lib: Add a new nitpick-style command for refuting word problems.
This commit is contained in:
Matthew Fernandez
parent
411ef475dc
commit
53376140e0
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(*
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* Copyright 2015, NICTA
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*
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* This software may be distributed and modified according to the terms of
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* the BSD 2-Clause license. Note that NO WARRANTY is provided.
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* See "LICENSE_BSD2.txt" for details.
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*
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* @TAG(NICTA_BSD)
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*)
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theory Etanercept imports
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"~~/src/HOL/Word/Word"
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NICTACompat
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SignedWords
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WordBitwiseSigned
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keywords
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"etanercept" :: diag
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begin
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text {*
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This theory implements a tool for refuting word propositions. It works by constructing a C program
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that exhaustively explores the state space of your proposition.
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It is currently a work in progress and has the following known issues:
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- Temporary files are just left for Isabelle to clean up when it exits. Should we be attempting
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to remove these ourselves?
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- The exploration strategy is completely naive, which simplifies the code, but sometimes leads to
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a failure to find trivial counter-examples.
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- There's no support for HOL binders like \<forall> and \<exists>. These could be supported relatively easily
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with GNU statement expressions, but I'm unsure if it's worth it.
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- We currently only support 8-, 16-, 32-, and 64-bit words. It would be straightforward to
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support other non-standard widths if required.
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- Much of the pattern matching in this theory was generated by a script and is quite verbose. It
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could probably be simplified.
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The tool is named after etanercept, an ill-advised treatment for primary progressive aphasia, a
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condition who's symptoms include an inability to find the right words for things. Amusingly the
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word "etanercept" is also quite hard to remember.
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*}
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ML {*
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signature ETANERCEPT =
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sig
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end;
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structure Etanercept : ETANERCEPT =
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struct
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(* Toggle this to enable debugging output. *)
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val debug = false
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(* XXX: Clagged from metis *)
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fun dropWhile p =
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let
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fun f [] = []
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| f (l as x :: xs) = if p x then f xs else l
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in
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f
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end
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(* Exponentiation. *)
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fun exp base n = Real.floor (Math.pow (Real.fromInt base, Real.fromInt n))
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(* Strip whitespace from the end of a string. *)
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fun rstrip s =
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s
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|> String.explode
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|> List.rev
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|> dropWhile Char.isSpace
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|> List.rev
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|> String.implode
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(* Generate a string that's safe to put in a C string. In particular, we escape backslashes and
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* remove trailing underscores. The latter is not for string safety, but because focusing leads to
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* a variable named, e.g. "x__", that originated from a meta-bound "x". Stripping these
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* underscores makes the counter-example output clearer to the user.
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*)
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fun safe_name s =
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s
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|> String.explode
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|> map (fn c => if c = #"\\" then "\\\\" else String.implode [c])
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|> List.rev
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|> dropWhile (fn c => c = "_")
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|> List.rev
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|> String.concat
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(* Find a C compiler. Prefer Clang. *)
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val cc =
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let
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val (clang, r1) = Isabelle_System.bash_output "which clang";
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val (gcc, r2) = Isabelle_System.bash_output "which gcc"
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in
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if r1 = 0 then SOME (rstrip clang ^ " -Wno-tautological-compare") else
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if r2 = 0 then SOME (rstrip gcc) else
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NONE
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end
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(* Compile a C program. *)
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fun compile file =
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case cc of
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SOME compiler =>
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let
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val serial = serial_string ();
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val tmp = File.shell_path (File.tmp_path (Path.explode ("etanercept" ^ serial ^ ".exe")));
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val (_, ret) = Isabelle_System.bash_output (compiler ^ " -O3 -o " ^ tmp ^ " " ^ file)
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in
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if ret = 0
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then tmp
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else error "failed to compile generated program (BUG)"
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end
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| NONE => error "no available C compiler"
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(* Find index of x in xs *)
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fun indexOf xs x =
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let
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fun indexOf' i xs x =
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case xs of
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[] => NONE
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| (y::ys) => if x = y then SOME i else indexOf' (i + 1) ys x
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in
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indexOf' 0 xs x
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end
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(* FIXME: ugh *)
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fun type_supported [typ] =
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(case typ of
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@{typ 8} => true
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| @{typ "8 signed"} => true
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| @{typ 16} => true
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| @{typ "16 signed"} => true
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| @{typ 32} => true
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| @{typ "32 signed"} => true
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| @{typ 64} => true
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| @{typ "64 signed"} => true
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| _ => false)
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| type_supported _ = false
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(* Find a previously seen variable's index or register a newly discovered variable. *)
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fun var_index vs v =
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case indexOf vs v of
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NONE => (vs @ [v], length vs)
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| SOME n => (vs, n)
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(* The C symbol for the nth variable. *)
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fun to_var n = "v" ^ Int.toString n
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fun min_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "INT8_MIN"
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| min_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "INT16_MIN"
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| min_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "INT32_MIN"
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| min_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "INT64_MIN"
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| min_of (Var (_, Type (@{type_name "Word.word"}, _))) = "0"
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| min_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "INT8_MIN"
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| min_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "INT16_MIN"
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| min_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "INT32_MIN"
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| min_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "INT64_MIN"
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| min_of (Var (_, Type (@{type_name nat}, _))) = "0"
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| min_of (Var (_, Type (@{type_name int}, _))) = "INTMAX_MIN"
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| min_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "INT8_MIN"
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| min_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "INT16_MIN"
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| min_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "INT32_MIN"
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| min_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "INT64_MIN"
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| min_of (Free (_, Type (@{type_name "Word.word"}, _))) = "0"
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| min_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "INT8_MIN"
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| min_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "INT16_MIN"
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| min_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "INT32_MIN"
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| min_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "INT64_MIN"
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| min_of (Free (_, Type (@{type_name nat}, _))) = "0"
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| min_of (Free (_, Type (@{type_name int}, _))) = "INTMAX_MIN"
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| min_of _ = error "unsupported type (BUG)"
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fun max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 8}]))) = "UINT8_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "INT8_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 16}]))) = "UINT16_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "INT16_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 32}]))) = "UINT32_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "INT32_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 64}]))) = "UINT64_MAX"
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| max_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "INT64_MAX"
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| max_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "INT8_MAX"
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| max_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "INT16_MAX"
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| max_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "INT32_MAX"
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| max_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "INT64_MAX"
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| max_of (Var (_, Type (@{type_name nat}, _))) = "UINTMAX_MAX"
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| max_of (Var (_, Type (@{type_name int}, _))) = "INTMAX_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 8}]))) = "UINT8_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "INT8_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 16}]))) = "UINT16_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "INT16_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 32}]))) = "UINT32_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "INT32_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 64}]))) = "UINT64_MAX"
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| max_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "INT64_MAX"
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| max_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "INT8_MAX"
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| max_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "INT16_MAX"
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| max_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "INT32_MAX"
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| max_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "INT64_MAX"
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| max_of (Free (_, Type (@{type_name nat}, _))) = "UINTMAX_MAX"
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| max_of (Free (_, Type (@{type_name int}, _))) = "INTMAX_MAX"
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| max_of _ = error "unsupported type (BUG)"
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fun type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 8}]))) = "uint8_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "int8_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 16}]))) = "uint16_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "int16_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 32}]))) = "uint32_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "int32_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 64}]))) = "uint64_t"
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| type_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "int64_t"
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| type_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "int8_t"
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| type_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "int16_t"
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| type_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "int32_t"
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| type_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "int64_t"
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| type_of (Var (_, Type (@{type_name nat}, _))) = "uintmax_t"
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| type_of (Var (_, Type (@{type_name int}, _))) = "intmax_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 8}]))) = "uint8_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "int8_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 16}]))) = "uint16_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "int16_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 32}]))) = "uint32_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "int32_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 64}]))) = "uint64_t"
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| type_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "int64_t"
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| type_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "int8_t"
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| type_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "int16_t"
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| type_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "int32_t"
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| type_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "int64_t"
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| type_of (Free (_, Type (@{type_name nat}, _))) = "uintmax_t"
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| type_of (Free (_, Type (@{type_name int}, _))) = "intmax_t"
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| type_of _ = error "unsupported type (BUG)"
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fun name_of (Var ((name, _), _)) = safe_name name
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| name_of (Free (name, _)) = safe_name name
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| name_of _ = error "unexpected variable (BUG)"
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fun format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 8}]))) = "PRIu8"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "PRId8"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 16}]))) = "PRIu16"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "PRId16"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 32}]))) = "PRIu32"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "PRId32"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ 64}]))) = "PRIu64"
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| format_of (Var (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "PRId64"
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| format_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "PRId8"
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| format_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "PRId16"
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| format_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "PRId32"
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| format_of (Var (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "PRId64"
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| format_of (Var (_, Type (@{type_name nat}, _))) = "PRIuMAX"
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| format_of (Var (_, Type (@{type_name int}, _))) = "PRIdMAX"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 8}]))) = "PRIu8"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "8 signed"}]))) = "PRId8"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 16}]))) = "PRIu16"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "16 signed"}]))) = "PRId16"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 32}]))) = "PRIu32"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "32 signed"}]))) = "PRId32"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ 64}]))) = "PRIu64"
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| format_of (Free (_, Type (@{type_name "Word.word"}, [@{typ "64 signed"}]))) = "PRId64"
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| format_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 8}]))) = "PRId8"
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| format_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 16}]))) = "PRId16"
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| format_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 32}]))) = "PRId32"
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| format_of (Free (_, Type (@{type_name "SignedWords.signed"}, [@{typ 64}]))) = "PRId64"
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| format_of (Free (_, Type (@{type_name nat}, _))) = "PRIuMAX"
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| format_of (Free (_, Type (@{type_name int}, _))) = "PRIdMAX"
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| format_of _ = error "unsupported type (BUG)"
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fun cast_to _ @{typ "8 signed word \<Rightarrow> 8 signed word"} = "int8_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 8 word"} = "uint8_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 16 signed word"} = "int16_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 16 word"} = "uint16_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 32 signed word"} = "int32_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 32 word"} = "uint32_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 64 signed word"} = "int64_t"
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| cast_to _ @{typ "8 signed word \<Rightarrow> 64 word"} = "uint64_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 8 signed word"} = "int8_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 8 word"} = "uint8_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 16 signed word"} = "int16_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 16 word"} = "uint16_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 32 signed word"} = "int32_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 32 word"} = "uint32_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 64 signed word"} = "int64_t"
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| cast_to _ @{typ "8 word \<Rightarrow> 64 word"} = "uint64_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 8 signed word"} = "int8_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 8 word"} = "uint8_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 16 signed word"} = "int16_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 16 word"} = "uint16_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 32 signed word"} = "int32_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 32 word"} = "uint32_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 64 signed word"} = "int64_t"
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| cast_to _ @{typ "16 signed word \<Rightarrow> 64 word"} = "uint64_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 8 signed word"} = "int8_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 8 word"} = "uint8_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 16 signed word"} = "int16_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 16 word"} = "uint16_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 32 signed word"} = "int32_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 32 word"} = "uint32_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 64 signed word"} = "int64_t"
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| cast_to _ @{typ "16 word \<Rightarrow> 64 word"} = "uint64_t"
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| cast_to _ @{typ "32 signed word \<Rightarrow> 8 signed word"} = "int8_t"
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| cast_to _ @{typ "32 signed word \<Rightarrow> 8 word"} = "uint8_t"
|
||||
| cast_to _ @{typ "32 signed word \<Rightarrow> 16 signed word"} = "int16_t"
|
||||
| cast_to _ @{typ "32 signed word \<Rightarrow> 16 word"} = "uint16_t"
|
||||
| cast_to _ @{typ "32 signed word \<Rightarrow> 32 signed word"} = "int32_t"
|
||||
| cast_to _ @{typ "32 signed word \<Rightarrow> 32 word"} = "uint32_t"
|
||||
| cast_to _ @{typ "32 signed word \<Rightarrow> 64 signed word"} = "int64_t"
|
||||
| cast_to _ @{typ "32 signed word \<Rightarrow> 64 word"} = "uint64_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 8 signed word"} = "int8_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 8 word"} = "uint8_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 16 signed word"} = "int16_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 16 word"} = "uint16_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 32 signed word"} = "int32_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 32 word"} = "uint32_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 64 signed word"} = "int64_t"
|
||||
| cast_to _ @{typ "32 word \<Rightarrow> 64 word"} = "uint64_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 8 signed word"} = "int8_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 8 word"} = "uint8_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 16 signed word"} = "int16_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 16 word"} = "uint16_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 32 signed word"} = "int32_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 32 word"} = "uint32_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 64 signed word"} = "int64_t"
|
||||
| cast_to _ @{typ "64 signed word \<Rightarrow> 64 word"} = "uint64_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 8 signed word"} = "int8_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 8 word"} = "uint8_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 16 signed word"} = "int16_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 16 word"} = "uint16_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 32 signed word"} = "int32_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 32 word"} = "uint32_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 64 signed word"} = "int64_t"
|
||||
| cast_to _ @{typ "64 word \<Rightarrow> 64 word"} = "uint64_t"
|
||||
| cast_to st t = error ("unsupported ucast/scast result type: " ^
|
||||
Pretty.string_of (Syntax.pretty_typ (Proof.context_of st) t))
|
||||
|
||||
(* A printf format string for printing the variables. *)
|
||||
fun format_string vs =
|
||||
case vs of
|
||||
[] => ""
|
||||
| (y::ys) => "\" " ^ name_of y ^ " = %\" " ^ format_of y ^ " \"\\n\" " ^ format_string ys
|
||||
|
||||
(* The variables as a list of arguments to be passed to a C function. *)
|
||||
fun as_args vs =
|
||||
let
|
||||
fun as_args' n vs =
|
||||
case vs of
|
||||
[] => ""
|
||||
| (_::ys) => ", " ^ to_var n ^ as_args' (n + 1) ys
|
||||
in
|
||||
as_args' 0 vs
|
||||
end
|
||||
|
||||
(* Initialisation for the variables. *)
|
||||
fun loop_header vs =
|
||||
let
|
||||
fun loop_header' i vs =
|
||||
case vs of
|
||||
[] => ""
|
||||
| (y::ys) => type_of y ^ " " ^ to_var i ^ ";\n" ^
|
||||
"for (" ^ to_var i ^ " = " ^ min_of y ^ "; ; " ^ to_var i ^ "++) {\n" ^
|
||||
loop_header' (i + 1) ys
|
||||
in
|
||||
loop_header' 0 vs
|
||||
end
|
||||
|
||||
(* Per-variable loop termination. *)
|
||||
fun loop_footer vs =
|
||||
let
|
||||
fun loop_footer' i vs =
|
||||
case vs of
|
||||
[] => ""
|
||||
| (y::ys) => loop_footer' (i + 1) ys ^
|
||||
"if (" ^ to_var i ^ " == " ^ max_of y ^ ") { break; }\n" ^
|
||||
"}\n"
|
||||
in
|
||||
loop_footer' 0 vs
|
||||
end
|
||||
|
||||
(* Translate an Isabelle term into the equivalent C expression, collecting discovered variables
|
||||
* along the way.
|
||||
*)
|
||||
fun translate state vs t =
|
||||
let
|
||||
val tr = translate state
|
||||
fun bin_op op1 op2 =
|
||||
let val (vs', s1) = tr vs op1;
|
||||
val (vs'', s2) = tr vs' op2
|
||||
in (vs'', s1, s2)
|
||||
end
|
||||
in
|
||||
case t of
|
||||
@{term "Trueprop"} $ t' => tr vs t'
|
||||
| @{term "True"} => (vs, "true")
|
||||
| @{term "False"} => (vs, "false")
|
||||
| Const (@{const_name HOL.eq}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " == " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name HOL.Not}, _) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "(!" ^ s ^ ")")
|
||||
end
|
||||
| Const (@{const_name less}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " < " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name less_eq}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " <= " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name plus}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " + " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name minus}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " - " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name times}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " * " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name uminus}, _) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "(-" ^ s ^ ")")
|
||||
end
|
||||
| Const (@{const_name div}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s2 ^ " == 0 ? 0 : (" ^ s1 ^ " / " ^ s2 ^ "))")
|
||||
end
|
||||
| Const (@{const_name mod}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s2 ^ " == 0 ? " ^ s1 ^ " : (" ^ s1 ^ " % " ^ s2 ^ "))")
|
||||
end
|
||||
| Const (@{const_name HOL.implies}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "((!" ^ s1 ^ ") || (" ^ s2 ^ "))")
|
||||
end
|
||||
| Const (@{const_name Bits.shiftl}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " << " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name Bits.shiftr}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " >> " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name Bits.bitAND}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " & " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name Bits.bitOR}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " | " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name Bits.bitXOR}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " ^ " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name Bits.bitNOT}, _) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "(~" ^ s ^ ")")
|
||||
end
|
||||
| Const (@{const_name Bits.test_bit}, _) $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " ^ & (1ULL << " ^ s2 ^ "))")
|
||||
end
|
||||
| Const (@{const_name Bits.lsb}, _) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "(" ^ s ^ " & 1)")
|
||||
end
|
||||
| Const (@{const_name Word.ucast}, typ) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "((" ^ cast_to state typ ^ ")" ^ s ^ ")")
|
||||
end
|
||||
| Const (@{const_name Word.scast}, typ) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "((" ^ cast_to state typ ^ ")" ^ s ^ ")")
|
||||
end
|
||||
| Free (name, Type (@{type_name "Word.word"}, typs)) =>
|
||||
if type_supported typs
|
||||
then let val (vs', n) = var_index vs t
|
||||
in (vs', to_var n)
|
||||
end
|
||||
else error ("unsupported word width of variable " ^ name)
|
||||
| Var ((name, _), Type (@{type_name "Word.word"}, typs)) =>
|
||||
if type_supported typs
|
||||
then let val (vs', n) = var_index vs t
|
||||
in (vs', to_var n)
|
||||
end
|
||||
else error ("unsupported word width of variable " ^ name)
|
||||
| Free (_, Type (@{type_name nat}, _)) =>
|
||||
let val (vs', n) = var_index vs t
|
||||
in (vs', to_var n)
|
||||
end
|
||||
| Var (_, Type (@{type_name nat}, _)) =>
|
||||
let val (vs', n) = var_index vs t
|
||||
in (vs', to_var n)
|
||||
end
|
||||
| Free (_, Type (@{type_name int}, _)) =>
|
||||
let val (vs', n) = var_index vs t
|
||||
in (vs', to_var n)
|
||||
end
|
||||
| Var (_, Type (@{type_name int}, _)) =>
|
||||
let val (vs', n) = var_index vs t
|
||||
in (vs', to_var n)
|
||||
end
|
||||
| @{const HOL.conj} $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " && " ^ s2 ^ ")")
|
||||
end
|
||||
| @{const HOL.disj} $ a $ b =>
|
||||
let val (vs', s1, s2) = bin_op a b
|
||||
in (vs', "(" ^ s1 ^ " || " ^ s2 ^ ")")
|
||||
end
|
||||
| Const (@{const_name Groups.zero}, _) => (vs, "(0)")
|
||||
| Const (@{const_name Groups.one}, _) => (vs, "(1)")
|
||||
| Const (@{const_name Suc}, _) $ a =>
|
||||
let val (vs', s) = tr vs a
|
||||
in (vs', "(1 + " ^ s ^ ")")
|
||||
end
|
||||
| Const (@{const_name numeral}, _) $ a =>
|
||||
(* XXX: Clagged from c-parser *)
|
||||
let fun calc acc base t = case t of
|
||||
Const (@{const_name "Num.num.Bit0"}, _) $ t' => calc acc (base * 2) t'
|
||||
| Const (@{const_name "Num.num.Bit1"}, _) $ t' => calc (acc + base) (base * 2) t'
|
||||
| Const (@{const_name "Num.num.One"}, _) => acc + base
|
||||
| _ => error "unexpected numeric literal case (BUG)";
|
||||
val v = calc 0 1 a;
|
||||
val suffix = if v > exp 2 32 - 1 then "ull" else ""
|
||||
in (vs, "(" ^ string_of_int (calc 0 1 a) ^ suffix ^ ")")
|
||||
end
|
||||
| _ => error ("unsupported subterm " ^ Pretty.string_of (Syntax.pretty_term (Proof.context_of state) t))
|
||||
end
|
||||
|
||||
(* Construct a C program to match the current goal state. *)
|
||||
fun make_program st =
|
||||
let
|
||||
val state = Toplevel.proof_of st;
|
||||
val {goal = g, ...} = Proof.raw_goal state;
|
||||
val (_, g') = Subgoal.focus (Proof.context_of state) 1 g
|
||||
val (gi, _) = Logic.goal_params (Thm.prop_of g') 1
|
||||
val (vars, expr) = translate state [] gi
|
||||
in
|
||||
"#include <inttypes.h>\n" ^
|
||||
"#include <limits.h>\n" ^
|
||||
"#include <stdbool.h>\n" ^
|
||||
"#include <stdint.h>\n" ^
|
||||
"#include <stdio.h>\n" ^
|
||||
"int main(void) {\n" ^
|
||||
loop_header vars ^
|
||||
"if (!" ^ expr ^ ") {\n" ^
|
||||
"printf(\"Found counter-example:\\n\"" ^ format_string vars ^ as_args vars ^ ");\n" ^
|
||||
"return 0;\n" ^
|
||||
"}\n" ^
|
||||
loop_footer vars ^
|
||||
"return -1;\n" ^
|
||||
"}"
|
||||
end
|
||||
|
||||
(* Try to refute the current goal by using a C program to find a counter example. *)
|
||||
fun refute st =
|
||||
case cc of
|
||||
SOME _ =>
|
||||
let
|
||||
val program = make_program st;
|
||||
val serial = serial_string ();
|
||||
val tmp = File.tmp_path (Path.explode ("etanercept" ^ serial ^ ".c"));
|
||||
val _ = File.write tmp program;
|
||||
val aout = compile (File.shell_path tmp);
|
||||
val (msg, ret) = Isabelle_System.bash_output aout
|
||||
in
|
||||
if debug
|
||||
then writeln ("Program:\n" ^ program ^ "\nWritten to: " ^ File.shell_path tmp ^ "\nCompiled to: " ^ aout)
|
||||
else ();
|
||||
(if ret = 0
|
||||
then msg
|
||||
else "Etanercept found no counter example")
|
||||
|> writeln
|
||||
end
|
||||
| NONE => writeln "no available C compiler"
|
||||
|
||||
(* Install the command itself. *)
|
||||
val _ = Outer_Syntax.command @{command_keyword etanercept}
|
||||
"Construct a C program to find counter-examples to word propositions"
|
||||
(Scan.succeed [] >> (fn _ => Toplevel.keep_proof refute))
|
||||
|
||||
end
|
||||
*}
|
||||
|
||||
lemma "True \<and> False"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
lemma "(x::32 word) = 0"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
etanercept
|
||||
|
||||
lemma "\<And>x. (x::32 word) \<noteq> y\<^sub>1 \<and> y \<ge> x"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
lemma "(x::8 word) = y"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
lemma "(x::64 word) < y"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
lemma "\<And>(x::32 word) y. x = y"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Previously, this example would give us a tautological comparison warning from Clang. *}
|
||||
lemma "y = y \<and> (x::32 word) << y = x"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Example that partially demonstrates Etanercept's utility. *}
|
||||
lemma "(x::8 word) > y \<or> x < y + y + y + y"
|
||||
(* quickcheck cannot handle this *)
|
||||
(* quickcheck *)
|
||||
(* quickcheck[random] takes a little while *)
|
||||
quickcheck[random]
|
||||
(* Etanercept immediately finds the trivial counterexample *)
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Example that demonstrates one of Etanercept's weaknesses. *}
|
||||
lemma "(x::32 word) div y = x"
|
||||
(* The naive exploration strategy means we wait for Etanercept to try every value of y before
|
||||
* moving x beyond 0.
|
||||
*)
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {*
|
||||
This is an interesting example that, due to Etanercept's exploration strategy, *should* be out of
|
||||
its reach with a reasonable time out. Instead, the C compiler folds the entire loop into immediate
|
||||
discovery of a counter-example.
|
||||
*}
|
||||
lemma "(x::64 word) \<ge> y \<and> x \<ge> y + y"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Various cases that test our handling of numeric literals. *}
|
||||
lemma "(x::32 word) && 45 = 0"
|
||||
etanercept
|
||||
oops
|
||||
lemma "(x::32 word) < 45"
|
||||
etanercept
|
||||
oops
|
||||
lemma "(x::32 word) < 0"
|
||||
etanercept
|
||||
oops
|
||||
lemma "(x::32 word) < 1"
|
||||
etanercept
|
||||
oops
|
||||
lemma "(x::32 word) < 0x45"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Test something non-trivial that we shouldn't be able to refute. *}
|
||||
lemma "(x::32 word) && 1 = 1 \<and> x && (~~ 1) = 0 \<longrightarrow> x = 1"
|
||||
etanercept
|
||||
apply word_bitwise
|
||||
done
|
||||
lemma "(x::32 signed word) && 1 = 1 \<and> x && (~~ 1) = 0 \<longrightarrow> x = 1"
|
||||
etanercept
|
||||
apply word_bitwise_signed
|
||||
done
|
||||
|
||||
text {* Test that division by zero is correctly modelled with Isabelle's semantics. *}
|
||||
lemma "(x::64 word) div 0 = 0"
|
||||
etanercept
|
||||
by (simp add: word_arith_nat_defs(6))
|
||||
|
||||
text {* Test we can handle large literals. *}
|
||||
lemma "(x::64 word) > 0xcafebeefcafebeef"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Test some casting operations. *}
|
||||
lemma "(ucast::32 signed word \<Rightarrow> 32 word) (x::32 signed word) = (y::32 word)"
|
||||
etanercept
|
||||
oops
|
||||
lemma "ucast (x::32 word) = (y:: 8 word)"
|
||||
etanercept
|
||||
oops
|
||||
lemma "ucast (x::32 word) = (y::32 word)"
|
||||
etanercept
|
||||
oops
|
||||
lemma "scast (x::32 signed word) = (y::8 word)"
|
||||
etanercept
|
||||
oops
|
||||
|
||||
text {* Try some things we shouldn't be able to refute. *}
|
||||
lemma "(x::64 word) >> 0 = x"
|
||||
etanercept
|
||||
by simp
|
||||
lemma "(x::64 word) >> 1 = x div 2"
|
||||
etanercept
|
||||
apply simp
|
||||
apply (rule shiftr_div_2n_w[where n=1, simplified])
|
||||
apply (simp add:word_size)
|
||||
done
|
||||
lemma "(x::64 word) << 1 = x * 2"
|
||||
etanercept
|
||||
apply (subst shiftl_t2n)
|
||||
apply simp
|
||||
done
|
||||
|
||||
end
|
||||
Loading…
Reference in New Issue