Topic: Syntax Directed Translations UNIT IV

Syntax-Directed Translations Translation of languages guided by CFGs Information associated with programming language constructs Attributes attached to grammar symbols Values of attributes computed by “semantic rules” associated with grammar productions Two notations for associating semantic rules Syntax-directed definitions Translation schemes

Semantic Rules Semantic rules perform various activities: Generation of code Save information in a symbol table Issue error messages Other activities Output of semantic rules is the translation of the token stream

Conceptual View Implementations do not need to follow outline literally Many “special cases” can be implemented in a single pass

SYNTAX DIRECTED DEFINATIONS A syntax directed defination is a generailization of a context free grammar in which each grammer symbol has an associated set of attributes, partitioned into two subsets called Synthesized attributes and inherited attributes.

Attributes Each grammar symbol (node in parse tree) has attributes attached to it ex: astring,a number,a type,a memory location etc. Values of a Synthesized attributes at a node is comuted from the values of attributes at the children of that node in the parse tree. Values of a Inherited attributes at a node is comuted from the values of attributes at the siblings and parent of that node. A dependency graph represents dependencies between attributes A parse tree showing the values of attributes at each node is an annotated parse tree

Semantic Rules Each semantic rule for production A -> α has the form b := f(c1, c2, …, ck) f is a function b may be a synthesized attribute of A or b may be an inherited attribute of one of the grammar symbol on the right side of the production c1, c2, …, ck are attributes belonging to grammar symbols of production An attribute grammar is one in which the functions in semantic rule cannot have side effects NOTE: a semantic rule may have side effects ex: printing a value or updating a global variable.

S-attributed Definitions Synthesized attributes are used extensively in practice S-attributed definition: A syntax-directed definition using only synthesized attributes Parse tree can be annotated by evaluation nodes during a single bottom up pass

S-attributed Definition Example Desk calculator Production Semantic Rules L  E n 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 * F.val T  F T.val := F.val F  (E) F.val := E.val F  digit F.val := digit.lexval

Annotated Parse Tree Example

NOTE In a syntax directed definations,terminals are assumed to have Synthesized attributes only,as the definations does not provide any semantic rules for terminals.values for attributes of terminals are usually supplied by the lexical analyser.Start symbol is assumed not to have any inherited attribute otherwise stated.

Inherited Attributes Inherited Attributes: Value at a node in a parse tree depends on attributes of parent and/or siblings Convenient for expressing dependencies of programming language constructs on context It is always possible to avoid inherited attributes, but they are often convenient

Inherited Attributes Example Production Semantic Rules D  T L L.in := T.type T  int T.type := integer T  real T.type := real L  L1, id L1.in := L.in addtype(id.entry, L.in) L  id

Annotated Inherited Attributes

Dependency Graphs Dependency graph: Numbered with a topological sort Depicts interdependencies among synthesized and inherited attributes Includes dummy nodes for procedure calls Numbered with a topological sort If mi  mj is an edge from mi to mj, then mi appears before mj in the ordering Gives valid order to evaluate semantic rules

Creating a Dependency Graph for each node n in parse tree for each attribute a of grammar symbol at n construct a node in dependency graph for a for each semantic rule b := f(c1, c2, …, ck) associated with production used at n for i := 1 to k construct edge from node for ci to node for b

Example(inherited attribute)

Syntax Trees (Abstract) Syntax Trees Condensed form of parse tree Useful for representing language constructs Operators and keywords appear as internal nodes Syntax-directed translation can be based on syntax trees as well as parse trees

Syntax Tree Examples

Implementing Syntax Trees Each node can be represented by a record with several fields Example: node representing an operator used in an expression: One field indicates the operator and others point to records for nodes representing operands The operator is referred to as the “label” of the node If being used for translation, records can have additional fields for attributes

Syntax Trees for Expressions Functions will create nodes for the syntax tree mknode (op, left, right) – creates an operator node with label op and pointers left and right which point to operand nodes mkleaf(id, entry) – creates an identifier node with label id and a pointer to the appropriate symbol table entry Mkleaf(num, val) – creates a number node with label num and value val Each function returns pointer to created node

Example: a - 4 + c p1 := mkleaf(id, pa); P2 := mkleaf(num, 4); p3 := mknode('-', p1, p2); p4 := mkleaf(id, pc); p5 := mknode('+', p3, p4);

Constructing Trees for Expressions Production Semantic Rules E  E1 + T E.np := mknode('+', E1.np, T.np) E  E1 – T E.np := mknode('-', E1.np, T.np) E  T E.np := T.np T  (E) T.np := E.np T  id T.np := mkleaf(id, id.entry) T  num T.np := mkleaf(num, value)

Directed Acyclic Graphs Called a dag for short Convenient for representing expressions As with syntax trees: Every subexpression will be represented by a node Interior nodes represent operators, children represent operands Unlike syntax trees, nodes may have more than one parent Can be created automatically (discussed in textbook)

Example: a + a * (b – c) + (b – c) * d

S-Attributed Definitions: only Two sub-classes of the syntax-directed definitions: S-Attributed Definitions: only synthesized attributes used in the syntax-directed definitions. L-Attributed Definitions: in addition to synthesized attributes, we may also use inherited attributes in a restricted fashion. To implement S-Attributed Definitions and L-Attributed Definitions we can evaluate semantic rules in a single pass during the parsing. Implementations of S-attributed Definitions are a little bit easier than implementations of L-Attributed Definitions

Bottom-Up Evaluation of S-Attributed Definitions We put the values of the synthesized attributes of the grammar symbols into a parallel stack. When an entry of the parser stack holds a grammar symbol X (terminal or non-terminal), the corresponding entry in the parallel stack will hold the synthesized attribute(s) of the symbol X. We evaluate the values of the attributes during reductions.

Bottom-Up Evaluation Example (1) Production Code Fragment (1) L  E \n Print(val[top]) (2) E  E1 + t val[ntop] := val[top-2] + val[top] (3) E  T (4) T  T1 * F val[ntop] := val[top-2] * val[top] (5) T  F (6) F  (E) val[ntop] := val[top-1] (7) F  digit

Bottom-Up Evaluation Example (2) Input State Val Rule 3*5+4\n --- *5+4\n 3 F (7) T (5) 5+4\n T* 3_ +4\n T*5 3_5 T*F (4) … Input State Val Rule … +4\n E 15 (3) 4\n E+ 15_ \n E+4 15_4 E+F (7) E+T (5) 19 (2) E\n 19_ L (1)

Evaluating Attributes Possible evaluation orders depend on order that nodes are created by parser Depth-first search is very common evaluation order L-attributed definitions use this technique Information appears to flow left-to-right Can handle all synthesized and some inherited attributes

Depth-First Evaluation procedure dfvisit(n: node); begin for each child m of n, from left to right evaluate inherited attributes of m dfvisit(m) end; evaluate synthesized attributes of n end

L-attributed Definitions A syntax-directed definition is L-attributed: If each inherited attribute of Xj, for production A  X1X2…Xn (1 <= j <= n), depends on: X1, X2, …, Xj-1 to the left of XJ in the production The inherited attributes of A Any synthesized attribute is OK All S-attributed definitions are, by this definition, L-attributed

Non-L-Attributed Example Production Semantic Rule 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)

Translation Schemes Semantic actions are inserted within the right side of productions Placement indicates order of evaluation If we are dealing with both inherited and synthesized attributes: Each inherited attribute must be computed by action before symbol appears on right side of production No action may refer to a synthesized attribute of a symbol to the right of the action Any synthesized attribute of nonterminal on left must be computed after computing all referenced attributes

Typesetting Example (1) Production Semantic Rules S  B B.ps := 10 S.ht := B.ht B  B1 B2 B1.ps := B.ps B2.ps := B.ps B.ht := max(B1.ht, B2.ht) B  B1 sub B2 B2.ps := shrink(B.ps) B.ht := disp(B1.ht, B2.ht) B  text B.ht := text.h * B.ps

Typesetting Example (2) S  {B.ps := 10} B {S.ht := B.ht} B  {B1.ps := B.ps} B1 {B2.ps := B.ps} B2 {B.ht := max(B1.ht, B2.ht)} B1 sub {B2.ps := shrink(B.ps)} B2 {B.ht := disp(B1.ht, B2.ht)} B  text {B.ht := text.h * B.ps}

Eliminating Left Recursion Have seen simple and general solution for CFGs Now we must take semantic actions and attributes into account as well First we will examine synthesized attributes A  A1 Y {A.a := g(A1.a, Y.y) A  X {A.a := f(X.x)} A  X {R.i := f(X.x)} R {A.a := R.s} R  Y {R1.i := g(R.i, Y.y)} R1 {R.s := R1.s} | ε {R.s := R.i}

Evaluating Expressions Example E  E1 + T {E.val := E1.val + T.val} E  E1 – T {E.val := E1.val – T.val} E  T {E.val := T.val} T  (E) {T.val := E.val} T  num {T.val := num.val} E  T {R.i := T.val} R {E.val := R.s} R  + T {R1.i := R.i + T.val} R1 {R.s := R1.s} | - T {R1.i := R.i + T.val} R1 {R.s := R1.s} | ε {R.s := R.i} T  (E) {T.val := E.val} T  num {T.val := num.val}

Creating Syntax Tree Example E  E1 + T {E.np := mknode('+', E1.np, T.np)} E  E1 – T {E.np := mknode('-', E1.np, T.np)} E  T {E.np := T.np} T  (E) {T.np := E.np} T  id {T.np := mkleaf(id, id.entry)} T  num {T.np := mkleaf(num, value)} E  T {R.i := T.np} R {E.np R.S} R  + T {R1.i := mknode('+', R.i, T.np)} R1 {R.s := R1.s} R  - T {R1.i := mknode(‘-', R.i, T.np)} R1 {R.s := R1.s} R  ε {R.s := R.i} T  (E) {T.np := E.np} T  id {T.np := mkleaf(id, id.entry)} T  num {T.np := mkleaf(num, value)}

Designing a Predictive Parser LL(1) Grammars can be implemented using relatively simple top-down parsing techniques For each nonterminal A, construct function: Parameter for each inherited attribute Returns synthesized attribute (or attributes) Code decides which production to use based on next input symbol Right side of production considered left to right: For token X with synthesized attribute x, store X.x For nonterminal B, generate c := B(b1,b2,…,bk) with call to function for B Copy other actions into the parser

Syntax Tree Code Example function R(i:↑syntax_tree_node):↑syntax_tree_node; var np, i1, s1, s: ↑syntax_tree_node; begin if lookahead = '+' then begin /* Case for R  + T R */ match('+'); np := T; i1 := mknode('+', i, np); s1 := R(il) s := s1; end else if lookahead = '-' then begin /* Case for R  - T R */ … else s := i; /* Case for R  ε */ return s

Generalized Bottom-Up Evaluation Can handle: All synthesized attributes All L-attributed definitions based on an LL(1) grammar Can handle some L-attributed definitions based on LR(1) grammars Relies on use of copy rules and markers

Copy Rules Consider reduction: A  X Y Suppose X has synthesized attribute X.s X.s will already be on stack before any reductions take place in subtree below Y Therefore, this value can be inherited by Y Define attribute Y.i using a copy rule: Y.i = X.s

Copy Rule Example (1) D  T {L.in := T.type} L T  int {T.type := integer} T  real {T.type := real} L  {L1.in := L.in} L1, id {addtype(id.entry, L.in)} L  id {addtype(id.entry, L.in)}

Copy Rule Example (2) Input State Production Used real p, q, r --- T  real ,q, r T id T L L  id q, r T L , , r T L , id L  L , id r D D  T L

Copy Rule Example (3) Production Code Fragment D  T L ; T  int val[ntop] := integer T  real val[ntop] := real L  L, id addtype(val[top], val[top-3]) L  id addtype(val[top], val[top-1])

Limitation of Copy Rules Production Semantic Rules S  aAC C.i := A.s S  bABC C  c C.s := g(C.i) Reaching into stack for an attribute value only works if the position of the value is predictable Here, C inherits synthesized attribute A.s There may or may not be a B between A and C C.i may be in either val[top-1] or val[top-2]

Markers Marker nonterminals generating ε are inserted into the grammar Each embedded action is replaced by a marker with the action attached Actions in the transformed translation scheme terminate productions Markers can often be used to move all actions to the right side of productions

Markers Example E  T R R  + T {print('+')} R | - T {print('-')} R | ε T  num {print(num.val)} E  T R R  + T M R | - T N R | ε M  ε {print('+')} N  ε {print('+')} T  num {print(num.val)}

Using Markers and Copy Rules Production Semantic Rules S  aAC C.i := A.s S  bABC C  c C.s := g(C.i) Production Semantic Rules S  aAC C.i := A.s S  bABMC M.i := A.s; C.i := M.s M  ε M.s := M.i C  c C.s := g(C.i)

Using Markers for Other Rules Production Semantic Rules S  aAC C.i := f(A.s) Production Semantic Rules S  aANC N.i := A.s; C.i := N.s N  ε N.s := f(N.i)

Avoiding Inherited Attributes It is sometimes possible to avoid inherited attributes by rewriting the underlying grammar The goal is to replace inherited attributes with synthesized attributes D  L : T T  integer | real L  L, id | id D  id L L  , id L | : T T  integer | real