COMMENT ⊗   VALID 00002 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	I seems to me that there should be a nice intuitive introduction
C00004 ENDMK
C⊗;
I seems to me that there should be a nice intuitive introduction
to scottery. Let's start with what we know reasonably well.


elementary numb theory.
  what is function: claim it's idealization; a denotational
abbreviation for operational primitive set

cf. discussion of fact. fact is a sequence of iteregers(infinite)

given nth we can find n+1th. later some clever person saw recurrence
relation. Ah! fact[n] = [...]

how do we do it precisely...its fixpointing off of sequence of fi's as in
notes.

syntax fact ::= int|int,fact; where x(n)εfact => x(n+1) = x*(n+1)

_________________
try domain equations:
eg: sexprs

sexpr ::= atom|(sexpr . sexpr)

goes to 
 S = A + (SxS).

how do we know such has a solution... maybe not. do fixpointing
off of seq of domain approximations.
_________________

try λ-calc

exp ::= var|λv.exp|(exp exp)

goes to

E = V+(E→E)+E ≡ V + (E→E)

screwed in general: no solution.

1. what's problem? it's "→".  question is there are restriction on "→"
so that we can fixpoint as above.

2. What is minimal restriction on "→"?