The proof on pages 24-25 of the corollary stated on the preceding page was checked by TLAPS.
From:
tlaplus@xxxxxxxxxxxxxxxx <tlaplus@xxxxxxxxxxxxxxxx> On Behalf Of
marta zhango
Sent: Thursday, April 25, 2024 9:35
To: tlaplus <tlaplus@xxxxxxxxxxxxxxxx>
Subject: Re: [tlaplus] TLA and TLAPIS
I am getting very confused. About (1) an easy outline of a proof and (2) the complete code for a proof system to check it.
The complete code for checking a proof can be enormously complicated, especially when one has to declare a significant
number of functions and constructs.
of Spivak’s proof. That is not the actual
complete code for a proof system to check it, am I right ?
Now, about comment regarding the proof in Cantor10.tla. Is that the actual complete code for a proof system to check the
correctness of the proof ? Or is it a description of the proof.
I want to write some proofs from signal processing that are more formal than the standard way of showing a proof in a
textbook, but not as complicated as the complete code required by a proof system. What would you suggest ?
On Friday, April 26, 2024 at 3:46:36 AM
UTC+12 Stephan Merz wrote:
The proof appearing at the beginning of appendix B of the paper you point to is checked by TLAPS, cf. also [1] that has 10 different versions
of the proof that are all checked by TLAPS. The proof in Cantor10.tla is even more succinct than the one appearing in the paper.
On 25 Apr 2024, at 16:58, marta zhango <marta...@xxxxxxxxx>
wrote:
For instance, consider the TLA+2 Proof of Cantor’s Theorem ( see first theorem of appendix B in
That would be more suitable than a TLAPS version of it. TLAPS is a translation of a TLA+2 Proof
for checking the proof. In such a description correct ?
As you say, a detailed proof written in a way that enables it to be checked by an automated system
requires substantial effortfrom the user.
For a textbook, an outline of the proof using TLA+2 could be the formal proof. Which can then be
checked out by coding the corresponding instructions for a proof checker.
On Friday, April 26, 2024 at 2:20:42 AM
UTC+12 Stephan Merz wrote:
Could you elaborate on what you mean by referring to TLA as a way to outline a proof? TLA stands for Temporal Logic of Actions, so it is
a logic rather than a proof system – although the TLA paper [1] includes proof rules that can be (mainly) used in paper-and-pencil proofs.
Like Coq and Lean, TLAPS is a mechanical proof assistant that allows you to write a detailed proof and have it checked by the system. These
tools indeed require substantial effort from the user, but unlike model checkers such as TLC they can (in principle) verify correctness properties for arbitrary specifications, not only finite-state systems.
There seems to exist a big difference between TLA and TLAPIS. TLA is a way to outline a proof, whilst TLAPIS, Coq, Lean provide ways to
check whether a proof is correct. With the
proof checkers being quite long and time consuming to construct.
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