Robin Milners pi calculus is typeless (Re: Milners fickle() in pi-WAM [For fun and profit])

From	Mild Shock <janburse@fastmail.fm>
Newsgroups	comp.lang.prolog
Subject	Robin Milners pi calculus is typeless (Re: Milners fickle() in pi-WAM [For fun and profit])
Date	2026-07-18 11:00 +0200
Message-ID	<113ffb7$32l$3@solani.org> (permalink)
References	(2 earlier) <112b732$20pmt$1@solani.org> <112b7iu$20q3i$1@solani.org> <113cqbm$85b9$1@solani.org> <113edfb$9aoh$1@solani.org> <113ef2k$9bi1$1@solani.org>

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Hi,

Mild Shock schrieb:
 > The π-calculus is a universal model of computation.
 > This was first observed by Milner in his paper
 > "Functions as Processes",[10] in which he presents
 > two encodings of the lambda-calculus in the π-calculus.
 > https://en.wikipedia.org/wiki/%CE%A0-calculus

Ross Finlayson schrieb:
 > Of course the lambda-calculus and pi-calculus
 > are great things for models of types and communicating
 > sequential processes.
 >
 > Roberto di Cosmo has a great book on types,
 > and more than one.
 >
 > 
https://books.google.com/books/about/Isomorphisms_of_Types.html?id=cdJZRjIxavwC

When a 1970s paper claims a relation ship between
pi-calculus and lambda calculus, then both calculi
refer to a typeless calculi.

Types are a later invention. The original lambda
calculus was typeless. Church encodings came later,
but for example the Church Turing hypotheses is

formulated along typeless lambda calculus.

Bye

P.S.: Prolog is also typeless. I do not intend to
add any types to pi-WAM either.


Mild Shock schrieb:
> Hi,
> 
> Milners fickle() is here:
> 
> Functions as processes
> https://inria.hal.science/inria-00075405
> 
> After Theorem 7.7:
> 
> So in P we construct a fickle ‘function’ which
> behaves differently on successive calls.
> 
> Here is a pi-WAM run in Dogelog Player, using the emulator:
> 
> Dogelog Spieler 2.2.4, Oracle Corporation, Java 26.0.1
> (c) 1985-2026, XLOG Technologies AG, Schweiz
> ?- ensure_loaded(library(edge/brainfog)).
> true.
> ?- emulate((between(1,2,Y),in(X),out(Y))).
> : 0
> 1
> : 0
> 2
> fail.
> 
> The emulator is portable, can be run every Prolog
> system. But it is only 1 process. So its better
> to use the n process backends for CPU or GPU.
> 
> Which are less portable, not anymore pure Prolog,
> a great deal of thread start and join infrastructure
> as well, and a native Hack VM.
> 
> The comms across process is not yet implemented.
> But the in/1 and out/1 instructions are already
> there. But they currently go to stdin/stdout.
> 
> Bye
> 
> Mild Shock schrieb:
>>
>> Hi,
>>
>> The pi in pi-WAM refers to pi-calculus.
>> pi-calculus has not atomic(i32).
>>
>> The π-calculus is a universal model of computation.
>> This was first observed by Milner in his paper
>> "Functions as Processes",[10] in which he presents
>> two encodings of the lambda-calculus in the π-calculus.
>> https://en.wikipedia.org/wiki/%CE%A0-calculus
>>
>> LoL
>>
>> Bye
>>
>> Chris M. Thomasson schrieb:
>>  > On 7/17/2026 2:16 AM, Mild Shock wrote:
>>  >> Hi,
>>  >>
>>  >> Maybe I should write a blog post, titled
>>  >> Introduction to AI Accelerator Prolog:
>>  >>
>>  >> - specialized jobs π-WAM (currently integerish stuff)
>>  >> - π-WAM uses no atomics, only comms
>>  >> - π-WAM uses warp, 30-40% more speed
>>  >> - π-WAM runs on GPU and CPU
>>  >> - π-WAM runs from within JavaScript, Python and Java
>>  >
>>  > [...]
>>  >
>>  > No atomic fetch-and-add?
>>
>

Thread

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          pi in pi-WAM refers to pi-calculus (Re: Introduction to AI Accelerator Prolog [π-WAM of Dogelog]) Mild Shock <janburse@fastmail.fm> - 2026-07-18 01:22 +0200
            Milners fickle() in pi-WAM [For fun and profit] (Re: pi in pi-WAM refers to pi-calculus (Re: Introduction to AI Accelerator Prolog [π-WAM of Dogelog]) Mild Shock <janburse@fastmail.fm> - 2026-07-18 01:49 +0200
              Robin Milners pi calculus is typeless (Re: Milners fickle() in pi-WAM [For fun and profit]) Mild Shock <janburse@fastmail.fm> - 2026-07-18 11:00 +0200
                Can the Church Turing hypotheses be refuted? [TLo @ FOM] (Re: Robin Milners pi calculus is typeless) Mild Shock <janburse@fastmail.fm> - 2026-07-18 11:10 +0200
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