Confluent Orthogonal Drawing for Syntax Diagrams S-expression ( - - PowerPoint PPT Presentation

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Confluent Orthogonal Drawing for Syntax Diagrams S-expression ( - - PowerPoint PPT Presentation

Nov 13, 2023 175 likes •491 views

Confluent Orthogonal Drawing for Syntax Diagrams S-expression ( S-expression S-expression ) . AZ AZ 09 Michael J. Bannister David A. Brown David Eppstein Context-Free Grammars LISP 1.5 S-expression: (

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. S-expression S-expression ( ) S-expression A–Z 0–9 A–Z

Confluent Orthogonal Drawing for Syntax Diagrams

Michael J. Bannister David A. Brown David Eppstein

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Context-Free Grammars

S-expression → atomic symbol | (S-expression.S-expression) | (S-expression list) S-expression list → ǫ | S-expressionS-expression list atomic-symbol → LETTERatom part atom part → ǫ | LETTERatom part | numberatom part LETTER → A | B | C | · · · | Z number → 0 | 1 | 2 | · · · | 9 (defun factorial (x) (if (zerop x) 1 (* x (factorial (- x 1)))))

Grammar for LISP 1.5: LISP 1.5 S-expression:

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Syntax Diagrams

Syntax Diagram from the CANDE Information Manual

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Syntax Diagrams

Syntax Diagram from the Pascal User Manual and Report

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Syntax Diagrams

JSON Data Interchange Standard

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Extended Backus–Naur Form

  • More expressive than BNF
  • Notation for lists:

natural number = digit { digit }

  • Notation for optionals:

integer = [ ”-” ] natural number

  • More expressive than BNF
  • Notation for lists:

natural number = digit { digit }

  • Notation for optionals:

integer = [ ”-” ] natural number

  • Direct translation to syntax diagrams

digit − −

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Extended Backus–Naur Form

  • More expressive than BNF
  • Notation for lists:

natural number = digit { digit }

  • Notation for optionals:

integer = [ ”-” ] natural number

  • More expressive than BNF
  • Notation for lists:

natural number = digit { digit }

  • Notation for optionals:

integer = [ ”-” ] natural number

  • Direct translation to syntax diagrams

digit − −

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Extended Backus–Naur Form

  • More expressive than BNF
  • Notation for lists:

natural number = digit { digit }

  • Notation for optionals:

integer = [ ”-” ] natural number

  • More expressive than BNF
  • Notation for lists:

natural number = digit { digit }

  • Notation for optionals:

integer = [ ”-” ] natural number

  • Direct translation to syntax diagrams

digit − −

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Hand Optimizations

JSON Data Interchange Standard

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Software Pipeline

NFA Conversion Global Optimization Local Optimization Layered Drawing Confluent Conversion Syntax Diagram BNF Grammar

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NFA Representation

S-expression → atomic symbol | (S-expression.S-expression) | (S-expression list) S-expression list → ǫ | S-expressionS-expression list atomic-symbol → LETTERatom part atom part → ǫ | LETTERatom part | numberatom part LETTER → A | B | C | · · · | Z number → 0 | 1 | 2 | · · · | 9

Grammar for LISP 1.5:

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NFA Representation

S-expression → atomic symbol | (S-expression.S-expression) | (S-expression list)

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NFA Representation

S-expression list → ǫ | S-expressionS-expression list

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NFA Representation

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NFA Representation

S-expression → atomic symbol | (S-expression.S-expression) | (S-expression list) S-expression list → ǫ | S-expressionS-expression list atomic-symbol → LETTERatom part atom part → ǫ | LETTERatom part | numberatom part LETTER → A | B | C | · · · | Z number → 0 | 1 | 2 | · · · | 9

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Global Optimization Can modify the entire NFA representation NFA state minimization

  • Combine graphs to reduce states
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Global Optimization Nesting!

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Local Optimizations

  • Hard to approximate
  • Existing heuristic applicable,

but complicated and slow

  • Use fast heuristics, motivated

by hand optimizations NFA state minimization: Crossing minimization:

  • Add states to reduce crossings

Changes one st-digraph at a time

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Local Optimizations Loop back!

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Local Optimizations Parallel state elimination!

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Local Optimizations Confluent pinch!

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Optimization

Global Optimization Local Optimization

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Sugiyama Layering

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Sugiyama Layering

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Sugiyama Layering

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Confluent Conversion

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Experimental Results Subset of JSON grammar

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Experimental Results Pascal Type Declarations

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Conclusion

Software pipeline producing syntax diagrams, uses standard GD techniques for final drawing. which optimizes the input grammar and Further directions:

  • Compare our simple heuristics against

existing NFA min heuristics

  • Reduce bends and crossings in layering
  • Perform user studies
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Conclusion

Software pipeline producing syntax diagrams, uses standard GD techniques for final drawing. which optimizes the input grammar and Further directions:

  • Compare our simple heuristics against

existing NFA min heuristics

  • Reduce bends and crossings in layering
  • Perform user studies

Thank you!