Project-declaredLean 4.32.0 · mathlib@81a5d257

Wp Except T bind

OracleComp.ProgramLogic.Loom.wp_ExceptT_bind

program verification separation logic cryptography quantitative

Plain-language statement

Quantitative Std.Do'.WP interpretation of OracleComp spec valued in ℝ≥0∞. The wpTrans is the existing MAlgOrdered.wp (i.e. expectation of post under evalDist); the EPost.nil argument is ignored since OracleComp has no first-class exception slot. The three WP axioms reduce to the existing MAlgOrdered.{wp_pure, wp_bind, wp_mono} equali...

Exact Lean statement

@[simp]
theorem wp_ExceptT_bind {ε : Type} (x : ExceptT ε (OracleComp spec) α)
    (f : α → ExceptT ε (OracleComp spec) β) (post : β → ℝ≥0∞)
    (epost : EPost.cons (ε → ℝ≥0∞) EPost.nil) :
    Std.Do'.wp (x >>= f) post epost =
      Std.Do'.wp x (fun a => Std.Do'.wp (f a) post epost) epost

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

@[simp]theorem wp_ExceptT_bind {ε : Type} (x : ExceptT ε (OracleComp spec) α)    (f : α → ExceptT ε (OracleComp spec) β) (post : β → ℝ≥0∞)    (epost : EPost.cons (ε → ℝ≥0∞) EPost.nil) :    Std.Do'.wp (x >>= f) post epost =      Std.Do'.wp x (fun a => Std.Do'.wp (f a) post epost) epost := by  change MAlgOrdered.wp (m := OracleComp spec) (l := ℝ≥0∞) ((x >>= f).run)      (epost.pushExcept post) =    MAlgOrdered.wp (m := OracleComp spec) (l := ℝ≥0∞) x.run      (epost.pushExcept fun a =>        MAlgOrdered.wp (m := OracleComp spec) (l := ℝ≥0∞) (f a).run          (epost.pushExcept post))  rw [ExceptT.run_bind, MAlgOrdered.wp_bind]  congr 1 with ea  cases ea <;> simp [EPost.cons.pushExcept, MAlgOrdered.wp_pure]

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/ProgramLogic/Unary/Loom/Quantitative.lean:330-344

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