Re: [tlaplus] Resources for learning TLA+ proofs

Hah! Thanks Calvin. Actually I've been looking at my own tree-sitter grammar I wrote to figure out the proof syntax: https://github.com/tlaplus-community/tree-sitter-tlaplus/blob/main/grammar.js

Ironic, I can parse the proof language but I cannot write one myself (yet!)

Like most proof languages, the TLA+ proof language is sort of a mirror version of the TLA+ language itself. Each TLA+ language construct has its corresponding proof language element that is used to "destructure" that construct in proofs. For example here's a (probably not yet correct) mental model I'm building about how to handle every TLA+ language construct when it's in either the P or Q spot of a P => Q we are trying to prove:

TLA+ Language Construct	Antecedent or Consequent (P => Q)?	Destructuring Element
e1 /\ e2	Antecedent (P)	Prove e1 => Q \/ e2 => Q
e1 /\ e2	Consequent (Q)	Prove P => e1 /\ P => e2
e1 \/ e2	Antecedent (P)	Prove e1 => Q /\ e2 => Q
e1 \/ e2	Consequent (Q)	Prove P => e1 \/ P => e2
IF e1 THEN e2 ELSE e3	Antecedent (P)	???
IF e1 THEN e2 ELSE e3	Consequent (Q)	Prove CASE e1 => e2 /\ CASE ~e1 => e3
\E e \in S : f(e)	Antecedent (P)	Prove (PICK e \in S : f(e)) => Q
\E e \in S : f(e)	Consequent (Q)	Prove (WITNESS e \in S) => f(e)
\A e \in S : f(e)	Antecedent (P)	Prove (PICK e \in S : f(e)) => Q
\A e \in S : f(e)	Consequent (Q)	Prove (TAKE e \in S) => f(e)

Andrew

On Tue, Mar 28, 2023 at 10:49 AM Calvin Loncaric <c.a.loncaric@xxxxxxxxx> wrote:

When I was first learning TLAPS back in 2019 I had a lot of trouble understanding the syntax. There are lots of awe-inspiring examples, but no clear reference for the actual structure of a proof. In particular, I couldn't seem to figure out how to begin a new proof for something I cared about without copying the structure of a similar proof from somewhere else. And when I did manage to find a similar proof, I was never sure what kinds of changes to the proof steps were syntactically valid.

I wrote myself the kind of reference I wish I'd had:
https://github.com/Calvin-L/util/blob/master/wisdom/Proofs.tla

Looking at it now I think it's a bit sparse, and I wouldn't recommend it as the first thing to look at when learning. Still, I hope it helps fill in gaps for you and others.

--
Calvin

On Fri, Mar 24, 2023 at 10:26 PM JosEdu Solsona <josedusolsona@xxxxxxxxx> wrote:
Some other resources i found useful are:
Proving Safety Properties (lamport.azurewebsites.net)
Auxiliary Variables in TLA+ (lamport.azurewebsites.net)
tlaps: The [+] Proof System (mpg.de)
Specifying Systems is not really about proofs. (In fact, in the introduction we have: "However, this book is about specification; it says almost nothing about proofs." )
On Saturday, March 25, 2023 at 1:38:14 AM UTC-3 Daniel Craig wrote:
There is also Specifying Systems by Dr Lamport

On Mar 24, 2023, at 5:56 PM, Andrew Helwer <andrew...@xxxxxxxxx> wrote:

What resources exist? I know of:
The TLA+ hyperbook (unfinished?)
Documentation on the TLAPS INRIA website
Specs with proofs in the tlaplus/examples repo
Any others? Those of you who have written TLA+ proofs, how did you learn?

Andrew

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