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SECD machine

The SECD machine is a highly influential virtual machine intended as a target for functional programming language compilers. The letters stand for Stack, Environment, Code, Dump, the internal registers of the machine. These registers point to linked lists in memory.

The machine was the first to be specifically designed to evaluate lambda calculus expressions. It was originally described by Peter J. Landin as part of his ISWIM programming language definition in 1963. However it is best known in connection with Peter Henderson's Lispkit Lisp compiler which has been distributed since 1980. Since then it has been used as the target for several other experimental compilers.

In 1989 researchers at the University of Calgary worked on a hardware implementation of the machine.

Table of contents
1 Registers and Memory
2 Instructions
3 Further Reading

Registers and Memory

The SECD machine is stack-based, functions (user-supplied and built-in) taking their parameters from the stack. Arguments to instructions, on the other hand, follow the instructions they belong to.

Like all internal data-structures, the stack is a list, with the S register pointing at the lists head or beginning. Due to the list structure, the stack need not be a continuous block of memory, so stack space is available as long as there is a single free memory cell. Even when all cells have been used, garbage collection may yield additional free memory.

The C register points at the head of the code list that will be evaluated. Once the instruction there has been executed, the C is pointed at the next instruction in the list -- it acts similar to an instruction pointer in conventional machines, only that subsequent instructions are often not in subsequent memory locations.

The current variable environment is managed by the E register, which points at a list of lists. Each individual list represents one environment level: the parameters of the current function are in the head of the list, variables that are free in the current function, but bound by a surrounding function are in subsequently later lists.

The dump, at which's head the D register points, is used as temporary storage for values of the other registers, for example during function calls. It can be likened to the return stack of other machines.

The memory organization of the SECD machine is similar to the model used by most functional language interpreters: a number of memory cells, each of which can hold either an atom (a simple value, for example 13), or represent an empty or non-empty list. In the latter case, the cell holds two pointers to other cells, one representing the first element, the other representing the list except for the first element. The two pointers are traditionally named car and cdr respectively. The different types of values that a cell can hold are distinguished by a tag. Often different types of atoms (integers, strings, etc.) are distinguished as well.

So a list holding the numbers 1, 2, and 3, usually written as "(1 2 3)", could be represented as follows:

Address   Tag       Content (value for integers, car & cdr for lists)

9 [ integer | 2 ] 8 [ integer | 3 ] 7 [ list | 8 | 0 ] 6 [ list | 9 | 7 ] ... 2 [ list | 1 | 6 ] 1 [ integer | 1 ] 0 [ nil ]

The memory cells 3 to 5 do not belong to our list, the cells of which can be distributed randomly over the memory. Cell 2 is the head of the list, it points to cell 1 which holds the first element's value, and the list containing only 2 and 3 (beginning at cell 6). Cell 6 points at a cell holding 2 and at cell 7, which represents the list containing only 3. It does so by pointing at cell 8 containing the value 3, and pointing at an empty list (nil) as cdr. In the SECD machine, cell 0 always implicitly represents the empty list, so no special tag value is needed to signal an empty list (everything needing that can simply point to cell 0).

That the cdr in a list cell has to point at another list is just a convention. If both car and cdr point at atoms, that will yield a pair, usually written like "(1 . 2)"


A number of additional instructions for basic functions like car, cdr, list construction, integer addition, I/O, etc. exist. They all take any necessary parameters from the stack.

Further Reading

Peter M. Kogge: The Architecture of Symbolic Computers. ISBN 0-07-035596-7

Peter Henderson, "Functional Programming: Application and Implementation", 1980, Prentice Hall

Anthony J. Field and Peter G. Harrison: Functional Programming. Addison-Wesley, 1988. ISBN 0201192497