85 lines
2.2 KiB
Plaintext
85 lines
2.2 KiB
Plaintext
theory Examples
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imports "../src/Frontend"
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begin
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definition cascade :: "nat instruction list" where
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"cascade = [Jump 127, Jump 130] @ replicate 128 Nop @ [Stop]"
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definition countdown :: "nat instruction list" where
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"countdown = [Inc, Inc, Inc, Dec, Zero 6, Jump 3, Stop]"
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definition forward :: "nat \<Rightarrow> nat instruction list" where
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"forward n = [Jump (Suc n)] @ replicate n Nop @ [Stop]"
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definition backward :: "nat \<Rightarrow> nat instruction list" where
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"backward n = replicate n Nop @ [Jump 0, Stop]"
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lemma cascade_rounds:
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"map (\<lambda>W. filter (\<lambda>i. i \<in> W) [0..<length cascade]) (history cascade {}) = [[], [1], [0,1]]"
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by eval
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lemma cascade_size: "map_option length (assemble cascade) = Some 135"
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by eval
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lemma forward_short: "layout (forward 127) = {}"
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by eval
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lemma forward_long: "layout (forward 128) = {0}"
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by eval
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lemma backward_short: "layout (backward 126) = {}"
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by eval
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lemma backward_long: "layout (backward 127) = {127}"
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by eval
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lemma countdown_execution:
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"execute (source_step countdown) 32 (0,0) = (6,0)"
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by eval
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lemma countdown_bytes:
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"assemble countdown = Some [1,1,1,2,17,130,16,123,3]"
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by eval
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lemma short_negative_boundary:
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"decode [16,0] = Some (Branch False False (-128), [])"
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by eval
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lemma long_negative_boundary:
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"decode [18,0,0] = Some (Branch False True (-32768), [])"
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by eval
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lemma long_positive_boundary:
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"decode [18,255,255] = Some (Branch False True 32767, [])"
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by eval
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lemma truncated_rejected: "decode [18,1] = None"
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by eval
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lemma unknown_rejected: "decode [255] = None"
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by eval
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lemma short_payload_rejected: "decode [16,256] = None"
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by eval
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lemma long_payload_rejected: "decode [19,0,256] = None"
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by eval
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lemma decoder_preserves_tail:
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"decode [19,255,255,3,255] = Some (Branch True True 32767, [3,255])"
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by eval
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lemma undefined_rejected:
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"compile ''jmp missing'' = Error ''undefined label missing''"
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by eval
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lemma duplicate_rejected:
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"compile (''label a'' @ newline @ ''label a'') = Error ''duplicate label a''"
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by eval
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lemma final_label_rejected:
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"compile (''jmp end'' @ newline @ ''label end'') = Error ''branch targets a label after the final instruction''"
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by eval
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end
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