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Typing Rules

• Abstruct syntax does not define well-formed programs only.
  • Phrase "(0=1)+2" allowed.
  • Cannot add boolean to integer.
• Refine abstract syntax definition.
  • Integer and boolean expressions.
  • Define two distinct syntax domains?
  • Better: add typing annotations!
• Attributed syntax trees
  • Type attributes to all phrase forms.
  • Syntax tree is well typed if type attributes can be attached to all of its nonterminals.

Inference rules used for describing type structures.