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*From*: Apostolis Xekoukoulotakis <apostolis.xe...@xxxxxxxxx>*Date*: Wed, 6 Feb 2019 03:44:36 +0200*References*: <4550f6e3-ace6-4e2a-a6d6-b379e7ebbb68@googlegroups.com> <7ca6b90f-8206-4f76-9b94-c16d10afc8fb@googlegroups.com>

I am not familiar with TLAPLUS, but with regards to the hierarchical structure of proofs that Leslie proposes, I think that it can also be done in Agda, but it requires the programmer to be thoughtful of the structure of the proof.(1)

On Wed, Feb 6, 2019 at 2:19 AM <saksha...@xxxxxxxxxxxxxx> wrote:

--Using terminology of [1,2], Coq follows procedural, Isabelle follows declarative and TLAPS follows hierarchical (declarative) style of proof writing. I recommend reading [1] which compares procedural and declarative styles, and then obviously [2] to know the story and insights behind TLAPS's hierarchical style and more. Some of my personal points/feelings are (please note that I'm not an expert in Coq or Isabelle or TLAPS):* Coq (procedural proofs) is very hard on beginners because of the huge vocabulary of procedures (aka tactics), TLAPS is not* I am not a huge fan of writing 'this(feels, wrong)' as 'this feels wrong'. It feels like my 20 years of math training has been challenged. TLAPS respects that.* Without comments, a procedural proof to me is as readable as Mandarin. For example, length_corr in here. TLAPS proofs on the other hand are easily readable because at each step it is clear what exactly is being proved.* TLAPS is one of the only systems that lets me number my equations - something I've done in, again, my 20 years of math training.* TLA+ is not typed, unlike many others. This for me means that when writing my spec, I can just focus on my spec and not worry about types. Later, I will write a TypeInvariant and prove it. This is a personal preference. For eg, when proving problem P is NP-Complete, I don't want to care while specifying P that P is in NP. I will first specify P, then prove that P is in NP (and later NP-hard).Best,Saksham[1] Harrison, John. "Proof style."International Workshop on Types for Proofs and Programs. Springer, Berlin, Heidelberg, 1996.[2] Lamport, Leslie. "How to write a 21st century proof."Journal of fixed point theory and applications11.1 (2012): 43-63.

On Tuesday, February 5, 2019 at 8:38:23 AM UTC-5, Roberto wrote:Hi All,

I am interested to know how TLA+/TLAPS compares to other proof assistants such as Coq, Isabelle, Spin (an others) especially in term of expressiveness power.

Regards,

Roberto

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**References**:**Comparison between TLAPS and other proof assitants***From:*Roberto

**Re: Comparison between TLAPS and other proof assitants***From:*saksha . . .

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