Re: Computability and logic


Tom wrote:
It is just that little
part I mentioned that has continued to make me bounce off for several
months now.

In this context (as opposed to the Post context), substitution is
for supplying arguments to functions, or for applying functions
defined with argument-VARIABLES, TO argument-TERMS.
You have a function definition like F(x,y,z)=df=
'stuff'x'otherstuff'y'morestuff'z
and you want to know what F(1,2,3) is; you want to substitute 1 for x,
2 for y,
and 3 for z to get F(1,2,3)='stuff'1'otherstuff'2'morestuff'3.

I have shown the thing on the right, the result, as a string, composed
of other concatenated strings, but in this paradigm, that is NOT the
default composition of things in general. Things in general are TERMS.
They look like p(a,b,c) or s(s(s(0)); they the SAME kind of TREE
structure
that function-applications and predicate-applications have.

These trees do not have to be binary but they can all be re-represented
as binary.

My point is that there is a vast amount of literature in logic and
term-
rewriting involving TERM-substitutions (for variables) as opposed to
substring
substitutions that will accomplish the same objective.

.

Relevant Pages

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