e532ce95ce
This PR changes the order of steps tried when proving equational theorems for structural recursion. In order to avoid goals that `split` cannot handle, avoid unfolding the LHS of the equation to `.brecOn` and `.rec` until after the RHS has been split into its final cases. Fixes: #10195
114 lines
3.2 KiB
Text
114 lines
3.2 KiB
Text
inductive Expr where
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| const (i : BitVec 32)
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| op (op : Unit) (e1 : Expr)
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def optimize : Expr → Expr
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| .const i => .const i
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| .op bop e1 =>
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match bop, optimize e1 with
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| _, .const _ => .op bop (.const 0)
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| _, _ => .const 0
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/--
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error: Failed to realize constant optimize.eq_def:
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failed to generate equational theorem for `optimize`
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e1 : Expr
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bop : Unit
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i : BitVec 32
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heq : optimize e1 = Expr.const i
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⊢ (match bop,
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(Expr.rec (fun i => ⟨Expr.const i, PUnit.unit⟩)
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(fun op e1 e1_ih =>
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⟨match op, e1_ih.1 with
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| x, Expr.const i => Expr.op op (Expr.const 0)
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| x, x_1 => Expr.const 0,
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e1_ih⟩)
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e1).1 with
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| x, Expr.const i => Expr.op bop (Expr.const 0)
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| x, x_1 => Expr.const 0) =
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Expr.op bop (Expr.const 0)
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---
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error: Failed to realize constant optimize.eq_def:
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failed to generate equational theorem for `optimize`
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e1 : Expr
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bop : Unit
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i : BitVec 32
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heq : optimize e1 = Expr.const i
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⊢ (match bop,
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(Expr.rec (fun i => ⟨Expr.const i, PUnit.unit⟩)
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(fun op e1 e1_ih =>
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⟨match op, e1_ih.1 with
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| x, Expr.const i => Expr.op op (Expr.const 0)
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| x, x_1 => Expr.const 0,
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e1_ih⟩)
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e1).1 with
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| x, Expr.const i => Expr.op bop (Expr.const 0)
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| x, x_1 => Expr.const 0) =
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Expr.op bop (Expr.const 0)
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---
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error: Unknown identifier `optimize.eq_def`
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-/
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#guard_msgs in
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#check optimize.eq_def
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/--
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error: failed to generate equational theorem for `optimize`
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e1 : Expr
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bop : Unit
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i : BitVec 32
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heq : optimize e1 = Expr.const i
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⊢ (match bop,
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(Expr.rec (fun i => ⟨Expr.const i, PUnit.unit⟩)
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(fun op e1 e1_ih =>
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⟨match op, e1_ih.1 with
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| x, Expr.const i => Expr.op op (Expr.const 0)
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| x, x_1 => Expr.const 0,
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e1_ih⟩)
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e1).1 with
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| x, Expr.const i => Expr.op bop (Expr.const 0)
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| x, x_1 => Expr.const 0) =
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Expr.op bop (Expr.const 0)
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-/
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#guard_msgs in
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#print equations optimize
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-- works:
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def optimize2 : Expr → Expr
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| .const i => .const i
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| .op bop e1 =>
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match optimize2 e1 with
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| .const _ => .op bop (.const 0)
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| _ => .const 0
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/--
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info: equations:
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@[defeq] theorem optimize2.eq_1 : ∀ (i : BitVec 32), optimize2 (Expr.const i) = Expr.const i
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@[defeq] theorem optimize2.eq_2 : ∀ (bop : Unit) (e1 : Expr),
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optimize2 (Expr.op bop e1) =
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match optimize2 e1 with
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| Expr.const i => Expr.op bop (Expr.const 0)
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| x => Expr.const 0
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-/
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#guard_msgs in
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#print equations optimize2
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-- also works:
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def optimize3 : Expr → Expr
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| .const i => .const i
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| .op bop e1 =>
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match bop, e1 with
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| _, .const _ => .op bop (optimize3 e1)
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| _, _ => .const 0
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/--
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info: equations:
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@[defeq] theorem optimize3.eq_1 : ∀ (i : BitVec 32), optimize3 (Expr.const i) = Expr.const i
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@[defeq] theorem optimize3.eq_2 : ∀ (bop : Unit) (i : BitVec 32),
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optimize3 (Expr.op bop (Expr.const i)) = Expr.op bop (optimize3 (Expr.const i))
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theorem optimize3.eq_3 : ∀ (bop : Unit) (e1 : Expr),
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(∀ (i : BitVec 32), e1 = Expr.const i → False) → optimize3 (Expr.op bop e1) = Expr.const 0
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-/
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#guard_msgs in
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#print equations optimize3
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