I'm studying for an exam on lambda-calculus and algebraic specifications, and I'm having trouble figuring out this problem. I was wondering if anyone here could help??
The given specification:
S: sorts O
Σ: constants
a: -> O
b: -> O
c: -> O
function
f: O -> O
E: equations
[1] f(a) = c
[2] f(f(x)) = x
Now, first off, I'm looking for a model that has three elements and contains confusion, but no junk. Right now I have: A = {A,B,C} , a = A, b = B, c = C, f(a) = C, f(b) = B and f(c) = A. I thought the confusion would arise from f(b) = B = b, but I'm not sure this works...
As a second question, I'm looking for the correct initial model for this specification.
Any help would be greatly appreciated!!
Regards,
Linus