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*From*: ns <nedsri1988@xxxxxxxxx>*Date*: Wed, 18 Jan 2023 18:50:15 -0800 (PST)

Yes sorry for some reason all the formatting was removed after I posted it. Here's the post again, this time with the specs in a courier font

I'm experimenting with implementation vs interface refinement using the HourClock spec as an example. Here's the HourClock spec

------- MODULE HourClock -------------

EXTENDS Naturals

VARIABLE h

CInit == h = 1 \* was \in (1..12)

CNext == h' = (h % 12) + 1

HC == CInit /\ [][CNext]_h

============================

In the Specifying Systems book, there is an hour clock that uses bit vectors instead of ints. This spec BinHourClock is treated as an interface refinement of HourClock. (valueOf converts a bit vector into its corresponding integer value)

--------------------------------------- MODULE BinHourClock -------------------------------

(*represents the time as a bit vector*)

EXTENDS Naturals

VARIABLE h_bv

valueOf(b) ==

LET n == CHOOSE i \in 0 .. 3 : DOMAIN b = 0 .. i

val[i \in 0 .. n] == IF i=0 THEN b[0]*(2^0)

ELSE (b[i]* (2^i)) + val[i - 1]

IN val[n]

hourVal(b) == IF b \in [(0 .. 3) -> {0,1}] THEN valueOf(b) ELSE 99

H(h) == INSTANCE HourClock \*substs param h for HourClock's var h

IR(h,b) == [] (h = hourVal(b))

BHC == \EE h: IR(h, h_bv) /\ H(h)!HC

========================================================

But now suppose I want to treat the BinHourClock as an implementation of HourClock rather than an interface refinement, I need to expose h (and possibly hide h_bv). I tried the following (changes to BinHourClock shown in red)

--------------------------------------- MODULE BinHourClockImpl -------------------------------

(*represents the time as a bit vector*)

EXTENDS Naturals

VARIABLE h_bv, h2

valueOf(b) ==

LET n == CHOOSE i \in 0 .. 3 : DOMAIN b = 0 .. i

val[i \in 0 .. n] == IF i=0 THEN b[0]*(2^0)

ELSE (b[i]* (2^i)) + val[i - 1]

IN val[n]

hourVal(b) == IF b \in [(0 .. 3) -> {0,1}] THEN valueOf(b) ELSE 99

H(h) == INSTANCE HourClock \*substs param h for HourClock's var h

IR(h,b) == [] (h = hourVal(b))

init_h_bv == h_bv = [i \in (0 .. 3) |-> IF i=0 THEN 1 ELSE 0]

BHCImpl == init_h_bv /\ IR(h2, h_bv) /\ H(h2)!HC

===========================================================

(I added a new variable h2 representing integer time, an initializer for h_bv so TLC doesn't complain, and changed the spec so it no longer hides the integer time)

But TLC produces the following error:

current state is not a legal state

While working on the initial state:

/\ h2 = null

/\ h_bv = (0 :> 1 @@ 1 :> 0 @@ 2 :> 0 @@ 3 :> 0)

If my understanding of INSTANCE is correct, h2 should be initialized to 1. Could someone tell me what I'm missing?

thanks

P.S. I changed HourClock to start at 1, not just to make TLC's life easier but also because TLC didn't like the initializer that implicitly initialized h_bv saying h2=hourVal(h_bv)

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