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

Mapping Priorities to Trees in Recursive Descent Parsers - summary and exercise -. Expressions with Two Operators. expr ::= ident | expr - expr | expr ^ expr | ( expr ). where: “-” is left-associative “^” is right-associative “^” has higher priority than “-”

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Mapping Priorities to Trees in Recursive Descent Parsers - summary and 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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