Attribute Grammars. Attribute Grammars

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1 Attribute Grammars Definitions: synthesized, inherited, dependence graph Example: syntax-directed translation S-attributed grammars -attributed grammars Bottom Up euation of inherited attributes Top Down translation Attribute Grammars! BGR, Fall05 Attribute Grammars Attributes: properties associated with nonterminal symbols of a context free grammar E.G., Binary numbers. B " 0 (B) = 0 2. B " (B) = 3. " B () = (B); len() = 4. " B () = 2*( ) + (B) len() = len( ) + Semantic rules defining attributes are side-effect free 5. N " (N) = (); len(n) = len() Attribute Grammars! BGR, Fall05 2

2 Parse Tree of 0 2 N, len Represent dependences between semantic functions of attributes, len, len B,len B B 0 Attribute Grammars! BGR, Fall05 3 Dependence Graph: acyclic, euated in topsort order, contains attribute instances Euate(Decorate) Parse Tree Initial ues N, len, len,len B, len B B 0 Attribute Grammars! BGR, Fall05 4 0

3 Euate Euate Parse Tree,len B N 5, len 2, len B 0 5, len Attribute Grammars! BGR, Fall05 5 B 0 Euate Parse Tree Euate len; Full euation yields (N) = 5; len(n) = 3. N, len, len 2, len B 3 3,len B B 0 Attribute Grammars! BGR, Fall05 6

4 Classifications Inherited attributes: Values based on attributes of parent (HS nonterminal) or siblings (nonterminals on RHS of same production Synthesized attributes: Values based on attributes of descendents (child nonterminals in same production) Attribute Grammars! BGR, Fall05 7 Classifications ocal context: always within focus of a single production Dependence edges go only one level in parse tree Terminals can be associated with ues returned by the scanner Distinguished nonterminal cannot have inherited attributes Attribute Grammars! BGR, Fall05 8

5 Example - Identifiers Identifiers with no letters repeated (e.g., moon - illegal, money - legal) D " I str(i) = {}; (D) = (I); accept, if (D)!= error I " I str() = str(i); str(i ) = (); (I) = (I ) I " str() = str(i); (I) = () " a b z () = concatenation of returned by scanner to str(), if this character is not a repeated letter, else error. (note: any comparison to error returns error.) Attribute Grammars! BGR, Fall05 9 Inherited Attributes D " I str(i) = {}; (D) = (I); accept, if (D)!= error I " I str() = str(i); str(i ) = (); (I) = (I ) I " str() = str(i); (I) = () " a b z () = concatenation of returned by scanner to str(), if this character is not a repeated letter, else error. (note: any comparison to error returns error.) Attribute Grammars! BGR, Fall05 0

6 Synthesized Attributes D " I str(i) = {}; (D) = (I); accept, if (D)!= error I " I str() = str(i); str(i ) = (); (I) = (I ) I " str() = str(i); (I) = () " a b z () = concatenation of returned by scanner to str(), if this character is not a repeated letter, else error. (note: any comparison to error returns error.) Attribute Grammars! BGR, Fall05 Parse Tree of abc D I str a str I str str I str b str Attribute Grammars! BGR, Fall05 2 c

7 Decorated Parse Tree a D I abc str abc I str str abc a a ab I str str a ab b str ab abc abc Attribute Grammars! BGR, Fall05 3 c symb is the symbol table gathered from the declarations and checked in the <declarations> statements. Compiler Example <Pgm> symb <body> symb Int-decl symb <assign_stmt> symb Integer <decl-list> symb <id> := <expr> <id>, <decl-list> symb symb symb symb <id> <id>, <decl-list> symb symb symb <id> symb Attribute Grammars! BGR, Fall05 4

8 Syntax-directed Translation Idea: to use attribute grammars to cover some of the context-sensitive issues in translation Syntax-directed definition: an attributed grammar such that every grammar symbol has an attribute. Conceptually, attribute euation is Build parse tree Find attribute dependences Decorate parse tree Attribute Grammars! BGR, Fall05 5 Euation Methods Want to interleave attribute euation with parsing Use dependence graph (but cannot handle circular dependences) Predetermine euation order at compiler construction time, using knowledge of grammar Ad-hoc: chosen parsing method imposes eution order when interleaved with parsing; restricts grammars that can be handled Attribute Grammars! BGR, Fall05 6

9 S-attributed Grammars S-attributed grammars: all attributes are synthesized Easy to interleave with BU parsing by using a parallel stack for attribute ues Euate as do a reduction Important: can code semantic functions a priori, because know all the handles from the grammar, so know where the associated attributes will be in the stack when a reduction is about to take place. Attribute Grammars! BGR, Fall05 7 Attribute Grammars Attributes: properties associated with nonterminal symbols of a context free grammar E.G., Binary numbers. B " 0 (B) = 0 2. B " (B) = 3. " B () = (B); len() = 4. " B () = 2*( ) + (B) len() = len( ) + Semantic rules defining attributes are side-effect free 5. N " (N) = (); len(n) = len() Attribute Grammars! BGR, Fall05 8

10 Example - Binary Nos. B " 0 (B) = 0 2. B " (B) = 3. " B () = (B); len() = 4. " B () = 2*( ) + (B) len() = len( ) + 5. N " (N) = (); len(n) = len() Stack Input $ $ shift $ (B _) $ red(2), find B $ ( ) $ red(3), find $ ( ) ( _) $ shift $ ( ) (B _) $ red(2), find B $ ( 3 2) $ red (5), find $ (N 3 2) $ accept (<symbol> () len()) Attribute Grammars! BGR, Fall05 9 -attributed Grammars Every attribute in the grammar is synthesized, or for production A " X X k an inherited attribute X k only depends on attributes of X X k- or inherited attributes of A. Can use depth-first euation scheme on parse tree Includes all syntax-directed definitions from () grammars Attribute Grammars! BGR, Fall05 20

11 -attributed Grammars Translation scheme: embeds semantic actions to euate attributes in RHS of productions (use { } to delimit actions) to accomplish depth-first euation order. An inherited attributed for a nonterminal on RHS of production, must be computed in an action BEFORE that symbol Attribute Grammars! BGR, Fall05 2 -attributed Grammars 2. An action cannot refer to a synthesized attribute of a symbol to the right of the action 3. A synthesized attribute of the HS nonterminal can only be computed after all attributes it refers to are computed; place this action at the end of the RHS of the production Attribute Grammars! BGR, Fall05 22

12 Example - Identifiers as a Translation Scheme D " {str(i) = # } I {(D) = (I)} {accept, if (D)!= error} I " { str() = str(i)} {str(i ) = ()!} I {(I) = (I )} I " { str() = str(i) } {(I) = ()} " a b z {() = concatenation of returned by scanner to str(), if this character is not a repeated letter, else error} Try to euate earlier example abc with depth-first walk and these rules. Attribute Grammars! BGR, Fall05 23 Intuition Can see TD parsing relates well to -attributed grammars Can see BU parsing relates well to S-attributed grammars Attribute Grammars! BGR, Fall05 24

13 BU E of Inherited Attribs Idea: transform grammar so all embedded actions of translation scheme occur at end of RHS of some production (at a reduction) without changing R(k) nature of the grammar Can handle all -attributed defns corresponding to () grammars plus some R() Attribute Grammars! BGR, Fall05 25 Marker Nonterminals Used to move all actions to end of RHS of productions Always X " # for X, a marker nonterminal. Replace an embedded action by a unique marker nonterminal that generates # Make the action for that nonterminal the same as the embedded action removed But: grammar must stay R(k) after these changes (this needs to be checked.) anguage accepted is same. Actions occur in same order during parse. Attribute Grammars! BGR, Fall05 26

14 Example, ASU p 309 S " E E " E + T E - T T T " num S " E E " T R R " + T { print + } R R " - T { print - } R R " # T " num {print num} becomes after recursion remo with actions: Attribute Grammars! BGR, Fall05 27 R() grammar Marker Nonterminals After transformation S " E S " E E " T R E " T R R " + T { print + } R R " +! T M R R " - T { print - } R R " - T N R R " # R " # T " num {print num} M " # { print + } N " # {print - } T " num {print num} Attribute Grammars! BGR, Fall05 28

15 Marker Nonterminals (Copies) Handling copy rules with marker nonterminals A " X Y where i(y) = s(x) Translation scheme would be: A " X {i(y) = s(x)} Y Example of this in our identifier grammar str(i ) = () in I " I would become I " {str(i ) = ()} I Attribute Grammars! BGR, Fall05 29 Example D I a I a ab Attribute Grammars! BGR, Fall05 30 b

16 Example Stack Input Attribute Stack $ a b $ $ $ a b $ $ $ b $ a (()) $ b $ a $ $ ab (( )) $ I $ ab ((I)) $ I $ ab ((I)) $ D $ ab ((D)) Attribute Grammars! BGR, Fall05 3 Marker Nonterminals,(Copies ii) In previous example, copies never need to be performed as ue is at top of attribute stack due to shape of grammar rules Not always this lucky S " a A C i(c) = s(a) [.] S " b A B C i(c) = s(a) [2.] C " c s(c) = g (i(c)) Problem: in., s(a) is in stack(top) when find C but in 2., s(a) is in stack(top-). Must rewrite grammar to try to make attribute ue end up in same place in both rules. Attribute Grammars! BGR, Fall05 32

17 Grammar Transformation S " a A C i(c) = s(a) [.] S " b A B M C i(m) = s(a); i(c) = s(m) [2. ] C " c s(c) = g (i(c)) M " # s(m) = i(m) M saves the ue of s(a) so it goes on the ue stack at the same place in both rules., 2. ; when encounter C, makes i(c) in same stack position. Attribute Grammars! BGR, Fall05 33 Marker Nonterminals,, (Non-copies) Previous transformation works even for non-copy actions: if S " b A C has action i(c) = f(s(a)) then s(a) is on stack, not f(s(a)). Fix: S " a A N C, i(n) = s(a), i(c) = s(n) N " #, s(n) = f(i(n)) Problem: can destroy the R() property of grammar with added markers; () grammars remain okay. Attribute Grammars! BGR, Fall05 34

18 Top Down Translation -attributed grammars work well with TD translation, but when remove left recursion must also transform attributes Involves changing all synthesized attributes to a mixture of inherited and synthesized Attribute Grammars! BGR, Fall05 35 S " E E " E + T E " E - T E " T T " int Example (S) = (E) (E) = (E ) + (T) (E) = (E ) - (T) (E) = (T) (T) = int_ue All synthesized attributes (-attributed). Attribute Grammars! BGR, Fall05 36

19 Removing eft Recursion E " E $ % & " % A; A " $ ' # E E E E $ $ becomes % $ A A % $ A Want to specify attribute transformations as well! # Attribute Grammars! BGR, Fall05 37 Example S " E {(S) = (E)} E " T {i(r) = (T)} R {(E) = s(r)} R " + T {i(r ) = i(r) + (T)} R {s(r) = s(r )} R " - T { i(r ) = i(r) - (T)} R {s(r) = s(r )} R " # {s(r) = i(r)} T " int {(T) = int_const} Attribute Grammars! BGR, Fall05 38

20 Corresponding Parse Trees E S + ( S E E - ( int(4) T R i s va l ( int(3) int(2) - T R i s int (2) int(3) + T R i s int(4) Attribute Grammars! BGR, Fall05 39 # Transformation, ASUp304ff A " A Y {a(a)= g(a(a ), y(y))} A " X {a(a) = f(x(x))} Becomes A " X {i(r) = f(x(x))} R { a(a) = s(r)} R " Y {i(r ) = g(i(r), y(y))} R {s(r) = s(r )} R " # {s(r) = i(r)} Attribute Grammars! BGR, Fall05 40

21 A A f(x(x)) A Y Transformation g{g(f(x(x)),y(y )),y(y 2 )} Y 2 g(f(x(x)),y(y )) X Y A R R g{g(f(x(x)),y(y )),y(y 2 )} f(x(x)) g(f(x(x)),y(y )) X Y 2 R g(g(f(x(x)),y(y )),y(y 2 )) # Attribute Grammars! BGR, Fall05 4

Syntactic Directed Translation

Syntactic Directed Translation Translation Schemes Copyright 2016, Pedro C. Diniz, all rights reserved. Students enrolled in the Compilers class at the University of Southern California have explicit permission