David Corfield intensional conjunction

Woods notes that many uses of ‘and’ rely on a conceptual connection.

were we to hear someone utter (viii), “I promised to go to the Hanson’s New Year’s party, and 2 is prime, and the butler did it, and goodness is a logical simple, and I’m going to faint”, we should be tempted to think him raving“ (p. 361)

However

there is an important use of ‘and’ – the listy use, which is deviant unless its listiness is made clear. (p. 361)

(But ‘List’ as a logical construct, an inductive type – logic-mathematics.)

What if the intensional conjunction ‘and’ is dependent sum (MHTT), and the further interpretation depends on the kind of types involved?

Listy ‘and’ is $a, b, c, d: A$, or $[a,b,c,d]: List(A)$.

References

• John Woods, Is There a Relation of Intensional Conjunction?, Mind New Series, Vol. 76, No. 303 (Jul., 1967), pp. 357-368, JSTOR

• Robert E. Gahringer, Intensional conjunction, Mind, Volume LXXIX, Issue 314, 1 April 1970, Pages 259–260,