src/HOL/SMT_Examples/boogie.ML
author paulson <lp15@cam.ac.uk>
Tue Apr 25 16:39:54 2017 +0100 (2017-04-25)
changeset 65578 e4997c181cce
parent 61424 c3658c18b7bc
child 67399 eab6ce8368fa
permissions -rw-r--r--
New material from PNT proof, as well as more default [simp] declarations. Also removed duplicate theorems about geometric series
     1 (*  Title:      HOL/SMT_Examples/boogie.ML
     2     Author:     Sascha Boehme, TU Muenchen
     3 
     4 Proving Boogie-generated verification conditions.
     5 *)
     6 
     7 signature BOOGIE =
     8 sig
     9   val boogie_prove: theory -> string list -> unit
    10 end;
    11 
    12 structure Boogie: BOOGIE =
    13 struct
    14 
    15 (* utility functions *)
    16 
    17 val as_int = fst o read_int o raw_explode
    18 
    19 val isabelle_name =
    20   let
    21     fun purge s = if Symbol.is_letter s orelse Symbol.is_digit s then s else
    22       (case s of
    23         "." => "_o_"
    24       | "_" => "_n_"
    25       | "$" => "_S_"
    26       | "@" => "_G_"
    27       | "#" => "_H_"
    28       | "^" => "_T_"
    29       | _   => ("_" ^ string_of_int (ord s) ^ "_"))
    30   in prefix "b_" o translate_string purge end
    31 
    32 
    33 (* context *)
    34 
    35 type context =
    36   typ Symtab.table * (term * bool) Symtab.table * term list * term list
    37 
    38 val empty_context: context = (Symtab.empty, Symtab.empty, [], [])
    39 
    40 fun add_type name (tds, fds, axs, vcs) =
    41   let
    42     val T = TFree (isabelle_name name, @{sort type})
    43     val tds' = Symtab.update (name, T) tds
    44   in (tds', fds, axs, vcs) end
    45 
    46 fun add_func name Ts T unique (tds, fds, axs, vcs) =
    47   let
    48     val t = Free (isabelle_name name, Ts ---> T)
    49     val fds' = Symtab.update (name, (t, unique)) fds
    50   in (tds, fds', axs, vcs) end
    51 
    52 fun add_axiom t (tds, fds, axs, vcs) = (tds, fds, t :: axs, vcs)
    53 
    54 fun add_vc t (tds, fds, axs, vcs) = (tds, fds, axs, t :: vcs)
    55 
    56 fun lookup_type (tds, _, _, _) name =
    57   (case Symtab.lookup tds name of
    58     SOME T => T
    59   | NONE => error "Undeclared type")
    60 
    61 fun lookup_func (_, fds, _, _) name =
    62   (case Symtab.lookup fds name of
    63     SOME t_unique => t_unique
    64   | NONE => error "Undeclared function")
    65 
    66 
    67 (* constructors *)
    68 
    69 fun mk_var name T = Free ("V_" ^ isabelle_name name, T)
    70 
    71 fun mk_arrayT (Ts, T) = Type (@{type_name "fun"}, [HOLogic.mk_tupleT Ts, T])
    72 
    73 fun mk_binary t (t1, t2) = t $ t1 $ t2
    74 
    75 fun mk_nary _ t [] = t
    76   | mk_nary f _ ts = uncurry (fold_rev f) (split_last ts)
    77 
    78 fun mk_distinct [] = @{const HOL.True}
    79   | mk_distinct [_] = @{const HOL.True}
    80   | mk_distinct (t :: ts) =
    81       let
    82         fun mk_noteq u u' =
    83           HOLogic.mk_conj (HOLogic.mk_not (HOLogic.mk_eq (t, u)), u')
    84       in fold_rev mk_noteq ts (mk_distinct ts) end
    85 
    86 fun mk_store m k v =
    87   let
    88     val mT = Term.fastype_of m and kT = Term.fastype_of k
    89     val vT = Term.fastype_of v
    90   in Const (@{const_name fun_upd}, mT --> kT --> vT --> mT) $ m $ k $ v end
    91 
    92 fun mk_quant q (Free (x, T)) t = q T $ absfree (x, T) t
    93   | mk_quant _ t _ = raise TERM ("bad variable", [t])
    94 
    95 val patternT = @{typ "SMT.pattern"}
    96 
    97 fun mk_pat t =
    98   Const (@{const_name "SMT.pat"}, Term.fastype_of t --> patternT) $ t
    99 
   100 fun mk_pattern [] = raise TERM ("mk_pattern", [])
   101   | mk_pattern ts = SMT_Util.mk_symb_list patternT (map mk_pat ts)
   102 
   103 fun mk_trigger [] t = t
   104   | mk_trigger pss t =
   105       @{term "SMT.trigger"} $
   106         SMT_Util.mk_symb_list @{typ "SMT.pattern SMT.symb_list"} (map mk_pattern pss) $ t
   107 
   108 
   109 (* parser *)
   110 
   111 fun repeat f n ls =
   112   let fun apply (xs, ls) = f ls |>> (fn x => x :: xs)
   113   in funpow (as_int n) apply ([], ls) |>> rev end
   114 
   115 fun parse_type _ (["bool"] :: ls) = (@{typ bool}, ls)
   116   | parse_type _ (["int"] :: ls) = (@{typ int}, ls)
   117   | parse_type cx (["array", arity] :: ls) =
   118       repeat (parse_type cx) arity ls |>> mk_arrayT o split_last
   119   | parse_type cx (("type-con" :: name :: _) :: ls) = (lookup_type cx name, ls)
   120   | parse_type _ _ = error "Bad type"
   121 
   122 fun parse_expr _ (["true"] :: ls) = (@{term True}, ls)
   123   | parse_expr _ (["false"] :: ls) = (@{term False}, ls)
   124   | parse_expr cx (["not"] :: ls) = parse_expr cx ls |>> HOLogic.mk_not
   125   | parse_expr cx (["and", n] :: ls) = parse_nary_expr cx n HOLogic.mk_conj @{term True} ls
   126   | parse_expr cx (["or", n] :: ls) = parse_nary_expr cx n HOLogic.mk_disj @{term False} ls
   127   | parse_expr cx (["implies"] :: ls) = parse_bin_expr cx (mk_binary @{term HOL.implies}) ls
   128   | parse_expr cx (["="] :: ls) = parse_bin_expr cx HOLogic.mk_eq ls
   129   | parse_expr cx (["var", name] :: ls) = parse_type cx ls |>> mk_var name
   130   | parse_expr cx (["fun", name, n] :: ls) =
   131       let val (t, _) = lookup_func cx name
   132       in repeat (parse_expr cx) n ls |>> curry Term.list_comb t end
   133   | parse_expr cx (("label" :: _) :: ls) = parse_expr cx ls
   134   | parse_expr _ (["int-num", n] :: ls) = (HOLogic.mk_number @{typ int} (as_int n), ls)
   135   | parse_expr cx (["<"] :: ls) = parse_bin_expr cx (mk_binary @{term "op < :: int => _"}) ls
   136   | parse_expr cx (["<="] :: ls) = parse_bin_expr cx (mk_binary @{term "op <= :: int => _"}) ls
   137   | parse_expr cx ([">"] :: ls) = parse_bin_expr cx (mk_binary @{term "op < :: int => _"}o swap) ls
   138   | parse_expr cx ([">="] :: ls) =
   139       parse_bin_expr cx (mk_binary @{term "op <= :: int => _"} o swap) ls
   140   | parse_expr cx (["+"] :: ls) = parse_bin_expr cx (mk_binary @{term "op + :: int => _"}) ls
   141   | parse_expr cx (["-"] :: ls) = parse_bin_expr cx (mk_binary @{term "op - :: int => _"}) ls
   142   | parse_expr cx (["*"] :: ls) = parse_bin_expr cx (mk_binary @{term "op * :: int => _"}) ls
   143   | parse_expr cx (["/"] :: ls) = parse_bin_expr cx (mk_binary @{term boogie_div}) ls
   144   | parse_expr cx (["%"] :: ls) = parse_bin_expr cx (mk_binary @{term boogie_mod}) ls
   145   | parse_expr cx (["select", n] :: ls) =
   146       repeat (parse_expr cx) n ls
   147       |>> (fn ts => hd ts $ HOLogic.mk_tuple (tl ts))
   148   | parse_expr cx (["store", n] :: ls) =
   149       repeat (parse_expr cx) n ls
   150       |>> split_last
   151       |>> (fn (ts, t) => mk_store (hd ts) (HOLogic.mk_tuple (tl ts)) t)
   152   | parse_expr cx (["forall", vars, pats, atts] :: ls) =
   153       parse_quant cx HOLogic.all_const vars pats atts ls
   154   | parse_expr cx (["exists", vars, pats, atts] :: ls) =
   155       parse_quant cx HOLogic.exists_const vars pats atts ls
   156   | parse_expr _ _ = error "Bad expression"
   157 
   158 and parse_bin_expr cx f ls = ls |> parse_expr cx ||>> parse_expr cx |>> f
   159 
   160 and parse_nary_expr cx n f c ls =
   161   repeat (parse_expr cx) n ls |>> mk_nary (curry f) c
   162 
   163 and parse_quant cx q vars pats atts ls =
   164   let
   165     val ((((vs, pss), _), t), ls') =
   166       ls
   167       |> repeat (parse_var cx) vars
   168       ||>> repeat (parse_pat cx) pats
   169       ||>> repeat (parse_attr cx) atts
   170       ||>> parse_expr cx
   171   in (fold_rev (mk_quant q) vs (mk_trigger pss t), ls') end
   172 
   173 and parse_var cx (["var", name] :: ls) = parse_type cx ls |>> mk_var name
   174   | parse_var _ _ = error "Bad variable"
   175 
   176 and parse_pat cx (["pat", n] :: ls) = repeat (parse_expr cx) n ls
   177   | parse_pat _ _ = error "Bad pattern"
   178 
   179 and parse_attr cx (["attribute", name, n] :: ls) =
   180       let
   181         fun attr (["expr-attr"] :: ls) = parse_expr cx ls |>> K ()
   182           | attr (("string-attr" :: _) :: ls) = ((), ls)
   183           | attr _ = error "Bad attribute value"
   184       in repeat attr n ls |>> K name end
   185   | parse_attr _ _ = error "Bad attribute"
   186 
   187 fun parse_func cx arity n ls =
   188   let
   189     val ((Ts, atts), ls') =
   190       ls |> repeat (parse_type cx) arity ||>> repeat (parse_attr cx) n
   191     val unique = member (op =) atts "unique"
   192   in ((split_last Ts, unique), ls') end
   193 
   194 fun parse_decl (("type-decl" :: name :: _) :: ls) cx = (ls, add_type name cx)
   195   | parse_decl (["fun-decl", name, arity, n] :: ls) cx =
   196       let val (((Ts, T), unique), ls') = parse_func cx arity n ls
   197       in (ls', add_func name Ts T unique cx) end
   198   | parse_decl (("axiom" :: _) :: ls) cx =
   199       let val (t, ls') = parse_expr cx ls
   200       in (ls', add_axiom t cx) end
   201   | parse_decl (("var-decl" :: _) :: ls) cx =
   202       parse_type cx ls |> snd |> rpair cx
   203   | parse_decl (("vc" :: _) :: ls) cx =
   204       let val (t, ls') = parse_expr cx ls
   205       in (ls', add_vc t cx) end
   206   | parse_decl _ _ = error "Bad declaration"
   207 
   208 fun parse_lines [] cx = cx
   209   | parse_lines ls cx = parse_decl ls cx |-> parse_lines
   210 
   211 
   212 (* splitting of text lines into a lists of tokens *)
   213 
   214 fun is_blank c = (c = " " orelse c = "\t" orelse c = "\r" orelse c = "\n")
   215 
   216 val token_lines =
   217   map (String.tokens (is_blank o str))
   218   #> filter (fn [] => false | _ => true)
   219 
   220 
   221 (* proving verification conditions *)
   222 
   223 fun add_unique_axioms (tds, fds, axs, vcs) =
   224   Symtab.fold (fn (_, (t, true)) => cons t | _ => I) fds []
   225   |> map (swap o Term.dest_Free)
   226   |> AList.group (op =)
   227   |> map (fn (T, ns) => mk_distinct (map (Free o rpair T) ns))
   228   |> (fn axs' => (tds, fds, axs' @ axs, vcs))
   229 
   230 fun build_proof_context thy (tds, fds, axs, vcs) =
   231   let
   232     val vc =
   233       (case vcs of
   234         [vc] => vc
   235       | _ => error "Bad number of verification conditions")
   236   in
   237     Proof_Context.init_global thy
   238     |> Symtab.fold (fn (_, T) => Variable.declare_typ T) tds
   239     |> Symtab.fold (fn (_, (t, _)) => Variable.declare_term t) fds
   240     |> fold Variable.declare_term axs
   241     |> fold Variable.declare_term vcs
   242     |> pair (map HOLogic.mk_Trueprop axs, HOLogic.mk_Trueprop vc)
   243   end
   244 
   245 val boogie_rules =
   246   [@{thm fst_conv}, @{thm snd_conv}, @{thm prod.collapse}] @
   247   [@{thm fun_upd_same}, @{thm fun_upd_apply}]
   248 
   249 fun boogie_tac ctxt axioms =
   250   ALLGOALS (SMT_Solver.smt_tac ctxt (boogie_rules @ axioms))
   251 
   252 fun boogie_prove thy lines =
   253   let
   254     val ((axioms, vc), ctxt) =
   255       empty_context
   256       |> parse_lines (token_lines lines)
   257       |> add_unique_axioms
   258       |> build_proof_context thy
   259 
   260     val _ = Goal.prove ctxt [] axioms vc (fn {prems, context} => boogie_tac context prems)
   261     val _ = writeln "Verification condition proved successfully"
   262 
   263   in () end
   264 
   265 
   266 (* Isar command *)
   267 
   268 val _ =
   269   Outer_Syntax.command @{command_keyword boogie_file}
   270     "prove verification condition from .b2i file"
   271     (Resources.provide_parse_files "boogie_file" >> (fn files =>
   272       Toplevel.theory (fn thy =>
   273         let
   274           val ([{lines, ...}], thy') = files thy;
   275           val _ = boogie_prove thy' lines;
   276         in thy' end)))
   277 
   278 end;