1. CSE 5317/4305 L5: Abstract Syntax1 Abstract Syntax Leonidas Fegaras

2. CSE 5317/4305 L5: Abstract Syntax2 Abstract Syntax Tree (AST)‏ A parser typically generates an Abstract Syntax Tree (AST): A parse tree is not an AST scannerparser get token token source file get next character AST E T E F T E F T F id(x) + id(y) * id(z)‏ + * x y z

3. CSE 5317/4305 L5: Abstract Syntax3 Building Abstract Syntax Trees in Java abstract class Exp { } class IntegerExp extends Exp { public int value; public IntegerExp ( int n ) { value=n; } } class TrueExp extends Exp { public TrueExp () {} } class FalseExp extends Exp { public FalseExp () {} } class VariableExp extends Exp { public String value; public VariableExp ( String n ) { value=n; } }

4. CSE 5317/4305 L5: Abstract Syntax4 Exp (cont.)‏ class BinaryExp extends Exp { public String operator; public Exp left; public Exp right; public BinaryExp ( String o, Exp l, Exp r ) { operator=o; left=l; right=r; } } class UnaryExp extends Exp { public String operator; public Exp operand; public UnaryExp ( String o, Exp e ) { operator=o; operand=e; } }

5. CSE 5317/4305 L5: Abstract Syntax5 Exp (cont.)‏ class CallExp extends Exp { public String name; public List arguments; public CallExp ( String nm, List s ){ name=nm; arguments=s; } class ProjectionExp extends Exp { public Exp value; public String attribute; public ProjectionExp ( Exp v, String a ) { value=v; attribute=a; } }

6. CSE 5317/4305 L5: Abstract Syntax6 Exp (cont.)‏ class RecordElement { public String attribute; public Exp value; public RecordElement ( String a, Exp v ) { attribute=a; value=v; } } class RecordExp extends Exp { public List elements; public RecordExp ( List el ) { elements=el; } } … or better: class RecordExp extends Exp { public Map elements; public RecordExp ( Map el ) { elements=el; } }

7. CSE 5317/4305 L5: Abstract Syntax7 Examples The AST for the input (x-2)+3 new BinaryExp("+", new BinaryExp("-", new VariableExp("x"), new IntegerExp(2)), new IntegerExp(3))‏ The AST for the input f(x.A,true)‏ new CallExp("f", Arrays.asList(new ProjectionExp(new VariableExp("x"), "A"), new TrueExp()))‏

8. CSE 5317/4305 L5: Abstract Syntax8 Building ASTs in Scala Use case classes: sealed abstract class Exp case class TrueExp () extends Exp case class FalseExp () extends Exp case class IntegerExp ( value: Int ) extends Exp case class StringExp ( value: String ) extends Exp case class VariableExp ( name: String ) extends Exp case class BinaryExp ( operator: String, left: Exp, right: Exp ) extends Exp case class UnaryExp ( operator: String, operand: Exp ) extends Exp case class CallExp ( name: String, arguments: List[Exp] ) extends Exp case class ProjectionExp ( record: Exp, attribute: String ) extends Exp case class RecordExp ( arguments: List[(String,Exp)] ) extends Exp For example, the AST for the input (x-2)+3 BinaryExp("+",BinaryExp("-",VariableExp("x"),IntegerExp(2)),IntegerExp(3)) the AST for the input f(x.A,true) CallExp("f",List(ProjectionExp(VariableExp("x"),"A"),TrueExp()))

9. CSE 5317/4305 L5: Abstract Syntax9 Adding Semantic Actions to a Parser Right-associative grammar: E ::= T + E | T - E T ::= num After left factoring: E ::= T E' E' ::= + E | - E T ::= num Recursive descent parser: int E () { int left = T(); if (current_token == '+') { read_next_token(); return left + E(); } else if (current_token == '-') { read_next_token(); return left - E(); } else error(); }; int T () { if (current_token=='num') { int n = num_value; read_next_token(); return n; } else error(); };

10. CSE 5317/4305 L5: Abstract Syntax10 Adding Semantic Actions to a Parser Left-associative grammar: E ::= E + T | E - T T ::= num After left recursion elimination: E ::= T E' E' ::= + T E' | - T E' | T ::= num Recursive descent parser: int E () { return Eprime(T()); }; int Eprime ( int left ) { if (current_token=='+') { read_next_token(); return Eprime(left + T()); } else if (current_token=='-') { read_next_token(); return Eprime(left - T()); } else return left; }; int T () { if (current_token=='num') { int n = num_value; read_next_token(); return n; } else error(); };

11. CSE 5317/4305 L5: Abstract Syntax11 Table-Driven Predictive Parsers Use the parse stack to push/pop both actions and symbols but they use a separate semantic stack to execute the actions push(S); read_next_token(); repeat X = pop(); if (X is a terminal or '$')‏ if (X == current_token)‏ read_next_token(); else error(); else if (X is an action)‏ perform the action; else if (M[X,current_token] == "X ::= Y1 Y2... Yk")‏ { push(Yk);... push(Y1); } else error(); until X == '$';

12. CSE 5317/4305 L5: Abstract Syntax12 Example Need to embed actions { code; } in the grammar rules Suppose that pushV and popV are the functions to manipulate the semantic stack The following is the grammar of an interpreter that uses the semantic stack to perform additions and subtractions: E ::= T E' $ { print(popV()); } E' ::= + T { pushV(popV() + popV()); } E' | - T { pushV(-popV() + popV()); } E' | T ::= num { pushV(num); } For example, for 1+5-2, we have the following sequence of actions: pushV(1); pushV(5); pushV(popV()+popV()); pushV(2); pushV(-popV()+popV()); print(popV());

13. CSE 5317/4305 L5: Abstract Syntax13 Bottom-Up Parsers can only perform an action after a reduction We can only have rules of the form X ::= Y1... Yn { action } where the action is always at the end of the rule; this action is evaluated after the rule X ::= Y1... Yn is reduced How? In addition to state numbers, the parser pushes values into the parse stack If we want to put an action in the middle of the right-hand-side of a rule, we use a dummy non-terminal, called a marker For example, X ::= a { action } b is equivalent to X ::= M b M ::= a { action }

14. CSE 5317/4305 L5: Abstract Syntax14 CUP Both terminals and non-terminals are associated with typed values –these values are instances of the Object class (or of some subclass of the Object class)‏ –the value associated with a terminal is in most cases an Object, except for an identifier which is a String, for an integer which is an Integer, etc –the typical values associated with non-terminals in a compiler are ASTs, lists of ASTs, etc You can retrieve the value of a symbol s at the right-hand-side of a rule by using the notation s:x, where x is a variable name that hasn't appeared elsewhere in this rule The value of the non-terminal defined by a rule is called RESULT and should always be assigned a value in the action –eg if the non-terminal E is associated with an Integer object, then E ::= E:n PLUS E:m {: RESULT = n+m; :}

15. CSE 5317/4305 L5: Abstract Syntax15 Machinery The parse stack elements are of type struct( state: int, value: Object )‏ –int is the state number –Object is the value When a reduction occurs, the RESULT value is calculated from the values in the stack and is pushed along with the GOTO state Example: after the reduction by E ::= E:n PLUS E:m {: RESULT = n+m; :} the RESULT value is stack[top-2].value + stack[top].value which is the new value pushed in the stack along with the GOTO state

16. CSE 5317/4305 L5: Abstract Syntax16 ASTs in CUP (calc.cup) Need to associate each non-terminal symbol with an AST type Using Scala case classes in Java (!) non terminal Expr exp; non terminal List expl; exp ::= exp:e1 PLUS exp:e2{: RESULT = new BinOpExp(“+”,e1,e2); :} | exp:e1 MINUS exp:e2{: RESULT = new BinOpExp(“-”,e1,e2); :} | id:nm LP expl:el RP{: RESULT = new CallExp(nm,el); :} | INT:n{: RESULT = new IntConst(n); :} ; expl ::= expl:el COMMA exp:e{: RESULT = append(e,el); :} | exp:e{: RESULT = cons(e,nil); :} ;