FunCPU - Instruction Set

FunCPU will operate with 7-bit numerals (to understand why see the next couple of posts) and will directly support the following built-in functions:
inc(x) is used for incrementing a value, that is for any x: x+1=inc(x).
dec(x) is used for decrementing a value in the similar fashion.
if-then-else is used for conditional evaluation. if cond then exp1 else exp2 will yield exp1 if and only if cond is true, otherwise it will yield exp2 (assuming that evaluation of the condition terminates).
In addition to the above built-in functions, user definable functions may be entered arbitrary in the available 32 slots. These functions may use the built-in functions as well as any other user-defined functions. Functions can be embedded one into other at arbitrary depth. Functions can be created with arity 1, 2, 3 and 4. Constant functions still can be constructed, but they must have at least one argument. Thus, for example, if F(x) is a one-argument constant function, then F(x)=c for any x, where c is a constant.
Functions will only accept numeral constants as arguments (no higher order functions are supported), and will return also numerical value. Note: „0” represents True, any other value is considered to be False by convention.
By design, no advanced data structures (i.e. list, record, object, etc. ) will be supported natively. 
At first it may seem suprising that with this very limited instruction set (and of course with the poweful construct of function embedding), any computable function can be defined and thus computed within this model, provided that its encoded algorithm (and also all expressions as a result of the function evaluation) fits in the memory. 

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