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Migrate most of the codebase (sans Reaching.lean / LICM left) to projections

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Danila Fedorin
2026-07-01 22:56:29 -05:00
parent 10b8fa97ca
commit 0e6976f9b4
7 changed files with 139 additions and 136 deletions
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55
lean/Spa/Language/Traces.lean
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@@ -93,12 +93,17 @@ def Trace.addEdge {g : Graph} {idx₁ idx₂ idx₃ : g.Index} {ρ₁ ρ₂ : En
| .single hnode, hedge => .cons hnode hedge .nil
| .edge hnode hedge' rest, hedge => .cons hnode hedge' (rest.addEdge hedge)
@[aesop simp]
def Traceₗ.append {g : Graph} {idx₁ idx₂ idx₃ : g.Index} {ρ₁ ρ₂ ρ₃ : Env} :
Traceₗ g idx₁ idx₂ ρ₁ ρ₂ → Traceₗ g idx₂ idx₃ ρ₂ ρ₃ →
Traceₗ g idx₁ idx₃ ρ₁ ρ₃
| .nil, rhs => rhs
| .cons hnode hedge rest, rhs => .cons hnode hedge (rest.append rhs)
@[simp] def traceₗ_append_nil {g : Graph} {idx₁ idx₂ : g.Index} {ρ₁ ρ₂ : Env}
{trₗ : Traceₗ g idx₁ idx₂ ρ₁ ρ₂} : trₗ.append Traceₗ.nil = trₗ := by
induction trₗ <;> aesop
def Traceₗ.appendTrace {g : Graph} {idx₁ idx₂ idx₃ : g.Index} {ρ₁ ρ₂ ρ₃ : Env} :
Traceₗ g idx₁ idx₂ ρ₁ ρ₂ → Trace g idx₂ idx₃ ρ₂ ρ₃ →
Trace g idx₁ idx₃ ρ₁ ρ₃
@@ -107,9 +112,7 @@ def Traceₗ.appendTrace {g : Graph} {idx₁ idx₂ idx₃ : g.Index} {ρ₁ ρ
def Traceₗ.appendStep {g : Graph} {idx₁ idx₂ : g.Index} {ρ₁ ρ₂ ρ₃ : Env} :
Traceₗ g idx₁ idx₂ ρ₁ ρ₂ → EvalBasicStmtOpt ρ₂ (g.nodes idx₂) ρ₃ →
Trace g idx₁ idx₂ ρ₁ ρ₃
| .nil, rhs => .single rhs
| .cons hnode hedge rest, rhs => .edge hnode hedge (rest.appendStep rhs)
Trace g idx₁ idx₂ ρ₁ ρ₃ := fun trₗ hbs => trₗ.appendTrace (Trace.single hbs)
def Trace.appendRight {g : Graph} {idx₁ idx₂ idx₃ : g.Index} {ρ₁ ρ₂ ρ₃ : Env} :
Trace g idx₁ idx₂ ρ₁ ρ₂ → Traceᵣ g idx₂ idx₃ ρ₂ ρ₃ →
@@ -133,53 +136,73 @@ instance instHAppendTraceTraceR {g : Graph} {idx₁ idx₂ idx₃ : g.Index} {ρ
HAppend (Trace g idx₁ idx₂ ρ₁ ρ₂) (Traceᵣ g idx₂ idx₃ ρ₂ ρ₃) (Trace g idx₁ idx₃ ρ₁ ρ₃) where
hAppend := Trace.appendRight
@[simp] lemma Traceₗ.append_addEdge {g : Graph}
{idx₁ idx₂ idx₃ idx₄ : g.Index} {ρ₁ ρ₂ ρ₃ ρ₄ : Env}
(trₗ : Traceₗ g idx₁ idx₂ ρ₁ ρ₂)
(hnode : EvalBasicStmtOpt ρ₂ (g.nodes idx₂) ρ₃)
(hedge : (idx₂, idx₃) ∈ g.edges)
(rest : Traceₗ g idx₃ idx₄ ρ₃ ρ₄) :
trₗ.append (Traceₗ.cons hnode hedge rest) =
(Trace.addEdge (trₗ.appendStep hnode) hedge).append rest := by
induction trₗ <;> simp [Traceₗ.append, Traceₗ.appendStep, Traceₗ.appendTrace, Trace.addEdge, *]
@[simp] lemma Traceₗ.appendTrace_addEdge {g : Graph}
{idx₁ idx₂ idx₃ idx₄ : g.Index} {ρ₁ ρ₂ ρ₃ ρ₄ : Env}
(trₗ : Traceₗ g idx₁ idx₂ ρ₁ ρ₂)
(hnode : EvalBasicStmtOpt ρ₂ (g.nodes idx₂) ρ₃)
(hedge : (idx₂, idx₃) ∈ g.edges)
(rest : Trace g idx₃ idx₄ ρ₃ ρ₄) :
trₗ.appendTrace (Trace.edge hnode hedge rest) =
(Trace.addEdge (trₗ.appendStep hnode) hedge).appendTrace rest := by
induction trₗ <;> simp [Traceₗ.appendTrace, Traceₗ.appendStep, Trace.addEdge, *]
/-- A beginning-to-end trace corresponding to the CFG `g`. -/
inductive EndToEndTrace (g : Graph) (ρ₁ ρ₂ : Env) : Type
| intro (idx₁ : g.Index) (idx₁_mem : idx₁ ∈ g.inputs)
(idx₂ : g.Index) (idx₂_mem : idx₂ ∈ g.outputs)
(trace : Trace g idx₁ idx₂ ρ₁ ρ₂) : EndToEndTrace g ρ₁ ρ₂
inductive MyReaches {prog : Program} : {s₁ s₂ : prog.State} → {ρ₁ ρ₂ : Env} →
inductive Reaches {prog : Program} : {s₁ s₂ : prog.State} → {ρ₁ ρ₂ : Env} →
Trace prog.cfg s₁ s₂ ρ₁ ρ₂ →
(s : prog.State) → (ρin ρout : Env) → Type
| single_here {s₁ : prog.State} {ρ₁ ρ₂ : Env}
(hnode : EvalBasicStmtOpt ρ₁ (prog.code s₁) ρ₂) :
MyReaches (.single hnode) s₁ ρ₁ ρ₂
Reaches (.single hnode) s₁ ρ₁ ρ₂
| edge_here {s₁ s₂ s₃ : prog.State} {ρ₁ ρ₂ ρ₃ : Env}
(hnode : EvalBasicStmtOpt ρ₁ (prog.code s₁) ρ₂)
(hedge : (s₁, s₂) ∈ prog.cfg.edges) (rest : Trace prog.cfg s₂ s₃ ρ₂ ρ₃) :
MyReaches (.edge hnode hedge rest) s₁ ρ₁ ρ₂
Reaches (.edge hnode hedge rest) s₁ ρ₁ ρ₂
| edge_there {s₁ s₂ s₃ : prog.State} {ρ₁ ρ₂ ρ₃ : Env}
(hnode : EvalBasicStmtOpt ρ₁ (prog.code s₁) ρ₂)
(hedge : (s₁, s₂) ∈ prog.cfg.edges) (rest : Trace prog.cfg s₂ s₃ ρ₂ ρ₃)
{s : prog.State} {ρin ρout : Env} :
MyReaches rest s ρin ρout →
MyReaches (.edge hnode hedge rest) s ρin ρout
Reaches rest s ρin ρout →
Reaches (.edge hnode hedge rest) s ρin ρout
def MyReaches.pre {prog : Program} {s₁ s₂ s: prog.State}
def Reaches.pre {prog : Program} {s₁ s₂ s: prog.State}
{ρ₁ ρ₂ ρin ρout : Env} {tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂} :
(r : MyReaches tr s ρin ρout) → Traceₗ prog.cfg s₁ s ρ₁ ρin
(r : Reaches tr s ρin ρout) → Traceₗ prog.cfg s₁ s ρ₁ ρin
| .single_here _ => .nil
| .edge_here _ _ _ => .nil
| .edge_there hnode hedge _ r => .cons hnode hedge r.pre
def MyReaches.post {prog : Program} {s₁ s₂ s: prog.State}
def Reaches.post {prog : Program} {s₁ s₂ s: prog.State}
{ρ₁ ρ₂ ρin ρout : Env} {tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂} :
(r : MyReaches tr s ρin ρout) → Trace prog.cfg s₁ s ρ₁ ρout
(r : Reaches tr s ρin ρout) → Trace prog.cfg s₁ s ρ₁ ρout
| .single_here hnode => .single hnode
| .edge_here hnode _ _ => .single hnode
| .edge_there hnode hedge _ r => .edge hnode hedge r.post
def MyReaches.first {prog : Program} {s₁ s₂ s: prog.State}
def Reaches.first {prog : Program} {s₁ s₂ s: prog.State}
{ρ₁ ρ₂ ρin ρout : Env} {tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂} :
(r : MyReaches tr s ρin ρout) → Σ ρ₁', MyReaches tr s₁ ρ₁ ρ₁'
(r : Reaches tr s ρin ρout) → Σ ρ₁', Reaches tr s₁ ρ₁ ρ₁'
| .single_here hnode => ⟨_, .single_here hnode⟩
| .edge_here hnode hedge hrest => ⟨_, .edge_here hnode hedge hrest⟩
| .edge_there hnode hedge hrest tmp' => ⟨_, .edge_here hnode hedge hrest⟩
def MyReaches.step {prog : Program} {s₁ s₂ s: prog.State}
def Reaches.step {prog : Program} {s₁ s₂ s: prog.State}
{ρ₁ ρ₂ ρin ρout : Env} {tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂} :
(r : MyReaches tr s ρin ρout) → EvalBasicStmtOpt ρin (prog.code s) ρout
(r : Reaches tr s ρin ρout) → EvalBasicStmtOpt ρin (prog.code s) ρout
| .single_here hnode => hnode
| .edge_here hnode hedge hrest => hnode
| .edge_there hnode hedge hrest tmp' => tmp'.step