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From: Mild Shock <janburse@fastmail.fm>
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Subject: =?UTF-8?Q?Grothendieck-Group_Rewriting_in_Dogelog_Player_=28Re:_?= =?UTF-8?Q?=cf=80-WAM_Assembly:_Jump_and_Link_for_Tseytin_Transform=29?=
Date: Tue, 25 Aug 2026 19:01:46 +0200
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Hi,

Since Prologers have their head full of DCG and
difference lists, using pairs to measure the Earth’s
circumference. They might also like the idea to use
difference pairs in rewriting. We attack the
commutative semiring N[x] where additive inverse
is missing, Grothendieck-Groups come handy.

The backtracking of Prolog is perfect to search
rewrite locations. Following Alexander Grothendieck
before category theory, a master in generalizing,
we apply rewriting on equations f = g and not only
individual terms f and g. The Lawvere example of
x⁷ = x from x = x² + 1 runs in less than 1 ms.

Bye

See also:

Grothendieck-Group Rewriting in Dogelog Player
https://medium.com/2989/51cccc82e3de

Mild Shock schrieb:
 > Hi,
 >
 > We can report some progress in the π-WAM
 > compilation using the recently introduced assembly
 > with labels. While we already showed disjunction
 > (;)/2 without resorting into TRY_ME_ELSE,
 > RETRY_ME_ELSE or TRUST_ME. In this take we show how
 > to do if-then-else (->)/2 .
 >
 > To aid in the compilation of (->)/2 we use the
 > front Dogelog VM transform that introduces
 > ‘$MARK’/1 and ‘$CUT’/1. While SWI-Prologs light
 > weight choice points store a link address, we
 > need also to do the same to call the fresh
 > Tseytin proposition. But we do so with
 > Jump and Link from RISC.
 >
 > Bye
 >
 > See also:
 >
 > π-WAM Assembly: Jump and Link for Tseytin Transformation
 > https://medium.com/2989/d81abe7cceb7