diff -r 6d1ecdb81ff0 -r 8e55aa1306c5 src/HOL/Tools/SMT/z3_model.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/SMT/z3_model.ML Wed May 12 23:54:02 2010 +0200 @@ -0,0 +1,146 @@ +(* Title: HOL/Tools/SMT/z3_model.ML + Author: Sascha Boehme and Philipp Meyer, TU Muenchen + +Parser for counterexamples generated by Z3. +*) + +signature Z3_MODEL = +sig + val parse_counterex: SMT_Translate.recon -> string list -> term list +end + +structure Z3_Model: Z3_MODEL = +struct + +(* counterexample expressions *) + +datatype expr = True | False | Number of int * int option | Value of int | + Array of array +and array = Fresh of expr | Store of (array * expr) * expr + + +(* parsing *) + +val space = Scan.many Symbol.is_ascii_blank +fun in_parens p = Scan.$$ "(" |-- p --| Scan.$$ ")" +fun in_braces p = (space -- Scan.$$ "{") |-- p --| (space -- Scan.$$ "}") + +val digit = (fn + "0" => SOME 0 | "1" => SOME 1 | "2" => SOME 2 | "3" => SOME 3 | + "4" => SOME 4 | "5" => SOME 5 | "6" => SOME 6 | "7" => SOME 7 | + "8" => SOME 8 | "9" => SOME 9 | _ => NONE) + +val nat_num = Scan.repeat1 (Scan.some digit) >> + (fn ds => fold (fn d => fn i => i * 10 + d) ds 0) +val int_num = Scan.optional ($$ "-" >> K (fn i => ~i)) I :|-- + (fn sign => nat_num >> sign) + +val is_char = Symbol.is_ascii_letter orf Symbol.is_ascii_digit orf + member (op =) (explode "_+*-/%~=<>$&|?!.@^#") +val name = Scan.many1 is_char >> implode + +fun array_expr st = st |> + in_parens (space |-- ( + Scan.this_string "const" |-- expr >> Fresh || + Scan.this_string "store" -- space |-- array_expr -- expr -- expr >> Store)) + +and expr st = st |> (space |-- ( + Scan.this_string "true" >> K True || + Scan.this_string "false" >> K False || + int_num -- Scan.option (Scan.$$ "/" |-- int_num) >> Number || + Scan.this_string "val!" |-- nat_num >> Value || + array_expr >> Array)) + +val mapping = space -- Scan.this_string "->" +val value = mapping |-- expr + +val args_case = Scan.repeat expr -- value +val else_case = space -- Scan.this_string "else" |-- value >> + pair ([] : expr list) + +val func = + let fun cases st = (else_case >> single || args_case ::: cases) st + in in_braces cases end + +val cex = space |-- Scan.repeat (space |-- name --| mapping -- + (func || expr >> (single o pair []))) + +fun read_cex ls = + explode (cat_lines ls) + |> try (fst o Scan.finite Symbol.stopper cex) + |> the_default [] + + +(* translation into terms *) + +fun lookup_term tab (name, e) = Option.map (rpair e) (Symtab.lookup tab name) + +fun with_name_context tab f xs = + let + val ns = Symtab.fold (Term.add_free_names o snd) tab [] + val nctxt = Name.make_context ns + in fst (fold_map f xs (Inttab.empty, nctxt)) end + +fun fresh_term T (tab, nctxt) = + let val (n, nctxt') = yield_singleton Name.variants "" nctxt + in (Free (n, T), (tab, nctxt')) end + +fun term_of_value T i (cx as (tab, _)) = + (case Inttab.lookup tab i of + SOME t => (t, cx) + | NONE => + let val (t, (tab', nctxt')) = fresh_term T cx + in (t, (Inttab.update (i, t) tab', nctxt')) end) + +fun trans_expr _ True = pair @{term True} + | trans_expr _ False = pair @{term False} + | trans_expr T (Number (i, NONE)) = pair (HOLogic.mk_number T i) + | trans_expr T (Number (i, SOME j)) = + pair (Const (@{const_name divide}, [T, T] ---> T) $ + HOLogic.mk_number T i $ HOLogic.mk_number T j) + | trans_expr T (Value i) = term_of_value T i + | trans_expr T (Array a) = trans_array T a + +and trans_array T a = + let val dT = Term.domain_type T and rT = Term.range_type T + in + (case a of + Fresh e => trans_expr rT e #>> (fn t => Abs ("x", dT, t)) + | Store ((a', e1), e2) => + trans_array T a' ##>> trans_expr dT e1 ##>> trans_expr rT e2 #>> + (fn ((m, k), v) => + Const (@{const_name fun_upd}, [T, dT, rT] ---> T) $ m $ k $ v)) + end + +fun trans_pat i T f x = + f (Term.domain_type T) ##>> trans (i-1) (Term.range_type T) x #>> + (fn (u, (us, t)) => (u :: us, t)) + +and trans i T ([], v) = + if i > 0 then trans_pat i T fresh_term ([], v) + else trans_expr T v #>> pair [] + | trans i T (p :: ps, v) = trans_pat i T (fn U => trans_expr U p) (ps, v) + +fun mk_eq' t us u = HOLogic.mk_eq (Term.list_comb (t, us), u) +fun mk_eq (Const (@{const_name apply}, _)) (u' :: us', u) = mk_eq' u' us' u + | mk_eq t (us, u) = mk_eq' t us u + +fun translate (t, cs) = + let val T = Term.fastype_of t + in + (case (can HOLogic.dest_number t, cs) of + (true, [c]) => trans 0 T c #>> (fn (_, u) => [mk_eq u ([], t)]) + | (_, (es, _) :: _) => fold_map (trans (length es) T) cs #>> map (mk_eq t) + | _ => raise TERM ("translate: no cases", [t])) + end + + +(* overall procedure *) + +fun parse_counterex ({terms, ...} : SMT_Translate.recon) ls = + read_cex ls + |> map_filter (lookup_term terms) + |> with_name_context terms translate + |> flat + +end