By Philip John Koopman Jr.
This booklet combines structure with implementation ideas for complicated programming languages
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Extra info for An Architecture for Combinator Graph Reduction
Implementation of the TIGRE Machine 44 $FIB X Figure 4-9. The $ F I B supercombinator. One example of supercombinator compilation is the "fib" bench mark, which recursively computes the n* Fibonacci number. Since the definition of fib is itself a supercombinator, then a single graph rewrite for the combinator $ F I B may be defined as shown in Figure 4-9. The idea behind the supercombinator definition is to eliminate the need for combi nations of graph rewriting combinators such as S, B, and C.
The first cell of each triple contains a subroutine call instruction while the second and third cells of the triple contain the left- and right-hand sides of the node, respectively. The hardware's native subroutine calling mechanism is used to traverse the spine, using the subroutine return stack as the spine stack. Figure 3-8 shows the example graph as it appears in the VAX assembly language implementation of TIGRE. ) While the graph shown in Figure 3-8 is simple, its operation is not necessarily obvious.
1. Hardware Definition Figure 4-1 shows a block diagram of the TIGRE abstract machine. As a minimum, TIGRE requires a processing unit, a scratchpad register stor age space, a spine stack/subroutine return stack, memory for holding combinator definitions, and heap memory for holding the graph nodes. TIGRE needs three memory spaces. The first memory space con tains the spine stack, which is used to save pointers to the nodes in the program graph that have been visited during stack unwinding. The second memory space contains the definitions for combinators (written in TIGRE assembly language).
An Architecture for Combinator Graph Reduction by Philip John Koopman Jr.