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GG ar91] D. GG artner. {Red + : ein interaktives codeausf uhrendes Reduktionssystem zur vollstt andigen Realisierung eines angewandten {Kalk uls. PhD thesis, Institut f ur In-14 Top{level abstractions returned after a pass through the processing phase are merely special cases of partial applications: they are not applied to any arguments at all. {extension applies them to the complete set of abstracted variables and sets up the full binding structure in front of this application. Thus reducing them to normal forms can accomplished in the same way. In case of structured objects (e.g. lists or applications with no abstraction in function position) the reduction has to be recursively driven into each component. As indicated in gure 7, reductions to normal forms essentially require that the processing phase which implements the function Reduce be supplemented by an interpreter phase which does the {extensions as formally speciied by the function Eta. What this interpreter does is basically described on page 11: For every partial application (or abstraction) received from the processing phase, it creates on the argument stack an argument frame for a full application by lling the missing argument position with the respective bound variables (or formal parameters). These variables are represented as pointers to tuples which include the variable names and the {nesting levels. These pointers are also pushed into a run{time stack which is supported by the interpreter in order to handle the recursive traversal of the expression. On each call of the interpreter, the {nesting level for each formal parameter is incremented by one, starting with the value zero.Figure 8: The graph structure of a variable introduced by {extension In another pass through the processing phase, the reduction of the full supercombinator application which constitutes the body of the {extended abstraction may now be resumed. This is done by pushing onto the return stack the address of an artiicially created EXIT{ instruction and then calling the supercombinator code. This code eventually terminates by executing a RETURN{instruction which pops the address of the EXIT{instruction. When doing this repeatedly in case of nested partial applications, the formal parameters of several nested {extensions may pile up on the run{time stack. If the body{expression returned from the processing phase is nally a normal form, i.e. no further {extensions need to be done, the interpreter pops the variables held in its run{time stack to put the {binders in front of this expression in …