es 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 different color
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
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)