feat: mono nat (algebra + bi)#409
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Further context found in the following Zulip conversation. https://leanprover.zulipchat.com/#narrow/channel/113488-general/topic/Did.20coercions.20stop.20being.20printed.20with.20.60.E2.86.91.60.3F/with/587821793
In the end, it seems like around `40` is quite a good precedence level. If we look at `Notation.lean`, we see the precedence levels of various notations. ``` @[inherit_doc] infixr:90 " ∘ " => Function.comp @[inherit_doc] infixr:35 " × " => Prod @[inherit_doc] infixr:35 " ×' " => PProd @[inherit_doc] infix:50 " ∣ " => Dvd.dvd @[inherit_doc] infixl:55 " ||| " => HOr.hOr @[inherit_doc] infixl:58 " ^^^ " => HXor.hXor @[inherit_doc] infixl:60 " &&& " => HAnd.hAnd @[inherit_doc] infixl:65 " + " => HAdd.hAdd @[inherit_doc] infixl:65 " - " => HSub.hSub @[inherit_doc] infixl:70 " * " => HMul.hMul @[inherit_doc] infixl:70 " / " => HDiv.hDiv @[inherit_doc] infixl:70 " % " => HMod.hMod @[inherit_doc] infixl:75 " <<< " => HShiftLeft.hShiftLeft @[inherit_doc] infixl:75 " >>> " => HShiftRight.hShiftRight @[inherit_doc] infixr:80 " ^ " => HPow.hPow @[inherit_doc] infixl:65 " ++ " => HAppend.hAppend @[inherit_doc] prefix:75 "-" => Neg.neg @[inherit_doc] prefix:100 "~~~" => Complement.complement @[inherit_doc] postfix:max "⁻¹" => Inv.inv @[inherit_doc] infixr:73 " • " => HSMul.hSMul ``` If we take further into account that the precedence of the arrow `→` is `25`, then my earlier choice of `40` makes it weaker than all other usual operators, but still stronger than implication, which is roughly where I wanted to place it.
One actually cannot make the definition of `NSteps` use `Iterate` because `Step` is a tagged relation, and `Iterate` does not support merging the observations between `Step`s.
Actually, we can see `List Obs` to be the free monoid of `Obs`, so we don't actually gain any expressivity by changing the definition. Maybe it would make for a nicer API, but it doesn't warrant making the change at this stage.
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Assuming there are no further changes to the set_option synthInstance.checkSynthOrder false in
@[rocq_alias mono_nat_auth_dfrac_is_op]
instance {dq dq1 dq2 : DFrac F} {n : MaxNat}
[h : IsOp io1 dq io2 dq1 io3 dq2] :
IsOp io1 (●MN{dq} n) io2 (●MN{dq1} n) io3 (●MN{dq2} n) where
is_op := by rw [h.is_op]; apply auth_dfrac_op
@[rocq_alias mono_nat_lb_max_is_op]
instance {n n1 n2 : MaxNat}
[h : IsOp io1 n io2 n1 io3 n2] :
IsOp io1 (◯MN n : MonoNat F) io2 (◯MN n1) io3 (◯MN n2) where
is_op := by rw [h.is_op]; .rfl |
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Description
Fixes #269 and #282
I would like to try to push for heap lang proofs before the workshop, and its one of the dependencies.
It might require changes depending on whether #401 gets merged before or after.
Checklist
PORTING.mdas appropriateauthorssection of any appropriate files