example of shift-reduce parsing - computer science

Example ofShift-Reduce Parsing

A SUCCESSFUL PARSE

Grammar:

Stack Input Action

$ x * x $e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Shift

$ t * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

NOTE: Reduction by t → e is also possible here

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Shift

$ t * x $ Shift

$ t * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Shift

$ t * x $ Shift

$ t * x $ Reduce by f → x

$ t * f $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Shift

$ t * x $ Shift

$ t * x $ Reduce by f → x

$ t * f $ Reduce by t → t * f

$ t $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Shift

$ t * x $ Shift

$ t * x $ Reduce by f → x

$ t * f $ Reduce by t → t * f

$ t $ Reduce by t → e

$ e $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Shift

$ t * x $ Shift

$ t * x $ Reduce by f → x

$ t * f $ Reduce by t → t * f

$ t $ Reduce by t → e

$ e $ Accept

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

A UNSUCCESSFUL PARSE

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

NOTE: This time reduce by t → e

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $ Shift

$ e * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $ Shift

$ e * x $ Shift

$ e * x $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $ Shift

$ e * x $ Shift

$ e * x $ Reduce by f → x

$ e * f $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $ Shift

$ e * x $ Shift

$ e * x $ Reduce by f → x

$ e * f $ Reduce by t → f

$ e * t $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $ Shift

$ e * x $ Shift

$ e * x $ Reduce by f → x

$ e * f $ Reduce by t → f

$ e * t $ Reduce by e → t

$ e * e $

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps:

Grammar:

Stack Input Action

$ x * x $ Shift

$ x * x $ Reduce by f → x

$ f * x $ Reduce by t → f

$ t * x $ Reduce by t → e

$ e * x $ Shift

$ e * x $ Shift

$ e * x $ Reduce by f → x

$ e * f $ Reduce by t → f

$ e * t $ Reduce by e → t

$ e * e $ Fail

e → e + t| t

t → t * f| f

f → ( e )| x

Parsing steps: