# Re: Simpler method of making multiple changes to a function in a single step

I think I have it. I have updated IsBalanced and BalancedAllocations to as follows:

IsBalanced(reg) ==
/\ \A m,n \in N : \/ m = n
\/ Cardinality(reg[m]) - Cardinality(reg[n]) \in {-1,0,1}
/\ \A m,n \in N : \/ m = n
\/ reg[m] \intersect reg[n] = {}
/\ \A r \in R : \E n \in N : r \in reg[n]

BalancedAllocations ==
{ reg \in [N -> SUBSET R] : IsBalanced(reg) }

It will generate a register such as: [n1 |-> {"r1"}, n2 |-> {"r2"}, n3 |-> {"r3", "r4"}]

The first line of IsBalanced ensures resources are well balanced,
The second ensures that resources are not assigned twice.
The third ensures that all resources are assigned.

It is much shorter and clearer than my first attempt, thank you very much for the help. (If you see any further improvements do let me know!)

Jack

On Wednesday, January 16, 2019 at 5:35:42 PM UTC+1, Jack Vanlightly wrote:
Hi,

I have a set of nodes N, a set of resources R and a function "register" that maps N to R. The algorithm is a resource allocation algorithm that must assign the resources of R evenly across the nodes N.

So if N is { "n1", "n2", "n3"} and R is {"r1", "r2", "r3", "r4" } then once allocation has taken place a valid value for register would be:
[n1 |-> <<"r4", "r1">>, n2 |-> <<"r2">>, n3 |-> <<"r3">>]

I want to set the values of register in a single step and I have managed it, though the formula seems overly complex and I wonder if there is a simpler way of doing that would help me also gain more insight into TLA+.

I have isolated the allocation logic into a toy spec as follows:

EXTENDS Integers, FiniteSets, Sequences, TLC
CONSTANT R, N
VARIABLE register

Init ==
register = [n \in N |-> << >>]

HasMinResources(counts, nd) ==
\A x \in N : counts[nd] <= counts[x]

Allocate ==
LET newRegister == [n \in N |-> << >>]
counts == [n \in N |-> 0]
al[pendingRes \in SUBSET R, assignCount \in [N -> Nat]] ==
LET n == CHOOSE nd \in N : HasMinResources(assignCount, nd)
r == LET int == R \intersect pendingRes
IN CHOOSE x \in int : TRUE
IN
IF Cardinality(pendingRes) = 0 THEN newRegister
ELSE
LET remaining == pendingRes \ { r }
newAssignCount == [assignCount EXCEPT ![n] = @ + 1]
IN [al[remaining, newAssignCount] EXCEPT ![n] = Append(@, r)]
IN al[R, counts]

Rebalance ==
/\ register' = Allocate
/\ PrintT(register')

(* ignore the spec, I just wanted to run the Rebalance action once *)
Spec == Init /\ [][Rebalance]_register

Notes:
- I made Allocate recursive as that is the only way I could figure out making all the changes to register in a single step.
- I did the intersect so that I could use CHOOSE. Else it complained that is was an unbounded CHOOSE so I figured if I did an intersect with R then it would be interpretted as bounded.

Any insights or suggestions would be great.

Thanks
Jack

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