Verified Commit a3a9eb26 authored by james's avatar james
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feat(encoding): prove canonical decoding and instruction injectivity

parent a68ad347

src/Encoding.thy

+17 −0
Changes for src/Encoding.thy: 17 added lines, 0 removed lines.
Original line number Diff line number Diff line
@@ -53,6 +53,23 @@ theorem decode_encode: 
  by (cases op)

    (auto simp: byte_join nat_less_iff div_less_iff_less_mult split: bool.splits if_splits)



theorem decode_canonical:

  "decode bs = Some (op, rest) \<Longrightarrow> encodable op \<and> bs = encode op @ rest"

  by (cases bs)

    (auto simp: nat_less_iff div_less_iff_less_mult mod_less div_eq_0_iff

      nat_add_distrib nat_mult_distrib

      split: if_splits list.splits)



corollary decode_progress:

  "decode bs = Some (op, rest) \<Longrightarrow> length rest < length bs"

  using decode_canonical[of bs op rest]

  by (cases op) (auto split: bool.splits)



theorem encode_injective:

  "encodable a \<Longrightarrow> encodable b \<Longrightarrow> encode a = encode b \<longleftrightarrow> a = b"

  using decode_encode[of a "[]"] decode_encode[of b "[]"]

  by (metis append_Nil option.inject prod.inject)



fun lower :: "nat instruction list \<Rightarrow> nat set \<Rightarrow> nat \<Rightarrow> nat instruction \<Rightarrow> operation" where

  "lower p W i Nop = Idle"

| "lower p W i Inc = Raise"

tests/Examples.thy

+10 −0
Changes for tests/Examples.thy: 10 added lines, 0 removed lines.
Original line number Diff line number Diff line
@@ -59,6 +59,16 @@ lemma truncated_rejected: "decode [18,1] = None" 
lemma unknown_rejected: "decode [255] = None"

  by eval



lemma short_payload_rejected: "decode [16,256] = None"

  by eval



lemma long_payload_rejected: "decode [19,0,256] = None"

  by eval



lemma decoder_preserves_tail:

  "decode [19,255,255,3,255] = Some (Branch True True 32767, [3,255])"

  by eval



lemma undefined_rejected:

  "compile ''jmp missing'' = Error ''undefined label missing''"

  by eval