Feb. 17th, 2024

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After many years I finally have an intuitive understanding of linear logic operators.
The λλ̃-calculus by V. Choudhury et al. shows how to understand the multiplicative disjunction A ⅋ B, while the Verse calculus by SPJ et al. shows how to understand the multiplicative exponential ?A.
A × B — tuple
A ⅋ B — junction (employing terminology by Larry Wall)
A + B — producer-controlled alternative
A & B — consumer-controlled alternative
!A — factory producing A's, in particular
!A = 𝟘 & A & A × A & A × A & ···
?A — junction of any number of A's, in particular
?A = ⊥ + A + A ⅋ A + A ⅋ A ⅋ A + ···
All variables in Verse calculus are secretly of the kind ?T, where T is a cartesian type. So, one can even assume they are ?!X.


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Juan-Carlos Gandhi

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