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Re: [tlaplus] Proving a Matrix Transpose



Sorry, StephAn!

On Wednesday, April 15, 2020 at 4:31:47 PM UTC+1, christi...@xxxxxxxxx wrote:
Thanks Stephen! I should have said that I'd already translated it, I didn't include the translation for brevity (always a mistake, when will I learn?).

I'll try moving my theorem to the end of the TLA+ translation, thanks!

On Wednesday, April 15, 2020 at 4:11:06 PM UTC+1, Stephan Merz wrote:
1. Your algorithm is written in PlusCal, which appears as a comment to TLA+. You first need to generate the TLA+ specification (File -> Translate PlusCal Algorithm in the Toolbox).

2. Your theorem should then be stated as a consequence of the specification in the form

THEOREM diagseq == Spec => (diag = tdiag)

Its proof will look like "BY DEF Spec, Init". Note that your assertion only talks about the initial state.

Regards,
Stephan


On 15 Apr 2020, at 17:04, christi...@xxxxxxxxx wrote:

Hi!

I've written a specification to transpose a matrix, but I don't know how I use TLAPS to prove correctness. I've tried:

---- MODULE transp ----
EXTENDS Naturals, TLC
CONSTANT n, m
(* --algorithm transpose
variables i=1, j=1, array = <<<<>>,<<>>>>,transp = <<<<>>,<<>>>>, diag = <<>>, tdiag = <<>>,

begin
while j <= m do
  i := 1;
  while i <= n do
     transp[i][j]:= array[j][i];
     if i = j then
        diag[j]:=array[j][i];
        tdiag[j]:=transp[i][j];
     end if;
   i := i+1;
  end while;
  j := j+1;
end while;

print array;
print transp;
     
end algorithm *)

THEOREM diagseq == diag=tdiag
PROOF
OBVIOUS

But I get the error that tdiag is unknown. I'm not sure what I'm not understanding so any help would be appreciated!


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