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https://github.com/leanprover/lean4.git
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08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
68 lines
2.0 KiB
Lean4
68 lines
2.0 KiB
Lean4
inductive Expr where
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| var (i : Nat)
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| op (lhs rhs : Expr)
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deriving Inhabited, Repr
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def List.getIdx : List α → Nat → α → α
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| [], i, u => u
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| a::as, 0, u => a
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| a::as, i+1, u => getIdx as i u
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structure Context (α : Type u) where
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op : α → α → α
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unit : α
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assoc : (a b c : α) → op (op a b) c = op a (op b c)
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comm : (a b : α) → op a b = op b a
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vars : List α
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theorem Context.left_comm (ctx : Context α) (a b c : α) : ctx.op a (ctx.op b c) = ctx.op b (ctx.op a c) := by
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rw [← ctx.assoc, ctx.comm a b, ctx.assoc]
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def Expr.denote (ctx : Context α) : Expr → α
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| Expr.op a b => ctx.op (denote ctx a) (denote ctx b)
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| Expr.var i => ctx.vars.getIdx i ctx.unit
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theorem Expr.denote_op (ctx : Context α) (a b : Expr) : denote ctx (Expr.op a b) = ctx.op (denote ctx a) (denote ctx b) :=
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rfl
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def Expr.length : Expr → Nat
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| op a b => 1 + b.length
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| _ => 1
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def Expr.sort (e : Expr) : Expr :=
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loop e.length e
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where
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loop : Nat → Expr → Expr
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| fuel+1, Expr.op a e =>
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let (e₁, e₂) := swap a e
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Expr.op e₁ (loop fuel e₂)
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| _, e => e
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swap : Expr → Expr → Expr × Expr
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| Expr.var i, Expr.op (Expr.var j) e =>
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if i > j then
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let (e₁, e₂) := swap (Expr.var j) e
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(e₁, Expr.op (Expr.var i) e₂)
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else
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let (e₁, e₂) := swap (Expr.var i) e
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(e₁, Expr.op (Expr.var j) e₂)
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| Expr.var i, Expr.var j =>
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if i > j then
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(Expr.var j, Expr.var i)
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else
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(Expr.var i, Expr.var j)
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| e₁, e₂ => (e₁, e₂)
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theorem Expr.denote_swap (ctx : Context α) (e₁ e₂ : Expr) : denote ctx (Expr.op (sort.swap e₁ e₂).1 (sort.swap e₁ e₂).2) = denote ctx (Expr.op e₁ e₂) := by
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induction e₂ generalizing e₁ with
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| op a b ih' ih =>
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cases e₁ with
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| var i =>
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have ih' := ih (var i)
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match h:sort.swap (var i) b with
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| (r₁, r₂) =>
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rw [denote_op _ (var i)] at ih'
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admit
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| _ => admit
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| _ => admit
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