Compilation of Functional Languages Using Flow Graph Analysis

syntax: G ::= fV 1 ; : : : ; V n g (A graph is a set of vertices) V ::= a ; LAMBDA ; ; ; (d; e) j (a; b) ; BIND ; ; ; d j (a; b) ; SWITCH ; ; ; (d; e) j (a; b; c) ; MERGE ; ; ; d j ; ; SOURCE ; v ; d j a ; SINK ; ; ; ; j ; ; IMPORT ; i ; d j a ; EXPORT ; i ; ; j a ; CALL ; ; ; d j a ; RETURN ; ; ; d j a ; USE ; ; ; d Semantic domains: ffi 1 ; ffi 2 ; : : : 2Dev ¸ = Error + Num + Bool + Func + f? l ; Nilg + [Dev \Theta Dev ] ffl 2Env = Ident ! Dev (Environments) Error =f? e g (? e is a type error) Num =f? n ; 0; : : :g (Domain of numeric values) Bool =f? b ; True; Falseg Func =Dev ! Dev Semantic functions: Fix : Func !Dev if : Bool !Dev !Dev !Dev Def : Graph ! Edge !Env !Dev Exp : Graph !Dev Figure 7: Abstract syntax, and syntactic and semantic domains of a flow graph second argument of the application of Def. The third argument to Def is a local environment, which expresses the meaning of all primitive functions and also contains bindings of all i k to the fixed poi..