is also the constructor.• If s1, . . . , sk are terms of type S, then L(s1, . . . , sn) is of type L,

L is also the list constructor.Additional Operators

• the selectors selk : T $ Tk returns the k-th subterm of a tuple• the usual list operations (rest, append, conc, ...)



Order-sorted Data Types (3)

Remarks: Order-sorted Data Types• generalise data types of functional languages by subtyping, a term

can belong to serveral types• are used in specification languages, e.g. OBJ3, MAX, ...• are a very compact form for type declaration• can be implemented by OO languages



Example: Order-sorted Data Types and OO Types

Declaration of order-sorted data types:• Exp = Add | Mult | Neg | Ident• Add (Exp left, Exp right)• Mult (Exp left, Exp right)• Neg (Exp val)



Implementation in Java

interface Exp {Exp left() throws IllegalSelectException;Exp right() throws IllegalSelectException;Exp val() throws IllegalSelectException;

}

class Add implements Exp {private Exp left;private Exp right;

Add( Exp l, Exp r ) {left = l; right = r; }

Exp left() { return left; }Exp right(){ return right; }Exp val() throws IllegalSelectException {

throw new IllegalSelectException(); }}



Implementation in Java (2)

class Mult implements Exp {// analog zu Add }

class Neg implements Exp {private Exp val;

Neg( Exp v ) { val = v; }

Exp left() throws IllegalSelectException {throw new IllegalSelectException(); }

Exp right() throws IllegalSelectException {throw new IllegalSelectException(); }

Exp val() { return val; }}



Implementation in Java (3)

class Ident implements Exp extends PredefIdent {

Exp left() throws IllegalSelectException {throw new IllegalSelectException(); }

Exp right() throws IllegalSelectException {throw new IllegalSelectException();}

Exp val() throws IllegalSelectException {throw new IllegalSelectException(); }

}



Transformation of Concrete to Abstract SyntaxTransformation konkreter in abstrakte Syntax:

S

E #

T

Mult(_,_)

F

F

T

E

Add(_,_)

E T

T

FF

( ID + ID ) * ID


a b c



Transformation to Abstract Syntax with JavaCUP

S ::= E:e #{: RESULT = e; :} ;

E ::= E:e ’+’ T:t{: RESULT = ADD(e,t); :} |T:t{: RESULT = t; :} ;

T ::= T:t ’*’ F:f{: RESULT = MULT(t,f); :} |F:f{: RESULT = f; :} ;

F ::= ’(’ E:e ’)’{: RESULT = e ; :} |ID:i{: RESULT = i; :} ;



Recommended Reading

• Wilhelm, Maurer: Section 9.1, pp. 406 + 407• Appel: Chapter 4, pp. 89 – 105


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