abstract-data-type


AbstractDataType - Nat


I got this abstract model here and try to understand how it works but can't figure it out.
type: NAT
constructor
null: → NAT
succ: NAT → NAT
operator
add: NAT×NAT→ NAT
axiom x,y : NAT
add(X, null) = X
add(X, succ(Y)) = succ(add(X, Y))
The problem is with the add. I tried to put some numbers in but ... how does it work? -
add(2, succ(3)) = succ(add(2, 3)) ... and now? I just want 2+3 = 5
NAT is the set of natural numbers together with '+' and succ is the successor function (often seen in relation with the Peano axioms)
Your example for 2+3 calculates like this:
add(2,3) = succ(add(2,2))
= succ(succ(add(2,1)))
= succ(succ(succ(add(2,0))))
= succ(succ(succ(2)))
= succ(succ(3))
= succ(4)
= 5

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