By Paulson L.C.
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We translate from into combina- pair n(f ( add 1 n)) and obtain (verify this) Y ( B ( S pair )( C B ( add 1))) Figures 3 and 4 give the graph reductions. A cyclic node, labelled , quickly appears. Its rather tortuous transformations generate a recursive occurrence of from deeper in the graph. The series of reductions presumes that the environment is demanding evaluation of the result; in lazy evaluation, nothing happens until it is forced to happen. 1 1 unevaluated until something demands Graph reduction will leave the term its value; the result of from (1) is really (1 (1 + 1 (1 + 1 + 1 : : :))).
If the current Environment is E then this yields the closure Y Y ? Clo(x M f = ? E ) Then the machine modifies the closure, replacing the ? by a pointer looping back to the closure itself: Clo(x M f = E ) When the closure is applied, recursive calls to f in M will re-apply the same closure. The cyclic environment supports recursion efficiently. The technique is called “tying the knot” and works only for function definitions. It does not work for recursive definitions of data structures, such as the infinite list 0 0 0 : : :], defined as ( l: 0 l).
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.