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ln030 - Defining Language THREE We a d d th e fo l l o w i...

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Defining Language THREE We add the following to Language TWO ML-style function values ML-style function application
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THREE: Syntax A subset of ML expressions This grammar is unambiguous Function application has highest precedence A sample Language Three expression: (fn x => x * x) 3 THREE: < exp >* ::= fn < variable > => < exp > | < addexp > < addexp > ::= < addexp > + < mulexp > | < mulexp > < mulexp > ::= < mulexp > * < funexp > | < funexp > < funexp > ::= < funexp > < rootexp > | < rootexp > < rootexp > ::= let val < variable > = < exp > in < exp > end | ( < exp > ) | < variable > | < constant >
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THREE: Abstract Syntax Two more kinds of AST nodes: apply(Function,Actual) applies the Function to the Actual parameter fn(Formal,Body) for an fn expression with the given Formal parameter and Body So for the Language Three program (fn x => x * x) 3 we have this AST: apply(fn(x,times(var(x,var(x)),const(3))
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Representing Functions A representation for functions: fval(Formal,Body) Formal is the formal parameter variable Body is the unevaluated function body So the AST node fn(Formal,Body) evaluates to fval(Formal,Body) (Why not just use the AST node itself to
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