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Project-declaredLean 4.31.0 · null

Opt compile correctness andor

Cedar.Thm.Opt.compile.correctness.andor

Project documentation

Correctness theorem for Opt.compile -- and and or cases

Exact Lean statement

theorem Opt.compile.correctness.andor (x₁ x₂ : Expr) (εnv : SymEnv) :
  Opt.compile (.and x₁ x₂) εnv = (do
    let term ← SymCC.compile (.and x₁ x₂) εnv
    let footprint := footprint (.and x₁ x₂) εnv
    .ok { term, footprint }
  )
  ∧
  Opt.compile (.or x₁ x₂) εnv = (do
    let term ← SymCC.compile (.or x₁ x₂) εnv
    let footprint := footprint (.or x₁ x₂) εnv
    .ok { term, footprint }
  )

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem Opt.compile.correctness.andor (x₁ x₂ : Expr) (εnv : SymEnv) :  Opt.compile (.and x₁ x₂) εnv = (do    let term  SymCC.compile (.and x₁ x₂) εnv    let footprint := footprint (.and x₁ x₂) εnv    .ok { term, footprint }  )    Opt.compile (.or x₁ x₂) εnv = (do    let term  SymCC.compile (.or x₁ x₂) εnv    let footprint := footprint (.or x₁ x₂) εnv    .ok { term, footprint }  ):= by  constructor  all_goals {    simp [Opt.compile, SymCC.compile, footprint]    rw [Opt.compile.correctness x₁ εnv, Opt.compile.correctness x₂ εnv]    simp [Opt.compileAnd, SymCC.compileAnd, Opt.compileOr, SymCC.compileOr, footprint.ofBranch, EmptyCollection.emptyCollection]    cases h₁ : SymCC.compile x₁ εnv <;> simp only [Except.bind_ok, Except.bind_err]    case ok t₁ =>      cases h₂ : SymCC.compile x₂ εnv <;> simp only [Except.bind_ok, Except.bind_err]      case error e => split <;> simp [*]      case ok t₂ =>        split <;> simp [*]        split <;> simp at *        split <;> simp [*]        first        | rw [Data.Set.union_empty_right (Data.Set.union_wf _ _)]        | rw [Data.Set.union_empty_right (footprint_wf _ _)]  }
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/SymCC/Opt/Compiler.lean:821-850

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