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Mapping Priorities to Trees: A Recursive Descent Parser Exercise

Learn how to prioritize expressions in recursive descent parsers using left and right associative operators with distinct priorities. Follow the provided exercise to build expressions using abstract classes and layers in the grammar.

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Mapping Priorities to Trees: A Recursive Descent Parser Exercise

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  1. Mapping Priorities to Trees in Recursive Descent Parsers- summary and exercise -

  2. Expressions with Two Operators expr ::= ident | expr - expr| expr^ expr | (expr) where: • “-” is left-associative • “^” is right-associative • “^” has higher priority than “-” Draw parentheses and a tree for token sequence: a – b – c ^ d ^ e – f ((a – b) – (c ^ (d ^ e)) ) – f

  3. Goal: Build Expressions • abstract class Expr • case class Variable(id : Identifier) extends Expr • case class Minus(e1 : Expr, e2 : Expr) extendsExpr • case class Exp(e1 : Expr, e2 : Expr) extends Expr

  4. 1) Layer the grammar by priorities expr ::= ident | expr - expr| expr^ expr | (expr) expr ::= term (- term)* term ::= factor (^ factor)* factor ::= id | (expr) lower priority binds weaker, so it goes outside

  5. 2) Build trees in the right way LEFT-associative operator x – y – z  (x – y) – z Minus(Minus(Var(“x”),Var(“y”)), Var(“z”)) defexpr : Expr = { var e = while (lexer.token == MinusToken) { lexer.next } e } term e = Minus(e, term)

  6. 2) Build trees in the right way RIGHT-associative operator – using a loop x ^ y ^ z  x ^ (y ^ z) Exp(Var(“x”), Exp(Var(“y”), Var(“z”)) ) defexpr : Expr = { val e = factor if (lexer.token == ExpToken) { lexer.next Exp(e, expr) } else e }

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