simple functional queue from Okasaki#558
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sorrachai
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May 16, 2026
sorrachai
reviewed
May 16, 2026
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| /-- Physicist method: a potential (lower bound on savings) defined on a | ||
| data structure -/ | ||
| class Potential α where |
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In general, potential function arguments do not require non-negativity of the potential.
sorrachai
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May 16, 2026
| | pop => | ||
| simp only [Amortized.Op.applyOp, applyOp, potential] | ||
| cases h_front : q.front <;> (rw [Raw.pop, h_front] at ⊢; grind [Raw.rebalance]) | ||
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Amortized cost is nice, but not immediately usable. To provide a good API for users, can you add a theorem about the total cost of a sequence of m operations on the queue of n elements? This should be at most 2m+n.
sorrachai
reviewed
May 16, 2026
| following Okasaki, chapter 5 -/ | ||
| def amortizedCost {α o : Type*} [Op α o] [Potential α] (x : α) (op : o) : ℕ := | ||
| (Op.applyOp x op).time + Potential.potential (Op.applyOp x op).ret - Potential.potential x | ||
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Some theorems/APIs about amortized cost imply that the total cost would be nice to have.
sorrachai
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May 16, 2026
| class Potential α where | ||
| /-- non-negative potential. Initial potential should be 0. | ||
| [Okasaki, *Purely Functional Data Structures*, 1996][okasaki1996] -/ | ||
| potential : α → Nat |
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Generic type is better. I wouldn't use Nat, as some applications may use real numbers. In some cases, we allow negative numbers.
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Hi, this is my first attempt at contributing Lean code.
I dug out the old Okasaki, and started off with the simple queue. This should
contain a correctness proof, a complexity proof, and a mapping to a ghost list
of elements.
TimeMdoesn't seem to be enough for amortized complexity soI added a module for that, and I also removed the
ZeroAddtypeclass constraintbecause
\Ndoesn't implement it(!).AI disclosure: all code is mine, but I had some assistance from GLM 5.1 to
tidy up proof terms and get unstuck.