1. 1 Compiler Construction 강의 8

2. 2 Context-Free Languages The inclusion hierarchy for context-free languages Context-free languages Deterministic languages (LR(k)) LL(k) languages Simple precedence languages LL(1) languages Operator precedence languages LR(k) ≡ LR(1)

3. 3 Context-Free Grammars Operator precedence includes some ambiguous grammars LL(1) is a subset of SLR(1) The inclusion hierarchy for context-free grammars Context-free grammars Floyd-Evans Parsable Unambiguous CFGs Operator Precedence LR(k) LR(1) LALR(1) SLR(1) LR(0) LL(1) LL(k)

4. 4 Beyond Syntax There is a level of correctness that is deeper than grammar fie(a,b,c,d) int a, b, c, d; { … } fee() { int f[3],g[0], h, i, j, k; char *p; fie(h,i,“ab”,j, k); k = f * i + j; h = g[17]; printf(“.\n”, p,q); p = 10; } What is wrong with this program? (let me count the ways …)

5. 5 Semantics There is a level of correctness that is deeper than grammar fie(a,b,c,d) int a, b, c, d; { … } fee() { int f[3],g[0], h, i, j, k; char *p; fie(h,i,“ab”,j, k); k = f * i + j; h = g[17]; printf(“.\n”, p,q); p = 10; } What is wrong with this program? (let me count the ways …) declared g[0], used g[17] wrong number of args to fie() “ab” is not an int wrong dimension on use of f undeclared variable q 10 is not a character string All of these are “deeper than syntax”

6. 6 Syntax-directed translation In syntax-directed translation, we attach ATTRIBUTES to grammar symbols. The values of the attributes are computed by SEMANTIC RULES associated with grammar productions. Conceptually, we have the following flow: In practice, however, we do everything in a single pass.

7. 7 Syntax-directed translation There are two ways to represent the semantic rules we associate with grammar symbols. − −SYNTAX-DIRECTED DEFINITIONS (SDDs) do not specify the order in which semantic actions should be executed − −TRANSLATION SCHEMES explicitly specify the ordering of the semantic actions. SDDs are higher level; translation schemes are closer to an implementation

8. 8 Syntax-Directed Definitions

9. 9 Syntax-directed definitions The SYNTAX-DIRECTED DEFINITION (SDD) is a generalization of the context-free grammar. Each grammar symbol in the CFG is given a set of ATTRIBUTES. Attributes can be any type (string, number, memory loc, etc) SYNTHESIZED attributes are computed from the values of the CHILDREN of a node in the parse tree. INHERITED attributes are computed from the attributes of the parents and/or siblings of a node in the parse tree.

10. 10 Attribute dependencies Given a SDD, we can describe the dependencies between the attributes with a DEPENDENCY GRAPH. A parse tree annotated with attributes is called an ANNOTATED parse tree. Computing the attributes of the nodes in a parse tree is called ANNOTATING or DECORATING the tree.

11. 11 Form of a syntax-directed definition In a SDD, each grammar production A -> α has associated with it semantic rules b := f( c 1, c 2, …, c k ) where f() is a function, and either 1. 1.b is a synthesized attribute of A, and c 1, c 2, …, are attributes of the grammar symbols of α, or 2. 2.b is an inherited attribute of one of the symbols on the RHS, and c 1, c 2, … are attributes of the grammar symbols of α in either case, we say b DEPENDS on c 1, c 2, …, c k.

12. 12 Semantic rules Usually we actually write the semantic rules with expressions instead of functions. If the rule has a SIDE EFFECT, e.g. updating the symbol table, we write the rule as a procedure call. When a SDD has no side effects, we call it an ATTRIBUTE GRAMMAR (Programming Languages course 에서 설명 ).

13. 13 Synthesized attributes Synthesized attributes depend only on the attributes of children. They are the most common attribute type. If a SDD has synthesized attributes ONLY, it is called a S- ATTRIBUTED DEFINITION. S-attributed definitions are convenient since the attributes can be calculated in a bottom-up traversal of the parse tree.

14. 14 Example SDD: desk calculator Production Semantic Rule L -> E newline print( E.val ) E -> E1 + T E.val := E1.val + T.val E -> T E.val := T.val T -> T1 * F T.val := T1.val x F.val T -> F T.val := F.val F -> ( E ) F.val := E.val F -> number F.val := number.lexval Notice the similarity to the yacc spec from last lecture.

15. 15 Calculating synthesized attributes Input string: 3*5+4 newline Annotated tree:

16. 16 Inherited attributes An inherited attribute is defined in terms of the attributes of the node’s parents and/or siblings. Inherited attributes are often used in compilers for passing contextual information forward, for example, the type keyword in a variable declaration statement.

17. 17 Example SDD with an inherited attribute Suppose we want to describe decls like “real x, y, z” Production Semantic Rules D -> T L L.in := T.type T -> int T.type := integer T -> real T.type := real L -> L 1, id L 1.in := L.in addtype( id.entry, L.in ) L -> id addtype( id.entry, L.in ) L.in is inherited since it depends on a sibling or parent. addtype() is just a procedure that sets the type field in the symbol table.

18. 18 Annotated parse tree for real id1, id2, id3 What are the dependencies?

19. 19 Dependency Graphs

20. 20 Dependency graphs If an attribute b depends on attribute c, then attribute b has to be evaluated AFTER c. DEPENDENCY GRAPHS visualize these requirements. − −Each attribute is a node − −We add edges from the node for attribute c to the node for attribute b, if b depends on c. − −For procedure calls, we introduce a dummy synthesized attribute that depends on the parameters of the procedure calls.

21. 21 Dependency graph example Production Semantic Rule E -> E1 + E2 E.val := E1.val + E2.val Wherever this rule appears in the parse, tree we draw:

22. 22 Example dependency graph

23. 23 Example dependency graph

24. 24 Finding a valid evaluation order A TOPOLOGICAL SORT of a directed acyclic graph orders the nodes so that for any nodes a and b such that a -> b, a appears BEFORE b in the ordering. There are many possible topological orderings for a DAG. Each of the possible orderings gives a valid order for evaluation of the semantic rules.

25. 25 Example dependency graph

26. 26 Syntax Trees

27. 27 Application: syntax tree construction One thing SDDs are useful for is construction of SYNTAX TREES. Recall from Lecture 1 that a syntax tree is a condensed form of parse tree. Syntax trees are useful for representing programming language constructs like expressions and statements. They help compiler design by decoupling parsing from translation.

28. 28 Syntax trees Leaf nodes for operators and keywords are removed. Internal nodes corresponding to uninformative non-terminals are replaced by the more meaningful operators.

29. 29 SDD for syntax tree construction We need some functions to help us build the syntax tree: − −mknode(op,left,right) constructs an operator node with label op, and two children, left and right − −mkleaf(id,entry) constructs a leaf node with label id and a pointer to a symbol table entry − −mkleaf(num,val) constructs a leaf node with label num and the token’s numeric value val Use these functions to build a syntax tree for a-4+c: − −P1 := mkleaf( id, st_entry_for_a ) − −P2 := …

30. 30 SDD for syntax tree construction Production Semantic Rules E -> E 1 + T E.nptr := mknode( ‘+’, E 1.nptr,T.nptr) E -> E 1 - T E.nptr := mknode( ‘-’, E 1.nptr,T.nptr) E -> T E.nptr := T.nptr T -> ( E ) T.nptr := E.nptr T -> id T.nptr := mkleaf( id, id.entry ) T -> num T.nptr := mkleaf( num, num.val ) Note that this is a S-attributed definition. Try to derive the annotated parse tree for a-4+c.

31. 31 Evaluating SDDs Bottom-up

32. 32 Bottom-up evaluation of S-attributed defn How can we build a translator for a given SDD? For S-attributed definitions, it’s pretty easy! A bottom-up shift-reduce parser can evaluate the (synthesized) attributes as the input is parsed. We store the computed attributes with the grammar symbols and states on the stack. When a reduction is made, we calculate the values of any synthesized attributes using the already-computed attributes from the stack.

33. 33 Bottom-up evaluation of S-attributed defns In the scheme, our parser’s stack now stores grammar symbols AND attribute values. For every production A -> XYZ with semantic rule A.a := f( X.x, Y.y, Z.z ), before XYZ is reduced to A, we should already have X.x Y.y and Z.z on the stack.

34. 34 Desk calculator example If attribute values are placed on the stack as described, it is now easy to implement the semantic rules for the desk calculator. Production Semantic Rule Code L -> E newline print( E.val ) print val[top-1] E -> E1 + T E.val := E1.val + T.val val[newtop] = val[top-2]+val[top] E -> T E.val := T.val /*newtop==top, so nothing to do*/ T -> T1 * F T.val := T1.val x F.val val[newtop] = val[top-2]+val[top] T -> F T.val := F.val /*newtop==top, so nothing to do*/ F -> ( E ) F.val := E.val val[newtop] = val[top-1] F -> number F.val := number.lexval /*newtop==top, so nothing to do*/

35. 35 Desk calculator example For input 3 * 5 + 4 newline, what happens? Assume when a terminal’s attribute is shifted when it is. Input States Values Action 3*5+4n shift *5+4n number 3 reduce F->number reduce T->F shift reduce F->number reduce T->T*F reduce E->T shift reduce F->number reduce T->F reduce E->E+T shift reduce E->En

36. 36 L-attributed definitions S-attributed definitions only allow synthesized attributes. We saw earlier that inherited attributes are useful. But we prefer definitions that can be evaluated in one pass. L-ATTRIBUTED definitions are the set of SDDs whose attributes can be evaluated in a DEPTH-FIRST traversal of the parse tree.

37. 37 Depth-first traversal algorithm dfvisit( node n ) { for each child m of n, in left-to-right order, do { evaluate the inherited attributes of m dfvisit( m ) } evaluate the synthesized attributes of n }

38. 38 L-attributed definitions If a definition can be evaluated by dfvisit() we say it is L- attributed. Another way of putting it: a SDD is L-attributed if each INHERITED attribute of Xi on the RHS of a production A -> X 1 X 2 … X n depends ONLY on: − −The attributes of X 1, …, X i-1 (to the LEFT of Xi in the production) − −The INHERITED attributes of A. Since S-attributed definitions have no inherited attributes, they are necessarily L-attributed.

39. 39 L-attributed definitions Is the following SDD L-attributed? Production Semantic Rules A -> L M L.i := l(A.i) M.i := m(L.s) A.s := f(M.s) A -> Q R R.i := r(A.i) Q.i := q(R.s) A.s := f(Q.s)

40. 40 Translation Schemes

41. 41 Translation schemes Translation schemes are another way to describe syntax- directed translation. Translation schemes are closer to a real implementation because the specify when, during the parse, attributes should be computed. Example, for conversion of INFIX expressions to POSTFIX: E -> T R R -> addop T { print ( addop.lexeme ) } | ε T -> num { print( num.val ) } This translation scheme will turn 9-5+2 into 95-2+

42. 42 Turning a SDD into a translation scheme For a translation scheme to work, it must be the case that an attribute is computed BEFORE it is used. If the SDD is S-attributed, it is easy to create the translation scheme implementing it: Production Semantic Rule T -> T1 * FT.val := T1.val x F.val Translation scheme: T -> T1 * F { T.val = T1.val * F.val } That is, we just turn the semantic rule into an action and add at the far right hand side. This DOES NOT WORK for inherited attribs!

43. 43 Turning a SDD into a translation scheme With inherited attributes, the translation scheme designer needs to follow three rules:   An inherited attribute for a symbol on the RHS MUST be computed in an action BEFORE the occurrence of the symbol.   An action MUST NOT refer to the synthesized attribute of a symbol to the right of the action.   A synthesized attribute for the LHS nonterminal can ONLY be computed in an action FOLLOWING the symbols for all the attributes it references.

44. 44 Example This translation scheme does NOT follow the rules: S -> A 1 A 2 { A 1.in = 1; A 2.in = 2 } A -> a { print( A.in ) } If we traverse the parse tree depth first, A1.in has not been set when referred to in the action print( A.in ) S -> { A 1.in = 1 } A1 { A 2.in = 2 } A 2 A -> a { print( A.in ) }

45. 45 Bottom-up evaluation of inherited attributes The first step is to convert the SDD to a valid translation scheme. Then a few “tricks” have to be applied to the translation scheme. It is possible, with the right tricks, to do one-pass bottom-up attribute evaluation for ALL LL(1) grammars and MOST LR(1) grammars, if the SDD is L-attributed. This means when adding semantic actions to your yacc specifications, you might run into trouble. See section 5.6 of the text!

46. 46 Beyond Syntax These questions are part of context-sensitive analysis Answers depend on values, not parts of speech Questions & answers involve non-local information Answers may involve computation How can we answer these questions? Use formal methods − −Context-sensitive grammars? − −Attribute grammars? (attributed grammars?) Use ad-hoc techniques − −Symbol tables − −Ad-hoc code (action routines) In scanning & parsing, formalism won; different story here.

47. 47 Beyond Syntax Telling the story The attribute grammar formalism is important − −Succinctly makes many points clear − −Sets the stage for actual, ad-hoc practice The problems with attribute grammars motivate practice − −Non-local computation − −Need for centralized information Some folks in the community still argue for attribute grammars We will cover attribute grammars, then move on to ad-hoc ideas

48. 48 Attribute Grammars What is an attribute grammar? A context-free grammar augmented with a set of rules Each symbol in the derivation has a set of values, or attributes The rules specify how to compute a value for each attribute Example grammar Number → Sign List Sign → + | – List → List Bit | Bit Bit → 0 | 1 This grammar describes signed binary numbers We would like to augment it with rules that compute the decimal value of each valid input string

49. 49 Examples For “-1” Number→ Sign List → – List → – Bit → – 1 Number SignList Bit – 1 For “-101” Number → Sign List → Sign List Bit → Sign List 1 → Sign List Bit 1 → Sign List 1 1 → Sign Bit 0 1 → Sign 1 0 1 → – 101 Number SignList Bit – 1 List BitList Bit 0 1

50. 50 Attribute Grammars Add rules to compute the decimal value of a signed binary number ProductionsAttribution Rules Number → Sign ListList.pos ← 0 If Sign.neg then Number.val ← – List.val else Number.val ← List.val Sign → +Sign.neg ← false | –Sign.neg ← true List 0 → List 1 BitList 1.pos ← List 0.pos + 1 Bit.pos ← List 0.pos List 0.val ← List 1.val + Bit.val | BitBit.pos ← List.pos List.val ← Bit.val Bit → 0Bit.val ← 0 | 1Bit.val ← 2 Bit.pos SymbolAttributesNumberval Signneg Listpos, val Bitpos, val

51. 51 Back to The Examples Knuth suggested a data-flow model for evaluation Independent attributes first Others in order as input values become available One possible evaluation order: 1.List.pos 2.Sign.neg 3.Bit.pos 4.Bit.val 5.List.val 6.Number.val Other orders are possible For “-1” neg ← true Number.val ← –List.val≡ –1 List.pos ← 0 List.val ← Bit.val≡ 1 Bit.pos ← 0 Bit.val ← 2 Bit.pos ≡ 1 Number Sign List Bit – 1 Rules + parse tree imply an attribute dependence graph Evaluation order must be consistent with the attribute dependence graph

52. 52 Back to the Examples This is the complete attribute dependence graph for “–101”. It shows the flow of all attribute values in the example. Some flow downward → inherited attributes Some flow upward → synthesized attributes A rule may use attributes in the parent, children, or siblings of a node

53. 53 The Rules of The Game Attributes associated with nodes in parse tree Rules are value assignments associated with productions Attribute is defined once, using local information Label identical terms in production for uniqueness Rules & parse tree define an attribute dependence graph − −Graph must be non-circular This produces a high-level, functional specification Synthesized attribute − −Depends on values from children Inherited attribute − −Depends on values from siblings & parent

54. 54 Using Attribute Grammars Attribute grammars can specify context-sensitive actions Take values from syntax Perform computations with values Insert tests, logic, … Synthesized Attributes Use values from children & from constants S-attributed grammars Evaluate in a single bottom-up pass Good match to LR parsing Inherited Attributes Use values from parent, constants, & siblings directly express context can rewrite to avoid them Thought to be more natural Not easily done at parse time We want to use both kinds of attribute

55. 55 Evaluation Methods Dynamic, dependence-based methods Build the parse tree Build the dependence graph Topological sort the dependence graph Define attributes in topological order Rule-based methods (treewalk) Analyze rules at compiler-generation time Determine a fixed (static) ordering Evaluate nodes in that order Oblivious methods (passes, dataflow) Ignore rules & parse tree Pick a convenient order (at design time) & use it

56. 56 Back to the Example Number SignList Bit – 1 List Bit 0 1 For “-101”

57. 57 Back to the Example Number SignList Bit – 1 List Bit 0 1 val: neg: pos:0 val: pos: val: pos: val: pos: val: pos: val: pos: val: For “-101”

58. 58 Back to the Example Number SignList Bit – 1 List Bit 0 1 For “-101” val:-5 neg:true pos:0 val:5 pos:1 val:4 pos:2 val:4 pos:2 val:4 pos:1 val:0 pos:0 val:1 Inherited Attributes

59. 59 Back to the Example Number SignList Bit – 1 List Bit 0 1 For “-101” val:-5 neg:true pos:0 val:5 pos:1 val:4 pos:2 val:4 pos:2 val:4 pos:1 val:0 pos:0 val:1 Synthesized Attributes

60. 60 Back to the Example Number SignList Bit – 1 List Bit 0 1 For “-101” val:-5 neg:true pos:0 val:5 pos:1 val:4 pos:2 val:4 pos:2 val:4 pos:1 val:0 pos:0 val:1 Synthesized Attributes

61. 61 Back to the Example Number SignList Bit – 1 List Bit 0 1 For “-101” val:-5 neg:true pos:0 val:5 pos:1 val:4 pos:2 val:4 pos:2 val:4 pos:1 val:0 pos:0 val:1 If we show the computation … & then peel away the parse tree …

62. 62 Back to the Example – 1 0 1 For “-101” val:-5 neg:true pos:0 val:5 pos:1 val:4 pos:2 val:4 pos:2 val:4 pos:1 val:0 pos:0 val:1 All that is left is the attribute dependence graph. This succinctly represents the flow of values in the problem instance. The dynamic methods sort this graph to find independent values, then work along graph edges. The rule-based methods try to discover “good” orders by analyzing the rules. The oblivious methods ignore the structure of this graph. The dependence graph must be acyclic

63. 63 Circularity We can only evaluate acyclic instances We can prove that some grammars can only generate instances with acyclic dependence graphs Largest such class is “strongly non-circular” grammars (SNC ) SNC grammars can be tested in polynomial time Failing the SNC test is not conclusive Many evaluation methods discover circularity dynamically ⇒ Bad property for a compiler to have SNC grammars were first defined by Kennedy & Warren

64. 64 A Circular Attribute Grammar ProductionsAttribution Rules Number → ListList.a ← 0 List 0 → List 1 BitList 1.a ← List 0.a + 1 List 0.b ← List 1.b List 1.c ← List 1.b + Bit.val | Bit List 0.b ← List 0.a + List 0.c + Bit.val Bit → 0Bit.val ← 0 | 1Bit.val ← 2 Bit.pos

65. 65 An Extended Example Block 0 → Block 1 Assign | Assign Assign → Ident = Expr ; Expr 0 → Expr 1 + Term | Expr 1 – Term | Term Term0 → Term 1 * Factor | Term 1 / Factor | Factor Factor → ( Expr ) | Number | Identifier Let’s estimate cycle counts Each operation has a COST Add them, bottom up Assume a load per value Assume no reuse Simple problem for an AG Hey, this looks useful ! Grammar for a basic block (§ 4.3.3)

66. 66 An Extended Example Adding attribution rules Block 0 → Block 1 Assign | Assign Assign → Ident = Expr ; Expr 0 → Expr 1 + Term | Expr 1 – Term | Term Term 0 → Term 1 * Factor | Term 1 / Factor | Factor Factor → ( Expr ) | Number | Identifier Block 0.cost ← Block 1.cost + Assign.cost Block 0.cost ← Assign.cost Assign.cost ← COST(st ore) + Expr.cost Expr 0.cost ← Expr 1.cost + COST(add) + Term.cost Expr 0.cost ← Expr 1.cost + COST(add) + Term.cost Expr 0.cost ← Term.cost Term 0.cost ← Term 1.cost + COST(mult ) + Factor.cost Term 0.cost ← Term 1.cost + COST(div) + Factor.cost Term 0.cost ← Factor.cost Factor.cost ← Expr.cost Factor.cost ← COST(loadI) Factor.cost ← COST(load) All these attributes are synthesized!

67. 67 An Extended Example Properties of the example grammar All attributes are synthesized ⇒ S-attributed grammar Rules can be evaluated bottom-up in a single pass − −Good fit to bottom-up, shift/reduce parser Easily understood solution Seems to fit the problem well What about an improvement? Values are loaded only once per block (not at each use) Need to track which values have been already loaded

68. 68 A Better Execution Model Adding load tracking Need sets Before and After for each production Must be initialized, updated, and passed around the tree Factor → ( Expr ) | Number | Identifier Factor.cost ← Expr.cost ; Expr.Before ← Factor.Before ; Factor.After ← Expr.After Factor.cost ← COST(loadi) ; Factor.After ← Factor.Before if(Identifier.name ∉ Factor.Before) then Factor.cost ← COST(load); Factor.After ← Factor.Before ∪ Identifier.name else Factor.cost ← 0 Factor.After ← Factor.Before This looks more complex!

69. 69 A Better Execution Model Load tracking adds complexity But, most of it is in the “copy rules” Every production needs rules to copy Before & After A Sample Production Expr 0 → Expr 1 + TermExpr 0.cost ← Expr 1.cost + COST(add) + Term.cost ; Expr 1.Before ← Expr 0.Before ; Term.Before ← Expr 1.After; Expr 0.After ← Term.After These copy rules multiply rapidly Each creates an instance of the set Lots of work, lots of space, lots of rules to write

70. 70 An Even Better Model What about accounting for finite register sets? Before & After must be of limited size Adds complexity to Factor→Identifier Requires more complex initialization Jump from tracking loads to tracking registers is small Copy rules are already in place Some local code to perform the allocation

71. 71 The Extended Example Tracking loads Introduced Before and After sets to record loads Added ≥ 2 copy rules per production − −Serialized evaluation into execution order Made the whole attribute grammar large & cumbersome Finite register set Complicated one production (Factor → Identifier) Needed a little fancier initialization Changes were quite limited Why is one change hard and the other easy?

72. 72 The Moral of the Story Non-local computation needed lots of supporting rules Complex local computation was relatively easy The Problems Copy rules increase cognitive overhead Copy rules increase space requirements − −Need copies of attributes − −Can use pointers, for even more cognitive overhead Result is an attributed tree − −Must build the parse tree − −Either search tree for answers or copy them to the root

73. 73 Addressing the Problem Ad-hoc techniques Introduce a central repository for facts Table of names − −Field in table for loaded/not loaded state Avoids all the copy rules, allocation & storage headaches All inter-assignment attribute flow is through table − −Clean, efficient implementation − −Good techniques for implementing the table (hashing, § B.4) − −When its done, information is in the table ! − −Cures most of the problems Unfortunately, this design violates the functional paradigm Do we care?

74. 74 The Realist’s Alternative Ad-hoc syntax-directed translation Associate a snippet of code with each production At each reduction, the corresponding snippet runs Allowing arbitrary code provides complete flexibility − −Includes ability to do tasteless & bad things To make this work Need names for attributes of each symbol on lhs & rhs − −Typically, one attribute passed through parser + arbitrary code (structures, globals, statics, …) − −Yacc introduced $$, $1, $2, … $n, left to right ANTLR allows defining variables Need an evaluation scheme − −Should fit into the parsing algorithm

75. 75 Reworking the Example Block 0 → Block 1 Assign | Assign Assign → Ident = Expr ; Expr 0 → Expr 1 + Term | Expr 1 – Term | Term Term 0 → Term 1 * Factor | Term 1 / Factor | Factor Factor → ( Expr ) | Number | Identifier cost← cost + COST(store); cost← cost + COST(add); cost← cost + COST(sub); cost← cost + COST(mult); cost← cost + COST(div); cost← cost + COST(loadi); { i← hash(Identifier); if(Table[i].loaded = false) then { cost ← cost + COST(load); Table[i].loaded ← true; } This looks cleaner & simpler than the AG sol’n ! One missing detail: initializing cost

76. 76 Reworking the Example Before parser can reach Block, it must reduce Init Reduction by Init sets cost to zero This is an example of splitting a production to create a reduction in the middle — for the sole purpose of hanging an action routine there! Start → Init Block Init → ε Block 0 → Block1 Assign | Assign Assign → Ident = Expr ; cost ← 0; cost← cost + COST(store); … and so on as in the previous version of the example …

77. 77 Reworking the Example Block 0 → Block 1 Assign | Assign Assign → Ident = Expr ; Expr 0 → Expr 1 + Term | Expr 1 – Term | Term Term 0 → Term 1 * Factor | Term 1 / Factor | Factor Factor → ( Expr ) | Number | Identifier $$ ← $1 + $2 ; $$ ← $1 ; $$ ← COST(store) + $3; $$ ← $1 + COST(add) + $3; $$ ← $1 + COST(sub) + $3; $$ ← $1; $$ ← $1 + COST(mult) + $3; $$ ← $1 + COST(div) + $3; $$ ← $1; $$ ← $2; $$ ← COST(loadi); { i← hash(Identifier); if (Table[i].loaded = false) then { $$ ← COST(load); Table[i].loaded ← true; } else $$ ← 0 } This version passes the values through attributes. It avoids the need for initializing “cost”

78. 78 Reworking the Example Assume constructors for each node Assume stack holds pointers to nodes Assume yacc syntax Goal → Expr Expr → Expr + Term | Expr – Term | Term Term → Term * Factor | Term / Factor | Factor Factor → ( Expr ) | number | id $$ = $1; $$ = MakeAddNode($1,$3); $$ = MakeSubNode($1,$3); $$ = $1; $$ = MakeMulNode($1,$3); $$ = MakeDivNode($1,$3); $$ = $1; $$ = $2; $$ = MakeNumNode(token); $$ = MakeIdNode(token);

79. 79 Reality Most parsers are based on this ad-hoc style of context-sensitive analysis Advantages Addresses the shortcomings of the AG paradigm Efficient, flexible Disadvantages Must write the code with little assistance Programmer deals directly with the details Annotate action code with grammar rules

80. 80 Typical Uses Building a symbol table − −Enter declaration information as processed − −At end of declaration syntax, do some post processing − −Use table to check errors as parsing progresses Simple error checking/type checking − −Define before use → lookup on reference − −Dimension, type,... → check as encountered − −Type conformability of expression → bottom-up walk − −Procedure interfaces are harder Build a representation for parameter list & types Create list of sites to check Check offline, or handle the cases for arbitrary orderings

81. 81 Is This Really “Ad-hoc” ? Relationship between practice and attribute grammars Similarities Both rules & actions associated with productions Application order determined by tools, not author (Somewhat) abstract names for symbols Differences Actions applied as a unit; not true for AG rules Anything goes in ad-hoc actions; AG rules are functional AG rules are higher level than ad-hoc actions

82. 82 Making Ad-hoc SDT Work What about a rule that must work in mid-production? Can transform the grammar − −Split it into two parts at the point where rule must go − −Apply the rule on reduction to the appropriate part Can also handle reductions on shift actions − −Add a production to create a reduction Was: fee → fum Make it: fee → fie → fum and tie action to this reduction ANTLR supports the above automatically Together, these let us apply rule at any point in the parse

83. 83 Limitations of Ad-hoc SDT Forced to evaluate in a given order: postorder − −Left to right only − −Bottom up only Implications − −Declarations before uses − −Context information cannot be passed down How do you know what rule you are called from within? Example: cannot pass bit position from right down − −Could you use globals? Requires initialization & some re-thinking of the solution − −Can we rewrite it in a form that is better for the ad-hoc sol’n

84. 84 Alternative Strategy Build an abstract syntax tree Use tree walk routines Use “visitor” design pattern to add functionality TreeNodeVisitor VisitAssignment(AssignmentNode) VisitVariableRef(VariableRefNode) TypeCheckVisitor VisitAssignment(AssignmentNode) VisitVariableRef(VariableRefNode) AnalysisVisitor VisitAssignment(AssignmentNode) VisitVariableRef(VariableRefNode)

85. 85 Visitor Treewalk Parallel structure of tree: Separates treewalk code from node handling code Facilitates change in processing without change to tree structure TreeNode Accept(NodeVisitor) AssignmentNode Accept(NodeVisitor v) v.VisitAssignment(this) VariableRefNode Accept(NodeVisitor v) v.VisitVariableRef(this)

86. 86 Summary Wrap-up of parsing − −More example to build LR(1) table Attribute Grammars − −Pros: Formal, powerful, can deal with propagation strategies − −Cons: Too many copy rules, no global tables, works on parse tree Ad-hoc SDT − −Annotate production with ad-hoc action code − −Postorder Code Execution Pros: Simple and functional, can be specified in grammar, does not require parse tree Cons: Rigid evaluation order, no context inheritance − −Generalized Tree Walk Pros: Full power and generality, operates on abstract syntax tree (using Visitor pattern) Cons: Requires specific code for each tree node type, more complicated Powerful tools like ANTLR can help with this