Comments (1)
I suspect the Inductive
syntax will have to insist that conjunctions not be used to separate clauses and that labels be used for all. (A "nice" syntax for separating clauses so that they don't get names is clearly possible, perhaps a label that looks like [/\]
or [∧]
.) The underlying, more primitive notation remains accessible.
This allows something like
Inductive lameq :
[~BETA:]
!x M N. (LAM x M) @@ N == [N/x]M
[~REFL:]
M == M
[~SYM:]
!M N. M == N ==> N == M
[~TRANS:]
!M N L. M == N /\ N == L ==> M == L
[~APPL:]
!M N Z. M == N ==> M @@ Z == N @@ Z
[~APPR:]
!M N Z. M == N ==> Z @@ M == Z @@ N
[~ABS:]
!M N x. M == N ==> LAM x M == LAM x N
End
It's very difficult to imagine handling conjunctions as clause separators in the above (notice the conjunction in the TRANS
rule).
The anonymous syntax might allow:
Inductive RTC:
[/\]
!x. RTC R x x
[/\]
!x y z. R x y /\ RTC R y z ==> RTC R x z
End
probably omitting the first label if desired.
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