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114 lines
7.2 KiB
Text
114 lines
7.2 KiB
Text
import SilverSight.Receipt
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namespace SilverSight
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open Semantics.FixedPoint
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open Semantics.FixedPoint.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Receipt composition (bind)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Compose two receipts into a single receipt.
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The resulting receipt:
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- has gateType = .compose
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- has cost = left.cost + right.cost (additive)
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- has invariant = left.invariant ++ " ∧ " ++ right.invariant (conjunction)
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- has timestamp = max(left.timestamp, right.timestamp) (latest)
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- is well-formed iff both inputs are well-formed
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This is the fundamental composition primitive for the SilverSight receipt ledger. -/
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def bindReceipt (left right : Receipt) : Receipt :=
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{ gateType := .compose
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cost := add left.cost right.cost
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invariant := left.invariant ++ " ∧ " ++ right.invariant
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timestamp := max left.timestamp right.timestamp
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wellFormed := left.wellFormed && right.wellFormed }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Well-formedness preservation
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- bind preserves well-formedness: if both inputs are well-formed,
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the result is well-formed. -/
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theorem bind_preservesWellFormed (left right : Receipt)
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(hl : left.wellFormed = true) (hr : right.wellFormed = true) :
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(bindReceipt left right).wellFormed = true := by
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simp [bindReceipt, hl, hr]
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/-- bind preserves well-formedness (forward direction): if the result
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is well-formed, both inputs must be well-formed. -/
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theorem bind_wellFormed_implies_inputs (left right : Receipt)
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(h : (bindReceipt left right).wellFormed = true) :
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left.wellFormed = true ∧ right.wellFormed = true := by
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simp only [bindReceipt] at h
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exact Bool.and_eq_true_iff.mp h
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Cost properties
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- bind cost is the sum of the component costs. -/
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theorem bind_cost_additive (left right : Receipt) :
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(bindReceipt left right).cost = add left.cost right.cost := by
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rfl
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Timestamp properties
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- bind timestamp is the maximum of the component timestamps. -/
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theorem bind_timestamp_max (left right : Receipt) :
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(bindReceipt left right).timestamp = max left.timestamp right.timestamp := by
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rfl
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/-- bind timestamp is commutative. -/
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theorem bind_timestamp_comm (left right : Receipt) :
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(bindReceipt left right).timestamp = (bindReceipt right left).timestamp := by
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simp [bindReceipt, Nat.max_comm]
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Associativity (well-formedness only)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- bind is associative on well-formedness. -/
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theorem bind_wellFormed_assoc (a b c : Receipt) :
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(bindReceipt (bindReceipt a b) c).wellFormed =
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(bindReceipt a (bindReceipt b c)).wellFormed := by
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simp [bindReceipt, Bool.and_assoc]
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Invariant properties
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- bind invariant is the conjunction of the component invariants. -/
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theorem bind_invariant_conjunction (left right : Receipt) :
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(bindReceipt left right).invariant = left.invariant ++ " ∧ " ++ right.invariant := by
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rfl
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Gate type properties
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- bind always produces a compose gate. -/
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theorem bind_gateType (left right : Receipt) :
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(bindReceipt left right).gateType = .compose := by
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rfl
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 #eval witnesses
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-- ═══════════════════════════════════════════════════════════════════════════
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def r1 := mkReceipt .encode (Q16_16.ofInt 50) "schema:UInt8" 1
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def r2 := mkReceipt .decode (Q16_16.ofInt 30) "schema:Bool" 2
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def r3 := mkReceipt .validate (Q16_16.ofInt 20) "wellformed" 3
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#eval (bindReceipt r1 r2).gateType -- expected: GateType.compose
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#eval (bindReceipt r1 r2).wellFormed -- expected: true
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#eval (bindReceipt r1 r2).invariant -- expected: "schema:UInt8 ∧ schema:Bool"
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#eval (bindReceipt r1 r2).timestamp -- expected: 2
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#eval (bindReceipt (bindReceipt r1 r2) r3).invariant -- expected: "schema:UInt8 ∧ schema:Bool ∧ wellformed"
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#eval (bindReceipt r1 r2).cost -- expected: 5242880 (Q16_16 of 80)
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#eval (bindReceipt r1 r2).wellFormed -- expected: true
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end SilverSight
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