By Paulson L.C.

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**Extra info for Foundations of functional programming**

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The closure will include the current Environment and will hold M as a list of commands, from compilation: x:M ]] = closure(x M ]]) app Applications are compiled to the command at compile time. Under the interpreted SECD machine, this work occurred at run time: MN ]] = N ]] M ]] app test We could add further instructions, say for conditionals. Let (C1 C2) be replaced by C1 or C2 , depending upon whether the value on top of the Stack is or : E then M else N ]] = E ]] ( M ]] N ]]) false if true test To allow built-in 2-place functions such as + and could be done in several ways.

Because is a strict function, the graph for P Q can only be reduced after P and Q have been reduced to numeric constants m and n. Then m n is replaced by the constant whose value is m n. Graph reduction proceeds by walking down the graph’s leftmost branch, seeking something to reduce. If the leftmost symbol is a , , , or , with the requisite number of operands, then it combinator like , applies the corresponding transformation. If the leftmost symbol is a strict combinator like , then it recursively traverses the operands, attempting to reduce them to numbers.

X = 3 f;= sqr return ;7 ! ;; f app ; ; ; ;) ( ; ; ; ;) ( ( The machine terminates in a final state, giving a value of 81. 10 The Compiled SECD Machine It takes 17 steps to evaluate (( x y:x+y ) 3) 5! Much faster execution is obtained by first compiling the -term. Write M ]] for the list of commands produced by compiling M ; there are cases for each of the four kinds of -term. command, which will (during later execution Constants are compiled to the of the code) push a constant onto the Stack: const k]] = const(k) var Variables are compiled to the command, which will push the variable’s value, from the Environment, onto the Stack: x]] = var(x) closure Abstractions are compiled to the command, which will push a closure onto the Stack.