--- a/src/HOL/Tools/SMT/smt_translate.ML Wed Dec 15 08:39:24 2010 +0100
+++ b/src/HOL/Tools/SMT/smt_translate.ML Wed Dec 15 10:12:44 2010 +0100
@@ -15,7 +15,7 @@
SLet of string * sterm * sterm |
SQua of squant * string list * sterm spattern list * int option * sterm
- (*configuration options*)
+ (*translation configuration*)
type prefixes = {sort_prefix: string, func_prefix: string}
type sign = {
header: string list,
@@ -24,17 +24,21 @@
funcs: (string * (string list * string)) list }
type config = {
prefixes: prefixes,
- header: Proof.context -> term list -> string list,
+ header: term list -> string list,
is_fol: bool,
has_datatypes: bool,
serialize: string list -> sign -> sterm list -> string }
type recon = {
+ context: Proof.context,
typs: typ Symtab.table,
terms: term Symtab.table,
- unfolds: thm list,
+ rewrite_rules: thm list,
assms: (int * thm) list }
- val translate: config -> Proof.context -> string list -> (int * thm) list ->
+ (*translation*)
+ val add_config: SMT_Utils.class * (Proof.context -> config) ->
+ Context.generic -> Context.generic
+ val translate: Proof.context -> string list -> (int * thm) list ->
string * recon
end
@@ -59,7 +63,7 @@
-(* configuration options *)
+(* translation configuration *)
type prefixes = {sort_prefix: string, func_prefix: string}
@@ -71,20 +75,416 @@
type config = {
prefixes: prefixes,
- header: Proof.context -> term list -> string list,
+ header: term list -> string list,
is_fol: bool,
has_datatypes: bool,
serialize: string list -> sign -> sterm list -> string }
type recon = {
+ context: Proof.context,
typs: typ Symtab.table,
terms: term Symtab.table,
- unfolds: thm list,
+ rewrite_rules: thm list,
assms: (int * thm) list }
-(* utility functions *)
+(* translation context *)
+
+fun make_tr_context {sort_prefix, func_prefix} =
+ (sort_prefix, 1, Typtab.empty, func_prefix, 1, Termtab.empty)
+
+fun string_of_index pre i = pre ^ string_of_int i
+
+fun add_typ T proper (cx as (sp, Tidx, typs, fp, idx, terms)) =
+ (case Typtab.lookup typs T of
+ SOME (n, _) => (n, cx)
+ | NONE =>
+ let
+ val n = string_of_index sp Tidx
+ val typs' = Typtab.update (T, (n, proper)) typs
+ in (n, (sp, Tidx+1, typs', fp, idx, terms)) end)
+
+fun add_fun t sort (cx as (sp, Tidx, typs, fp, idx, terms)) =
+ (case Termtab.lookup terms t of
+ SOME (n, _) => (n, cx)
+ | NONE =>
+ let
+ val n = string_of_index fp idx
+ val terms' = Termtab.update (t, (n, sort)) terms
+ in (n, (sp, Tidx, typs, fp, idx+1, terms')) end)
+
+fun sign_of header dtyps (_, _, typs, _, _, terms) = {
+ header = header,
+ sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
+ dtyps = dtyps,
+ funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
+
+fun recon_of ctxt rules thms ithms revertT revert (_, _, typs, _, _, terms) =
+ let
+ fun add_typ (T, (n, _)) = Symtab.update (n, revertT T)
+ val typs' = Typtab.fold add_typ typs Symtab.empty
+
+ fun add_fun (t, (n, _)) = Symtab.update (n, revert t)
+ val terms' = Termtab.fold add_fun terms Symtab.empty
+
+ val assms = map (pair ~1) thms @ ithms
+ in
+ {context=ctxt, typs=typs', terms=terms', rewrite_rules=rules, assms=assms}
+ end
+
+
+
+(* preprocessing *)
+
+(** mark built-in constants as Var **)
+
+fun mark_builtins ctxt =
+ let
+ (*
+ Note: schematic terms cannot occur anymore in terms at this stage.
+ *)
+ fun mark t =
+ (case Term.strip_comb t of
+ (u as Const (@{const_name If}, _), ts) => marks u ts
+ | (u as Const c, ts) =>
+ (case B.builtin_num ctxt t of
+ SOME (n, T) =>
+ let val v = ((n, 0), T)
+ in Vartab.update v #> pair (Var v) end
+ | NONE =>
+ (case B.builtin_fun ctxt c ts of
+ SOME ((ni, T), us, U) =>
+ Vartab.update (ni, U) #> marks (Var (ni, T)) us
+ | NONE => marks u ts))
+ | (Abs (n, T, u), ts) => mark u #-> (fn u' => marks (Abs (n, T, u')) ts)
+ | (u, ts) => marks u ts)
+
+ and marks t ts = fold_map mark ts #>> Term.list_comb o pair t
+
+ in (fn ts => swap (fold_map mark ts Vartab.empty)) end
+
+fun mark_builtins' ctxt t = hd (snd (mark_builtins ctxt [t]))
+
+
+(** FIXME **)
+
+local
+ (*
+ mark constructors and selectors as Vars (forcing eta-expansion),
+ add missing datatype selectors via hypothetical definitions,
+ also return necessary datatype and record theorems
+ *)
+in
+
+fun collect_datatypes_and_records (tr_context, ctxt) ts =
+ (([], tr_context, ctxt), ts)
+
+end
+
+
+(** eta-expand quantifiers, let expressions and built-ins *)
+
+local
+ fun eta T t = Abs (Name.uu, T, Term.incr_boundvars 1 t $ Bound 0)
+
+ fun exp T = eta (Term.domain_type (Term.domain_type T))
+
+ fun exp2 T q =
+ let val U = Term.domain_type T
+ in Abs (Name.uu, U, q $ eta (Term.domain_type U) (Bound 0)) end
+
+ fun exp2' T l =
+ let val (U1, U2) = Term.dest_funT T ||> Term.domain_type
+ in Abs (Name.uu, U1, eta U2 (l $ Bound 0)) end
+
+ fun expf t i T ts =
+ let val Ts = U.dest_funT i T |> fst |> drop (length ts)
+ in Term.list_comb (t, ts) |> fold_rev eta Ts end
+
+ fun expand ((q as Const (@{const_name All}, _)) $ Abs a) = q $ abs_expand a
+ | expand ((q as Const (@{const_name All}, T)) $ t) = q $ exp T t
+ | expand (q as Const (@{const_name All}, T)) = exp2 T q
+ | expand ((q as Const (@{const_name Ex}, _)) $ Abs a) = q $ abs_expand a
+ | expand ((q as Const (@{const_name Ex}, T)) $ t) = q $ exp T t
+ | expand (q as Const (@{const_name Ex}, T)) = exp2 T q
+ | expand ((l as Const (@{const_name Let}, _)) $ t $ Abs a) =
+ l $ expand t $ abs_expand a
+ | expand ((l as Const (@{const_name Let}, T)) $ t $ u) =
+ l $ expand t $ exp (Term.range_type T) u
+ | expand ((l as Const (@{const_name Let}, T)) $ t) = exp2 T (l $ expand t)
+ | expand (l as Const (@{const_name Let}, T)) = exp2' T l
+ | expand (Abs a) = abs_expand a
+ | expand t =
+ (case Term.strip_comb t of
+ (u as Const (@{const_name If}, T), ts) => expf u 3 T (map expand ts)
+ | (u as Var ((_, i), T), ts) => expf u i T (map expand ts)
+ | (u, ts) => Term.list_comb (u, map expand ts))
+
+ and abs_expand (n, T, t) = Abs (n, T, expand t)
+in
+
+val eta_expand = map expand
+
+end
+
+
+(** lambda-lifting **)
+
+local
+ fun mk_def Ts T lhs rhs =
+ let
+ val eq = HOLogic.eq_const T $ lhs $ rhs
+ val trigger =
+ [[Const (@{const_name SMT.pat}, T --> @{typ SMT.pattern}) $ lhs]]
+ |> map (HOLogic.mk_list @{typ SMT.pattern})
+ |> HOLogic.mk_list @{typ "SMT.pattern list"}
+ fun mk_all T t = HOLogic.all_const T $ Abs (Name.uu, T, t)
+ in fold mk_all Ts (@{const SMT.trigger} $ trigger $ eq) end
+
+ fun replace_lambda Us Ts t (cx as (defs, ctxt)) =
+ let
+ val T = Term.fastype_of1 (Us @ Ts, t)
+ val lev = length Us
+ val bs = sort int_ord (Term.add_loose_bnos (t, lev, []))
+ val bss = map_index (fn (i, j) => (j, Integer.add lev i)) bs
+ val norm = perhaps (AList.lookup (op =) bss)
+ val t' = Term.map_aterms (fn Bound i => Bound (norm i) | t => t) t
+ val Ts' = map (nth Ts) bs
+
+ fun mk_abs U u = Abs (Name.uu, U, u)
+ val abs_rhs = fold mk_abs Ts' (fold mk_abs Us t')
+ in
+ (case Termtab.lookup defs abs_rhs of
+ SOME (f, _) => (Term.list_comb (f, map Bound bs), cx)
+ | NONE =>
+ let
+ val (n, ctxt') =
+ yield_singleton Variable.variant_fixes Name.uu ctxt
+ val f = Free (n, rev Ts' ---> (rev Us ---> T))
+ fun mk_bapp i t = t $ Bound i
+ val lhs =
+ f
+ |> fold_rev (mk_bapp o snd) bss
+ |> fold_rev mk_bapp (0 upto (length Us - 1))
+ val def = mk_def (Us @ Ts') T lhs t'
+ in (f, (Termtab.update (abs_rhs, (f, def)) defs, ctxt')) end)
+ end
+
+ fun dest_abs Ts (Abs (_, T, t)) = dest_abs (T :: Ts) t
+ | dest_abs Ts t = (Ts, t)
+
+ fun traverse Ts t =
+ (case t of
+ (q as Const (@{const_name All}, _)) $ Abs a =>
+ abs_traverse Ts a #>> (fn a' => q $ Abs a')
+ | (q as Const (@{const_name Ex}, _)) $ Abs a =>
+ abs_traverse Ts a #>> (fn a' => q $ Abs a')
+ | (l as Const (@{const_name Let}, _)) $ u $ Abs a =>
+ traverse Ts u ##>> abs_traverse Ts a #>>
+ (fn (u', a') => l $ u' $ Abs a')
+ | Abs _ =>
+ let val (Us, u) = dest_abs [] t
+ in traverse (Us @ Ts) u #-> replace_lambda Us Ts end
+ | u1 $ u2 => traverse Ts u1 ##>> traverse Ts u2 #>> (op $)
+ | _ => pair t)
+
+ and abs_traverse Ts (n, T, t) = traverse (T::Ts) t #>> (fn t' => (n, T, t'))
+in
+
+fun lift_lambdas ctxt ts =
+ (Termtab.empty, ctxt)
+ |> fold_map (traverse []) ts
+ |> (fn (us, (defs, ctxt')) =>
+ (ctxt', Termtab.fold (cons o snd o snd) defs us))
+
+end
+
+
+(** introduce explicit applications **)
+
+local
+ (*
+ Make application explicit for functions with varying number of arguments.
+ *)
+
+ fun add t ts =
+ Termtab.map_default (t, []) (Ord_List.insert int_ord (length ts))
+
+ fun collect t =
+ (case Term.strip_comb t of
+ (u as Const _, ts) => add u ts #> fold collect ts
+ | (u as Free _, ts) => add u ts #> fold collect ts
+ | (Abs (_, _, u), ts) => collect u #> fold collect ts
+ | (_, ts) => fold collect ts)
+
+ fun app ts (t, T) =
+ let val f = Const (@{const_name SMT.fun_app}, T --> T)
+ in (Term.list_comb (f $ t, ts), snd (U.dest_funT (length ts) T)) end
+
+ fun appl _ _ [] = fst
+ | appl _ [] ts = fst o app ts
+ | appl i (k :: ks) ts =
+ let val (ts1, ts2) = chop (k - i) ts
+ in appl k ks ts2 o app ts1 end
+
+ fun appl0 [_] ts (t, _) = Term.list_comb (t, ts)
+ | appl0 (0 :: ks) ts tT = appl 0 ks ts tT
+ | appl0 ks ts tT = appl 0 ks ts tT
+
+ fun apply terms T t ts = appl0 (Termtab.lookup_list terms t) ts (t, T)
+
+ fun get_arities i t =
+ (case Term.strip_comb t of
+ (Bound j, ts) =>
+ (if i = j then Ord_List.insert int_ord (length ts) else I) #>
+ fold (get_arities i) ts
+ | (Abs (_, _, u), ts) => get_arities (i+1) u #> fold (get_arities i) ts
+ | (_, ts) => fold (get_arities i) ts)
+in
+
+fun intro_explicit_application ts =
+ let
+ val terms = fold collect ts Termtab.empty
+
+ fun traverse (env as (arities, Ts)) t =
+ (case Term.strip_comb t of
+ (u as Const (_, T), ts) => apply terms T u (map (traverse env) ts)
+ | (u as Free (_, T), ts) => apply terms T u (map (traverse env) ts)
+ | (u as Bound i, ts) =>
+ appl0 (nth arities i) (map (traverse env) ts) (u, nth Ts i)
+ | (Abs (n, T, u), ts) =>
+ let val env' = (get_arities 0 u [] :: arities, T :: Ts)
+ in traverses env (Abs (n, T, traverse env' u)) ts end
+ | (u, ts) => traverses env u ts)
+ and traverses env t ts = Term.list_comb (t, map (traverse env) ts)
+ in map (traverse ([], [])) ts end
+
+val fun_app_eq = mk_meta_eq @{thm SMT.fun_app_def}
+
+end
+
+
+(** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
+
+val tboolT = @{typ SMT.term_bool}
+val term_true = Const (@{const_name True}, tboolT)
+val term_false = Const (@{const_name False}, tboolT)
+
+val term_bool = @{lemma "True ~= False" by simp}
+val term_bool_prop =
+ let
+ fun replace @{const HOL.eq (bool)} = @{const HOL.eq (SMT.term_bool)}
+ | replace @{const True} = term_true
+ | replace @{const False} = term_false
+ | replace t = t
+ in
+ Term.map_aterms replace (HOLogic.dest_Trueprop (Thm.prop_of term_bool))
+ end
+
+val fol_rules = [
+ Let_def,
+ @{lemma "P = True == P" by (rule eq_reflection) simp},
+ @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
+
+fun reduce_let (Const (@{const_name Let}, _) $ t $ u) =
+ reduce_let (Term.betapply (u, t))
+ | reduce_let (t $ u) = reduce_let t $ reduce_let u
+ | reduce_let (Abs (n, T, t)) = Abs (n, T, reduce_let t)
+ | reduce_let t = t
+
+fun is_pred_type NONE = false
+ | is_pred_type (SOME T) = (Term.body_type T = @{typ bool})
+
+fun is_conn_type NONE = false
+ | is_conn_type (SOME T) =
+ forall (equal @{typ bool}) (Term.body_type T :: Term.binder_types T)
+
+fun revert_typ @{typ SMT.term_bool} = @{typ bool}
+ | revert_typ (Type (n, Ts)) = Type (n, map revert_typ Ts)
+ | revert_typ T = T
+
+val revert_types = Term.map_types revert_typ
+
+fun folify ctxt builtins =
+ let
+ fun as_term t = @{const HOL.eq (SMT.term_bool)} $ t $ term_true
+
+ fun as_tbool @{typ bool} = tboolT
+ | as_tbool (Type (n, Ts)) = Type (n, map as_tbool Ts)
+ | as_tbool T = T
+ fun mapTs f g i = U.dest_funT i #> (fn (Ts, T) => map f Ts ---> g T)
+ fun predT i = mapTs as_tbool I i
+ fun funcT i = mapTs as_tbool as_tbool i
+ fun func i (n, T) = (n, funcT i T)
+
+ fun map_ifT T = T |> Term.dest_funT ||> funcT 2 |> (op -->)
+ val if_term = @{const If (bool)} |> Term.dest_Const ||> map_ifT |> Const
+ fun wrap_in_if t = if_term $ t $ term_true $ term_false
+
+ fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
+
+ fun in_term t =
+ (case Term.strip_comb t of
+ (Const (n as @{const_name If}, T), [t1, t2, t3]) =>
+ Const (n, map_ifT T) $ in_form t1 $ in_term t2 $ in_term t3
+ | (Const (@{const_name HOL.eq}, _), _) => wrap_in_if (in_form t)
+ | (Var (ni as (_, i), T), ts) =>
+ let val U = Vartab.lookup builtins ni
+ in
+ if is_conn_type U orelse is_pred_type U then wrap_in_if (in_form t)
+ else Term.list_comb (Var (ni, funcT i T), map in_term ts)
+ end
+ | (Const c, ts) =>
+ Term.list_comb (Const (func (length ts) c), map in_term ts)
+ | (Free c, ts) =>
+ Term.list_comb (Free (func (length ts) c), map in_term ts)
+ | _ => t)
+
+ and in_weight ((c as @{const SMT.weight}) $ w $ t) = c $ w $ in_form t
+ | in_weight t = in_form t
+
+ and in_pat (Const (c as (@{const_name pat}, _)) $ t) =
+ Const (func 1 c) $ in_term t
+ | in_pat (Const (c as (@{const_name nopat}, _)) $ t) =
+ Const (func 1 c) $ in_term t
+ | in_pat t = raise TERM ("bad pattern", [t])
+
+ and in_pats ps =
+ in_list @{typ "pattern list"} (in_list @{typ pattern} in_pat) ps
+
+ and in_trig ((c as @{const trigger}) $ p $ t) = c $ in_pats p $ in_weight t
+ | in_trig t = in_weight t
+
+ and in_form t =
+ (case Term.strip_comb t of
+ (q as Const (qn, _), [Abs (n, T, u)]) =>
+ if member (op =) [@{const_name All}, @{const_name Ex}] qn then
+ q $ Abs (n, as_tbool T, in_trig u)
+ else as_term (in_term t)
+ | (u as Const (@{const_name If}, _), ts) =>
+ Term.list_comb (u, map in_form ts)
+ | (b as @{const HOL.eq (bool)}, ts) => Term.list_comb (b, map in_form ts)
+ | (Const (n as @{const_name HOL.eq}, T), ts) =>
+ Term.list_comb (Const (n, predT 2 T), map in_term ts)
+ | (b as Var (ni as (_, i), T), ts) =>
+ if is_conn_type (Vartab.lookup builtins ni) then
+ Term.list_comb (b, map in_form ts)
+ else if is_pred_type (Vartab.lookup builtins ni) then
+ Term.list_comb (Var (ni, predT i T), map in_term ts)
+ else as_term (in_term t)
+ | _ => as_term (in_term t))
+ in
+ map (reduce_let #> in_form) #>
+ cons (mark_builtins' ctxt term_bool_prop) #>
+ pair (fol_rules, [term_bool])
+ end
+
+
+
+(* translation into intermediate format *)
+
+(** utility functions **)
val quantifier = (fn
@{const_name All} => SOME SForall
@@ -101,14 +501,14 @@
fun dest_pat (Const (@{const_name pat}, _) $ t) = (t, true)
| dest_pat (Const (@{const_name nopat}, _) $ t) = (t, false)
- | dest_pat t = raise TERM ("dest_pat", [t])
+ | dest_pat t = raise TERM ("bad pattern", [t])
fun dest_pats [] = I
| dest_pats ts =
(case map dest_pat ts |> split_list ||> distinct (op =) of
(ps, [true]) => cons (SPat ps)
| (ps, [false]) => cons (SNoPat ps)
- | _ => raise TERM ("dest_pats", ts))
+ | _ => raise TERM ("bad multi-pattern", ts))
fun dest_trigger (@{const trigger} $ tl $ t) =
(rev (fold (dest_pats o HOLogic.dest_list) (HOLogic.dest_list tl) []), t)
@@ -124,233 +524,19 @@
fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
| fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
-fun prop_of thm = HOLogic.dest_Trueprop (Thm.prop_of thm)
-
-
-(* map HOL formulas to FOL formulas (i.e., separate formulas froms terms) *)
-
-val tboolT = @{typ SMT.term_bool}
-val term_true = Const (@{const_name True}, tboolT)
-val term_false = Const (@{const_name False}, tboolT)
-
-val term_bool = @{lemma "True ~= False" by simp}
-val term_bool_prop =
- let
- fun replace @{const HOL.eq (bool)} = @{const HOL.eq (SMT.term_bool)}
- | replace @{const True} = term_true
- | replace @{const False} = term_false
- | replace t = t
- in Term.map_aterms replace (prop_of term_bool) end
-
-val needs_rewrite = Thm.prop_of #> Term.exists_subterm (fn
- Const (@{const_name Let}, _) => true
- | @{const HOL.eq (bool)} $ _ $ @{const True} => true
- | Const (@{const_name If}, _) $ _ $ @{const True} $ @{const False} => true
- | _ => false)
-
-val rewrite_rules = [
- Let_def,
- @{lemma "P = True == P" by (rule eq_reflection) simp},
- @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
-
-fun rewrite ctxt ct =
- Conv.top_sweep_conv (fn ctxt' =>
- Conv.rewrs_conv rewrite_rules then_conv rewrite ctxt') ctxt ct
-
-fun normalize ctxt thm =
- if needs_rewrite thm then Conv.fconv_rule (rewrite ctxt) thm else thm
-
-fun revert_typ @{typ SMT.term_bool} = @{typ bool}
- | revert_typ (Type (n, Ts)) = Type (n, map revert_typ Ts)
- | revert_typ T = T
-
-val revert_types = Term.map_types revert_typ
-
-fun folify ctxt =
- let
- fun is_builtin_conn (@{const_name True}, _) _ = false
- | is_builtin_conn (@{const_name False}, _) _ = false
- | is_builtin_conn c ts = B.is_builtin_conn ctxt c ts
-
- fun as_term t = @{const HOL.eq (SMT.term_bool)} $ t $ term_true
-
- fun as_tbool @{typ bool} = tboolT
- | as_tbool (Type (n, Ts)) = Type (n, map as_tbool Ts)
- | as_tbool T = T
- fun mapTs f g = Term.strip_type #> (fn (Ts, T) => map f Ts ---> g T)
- fun predT T = mapTs as_tbool I T
- fun funcT T = mapTs as_tbool as_tbool T
- fun func (n, T) = Const (n, funcT T)
-
- fun map_ifT T = T |> Term.dest_funT ||> funcT |> (op -->)
- val if_term = @{const If (bool)} |> Term.dest_Const ||> map_ifT |> Const
- fun wrap_in_if t = if_term $ t $ term_true $ term_false
-
- fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t))
-
- fun in_term t =
- (case Term.strip_comb t of
- (Const (c as @{const_name If}, T), [t1, t2, t3]) =>
- Const (c, map_ifT T) $ in_form t1 $ in_term t2 $ in_term t3
- | (Const c, ts) =>
- if is_builtin_conn c ts orelse B.is_builtin_pred ctxt c ts
- then wrap_in_if (in_form t)
- else Term.list_comb (func c, map in_term ts)
- | (Free (n, T), ts) => Term.list_comb (Free (n, funcT T), map in_term ts)
- | _ => t)
-
- and in_weight ((c as @{const SMT.weight}) $ w $ t) = c $ w $ in_form t
- | in_weight t = in_form t
-
- and in_pat (Const (c as (@{const_name pat}, _)) $ t) = func c $ in_term t
- | in_pat (Const (c as (@{const_name nopat}, _)) $ t) = func c $ in_term t
- | in_pat t = raise TERM ("in_pat", [t])
-
- and in_pats ps =
- in_list @{typ "pattern list"} (in_list @{typ pattern} in_pat) ps
-
- and in_trig ((c as @{const trigger}) $ p $ t) = c $ in_pats p $ in_weight t
- | in_trig t = in_weight t
+(** translation from Isabelle terms into SMT intermediate terms **)
- and in_form t =
- (case Term.strip_comb t of
- (q as Const (qn, _), [Abs (n, T, t')]) =>
- if is_some (quantifier qn) then q $ Abs (n, as_tbool T, in_trig t')
- else as_term (in_term t)
- | (Const (c as (n as @{const_name distinct}, T)), [t']) =>
- if B.is_builtin_fun ctxt c [t'] then
- Const (n, predT T) $ in_list T in_term t'
- else as_term (in_term t)
- | (Const (c as (n, T)), ts) =>
- if B.is_builtin_conn ctxt c ts
- then Term.list_comb (Const c, map in_form ts)
- else if B.is_builtin_pred ctxt c ts
- then Term.list_comb (Const (n, predT T), map in_term ts)
- else as_term (in_term t)
- | _ => as_term (in_term t))
- in
- map (apsnd (normalize ctxt)) #> (fn irules =>
- ((rewrite_rules, (~1, term_bool) :: irules),
- term_bool_prop :: map (in_form o prop_of o snd) irules))
- end
-
-
-
-(* translation from Isabelle terms into SMT intermediate terms *)
-
-val empty_context = (1, Typtab.empty, [], 1, Termtab.empty)
-
-fun make_sign header (_, typs, dtyps, _, terms) = {
- header = header,
- sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
- funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms [],
- dtyps = rev dtyps }
-
-fun make_recon (unfolds, assms) (_, typs, _, _, terms) = {
- typs = Symtab.make (map (apfst fst o swap) (Typtab.dest typs)),
- (*FIXME: don't drop the datatype information! *)
- terms = Symtab.make (map (fn (t, (n, _)) => (n, t)) (Termtab.dest terms)),
- unfolds = unfolds,
- assms = assms }
-
-fun string_of_index pre i = pre ^ string_of_int i
-
-fun new_typ sort_prefix proper T (Tidx, typs, dtyps, idx, terms) =
+fun intermediate header dtyps ctxt ts trx =
let
- val s = string_of_index sort_prefix Tidx
- val U = revert_typ T
- in (s, (Tidx+1, Typtab.update (U, (s, proper)) typs, dtyps, idx, terms)) end
-
-fun lookup_typ (_, typs, _, _, _) = Typtab.lookup typs o revert_typ
-
-fun fresh_typ T f cx =
- (case lookup_typ cx T of
- SOME (s, _) => (s, cx)
- | NONE => f T cx)
-
-fun new_fun func_prefix t ss (Tidx, typs, dtyps, idx, terms) =
- let
- val f = string_of_index func_prefix idx
- val terms' = Termtab.update (revert_types t, (f, ss)) terms
- in (f, (Tidx, typs, dtyps, idx+1, terms')) end
-
-fun fresh_fun func_prefix t ss (cx as (_, _, _, _, terms)) =
- (case Termtab.lookup terms (revert_types t) of
- SOME (f, _) => (f, cx)
- | NONE => new_fun func_prefix t ss cx)
-
-fun mk_type (_, Tfs) (d as Datatype.DtTFree _) = the (AList.lookup (op =) Tfs d)
- | mk_type Ts (Datatype.DtType (n, ds)) = Type (n, map (mk_type Ts) ds)
- | mk_type (Tds, _) (Datatype.DtRec i) = nth Tds i
-
-fun mk_selector ctxt Ts T n (i, d) =
- (case Datatype_Selectors.lookup_selector ctxt (n, i+1) of
- NONE => raise Fail ("missing selector for datatype constructor " ^ quote n)
- | SOME m => mk_type Ts d |> (fn U => (Const (m, T --> U), U)))
-
-fun mk_constructor ctxt Ts T (n, args) =
- let val (sels, Us) = split_list (map_index (mk_selector ctxt Ts T n) args)
- in (Const (n, Us ---> T), sels) end
-
-fun lookup_datatype ctxt n Ts =
- if member (op =) [@{type_name bool}, @{type_name nat}] n then NONE
- else
- Datatype.get_info (ProofContext.theory_of ctxt) n
- |> Option.map (fn {descr, ...} =>
- let
- val Tds = map (fn (_, (tn, _, _)) => Type (tn, Ts))
- (sort (int_ord o pairself fst) descr)
- val Tfs = (case hd descr of (_, (_, tfs, _)) => tfs ~~ Ts)
- in
- descr |> map (fn (i, (_, _, cs)) =>
- (nth Tds i, map (mk_constructor ctxt (Tds, Tfs) (nth Tds i)) cs))
- end)
-
-fun relaxed irules = (([], irules), map (prop_of o snd) irules)
-
-fun with_context header f (ths, ts) =
- let val (us, context) = fold_map f ts empty_context
- in ((make_sign (header ts) context, us), make_recon ths context) end
-
-
-fun translate config ctxt comments =
- let
- val {prefixes, is_fol, header, has_datatypes, serialize} = config
- val {sort_prefix, func_prefix} = prefixes
-
- fun transT (T as TFree _) = fresh_typ T (new_typ sort_prefix true)
- | transT (T as TVar _) = (fn _ => raise TYPE ("smt_translate", [T], []))
- | transT (T as Type (n, Ts)) =
+ fun transT (T as TFree _) = add_typ T true
+ | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
+ | transT (T as Type _) =
(case B.builtin_typ ctxt T of
SOME n => pair n
- | NONE => fresh_typ T (fn _ => fn cx =>
- if not has_datatypes then new_typ sort_prefix true T cx
- else
- (case lookup_datatype ctxt n Ts of
- NONE => new_typ sort_prefix true T cx
- | SOME dts =>
- let val cx' = new_dtyps dts cx
- in (fst (the (lookup_typ cx' T)), cx') end)))
+ | NONE => add_typ T true)
- and new_dtyps dts cx =
- let
- fun new_decl i t =
- let val (Ts, T) = U.dest_funT i (Term.fastype_of t)
- in
- fold_map transT Ts ##>> transT T ##>>
- new_fun func_prefix t NONE #>> swap
- end
- fun new_dtyp_decl (con, sels) =
- new_decl (length sels) con ##>> fold_map (new_decl 1) sels #>>
- (fn ((con', _), sels') => (con', map (apsnd snd) sels'))
- in
- cx
- |> fold_map (new_typ sort_prefix false o fst) dts
- ||>> fold_map (fold_map new_dtyp_decl o snd) dts
- |-> (fn (ss, decls) => fn (Tidx, typs, dtyps, idx, terms) =>
- (Tidx, typs, (ss ~~ decls) :: dtyps, idx, terms))
- end
+ val unmarked_builtins = [@{const_name If}, @{const_name HOL.eq}]
fun app n ts = SApp (n, ts)
@@ -361,37 +547,84 @@
SOME (q, Ts, ps, w, b) =>
fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', w, b'))
- | NONE => raise TERM ("intermediate", [t]))
+ | NONE => raise TERM ("unsupported quantifier", [t]))
| (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
transT T ##>> trans t1 ##>> trans t2 #>>
(fn ((U, u1), u2) => SLet (U, u1, u2))
- | (h as Const (c as (@{const_name distinct}, T)), ts) =>
- (case B.builtin_fun ctxt c ts of
- SOME (n, ts) => fold_map trans ts #>> app n
- | NONE => transs h T ts)
- | (h as Const (c as (_, T)), ts) =>
- (case B.builtin_num ctxt t of
- SOME n => pair (SApp (n, []))
- | NONE =>
- (case B.builtin_fun ctxt c ts of
- SOME (n, ts') => fold_map trans ts' #>> app n
- | NONE => transs h T ts))
- | (h as Free (_, T), ts) => transs h T ts
+ | (Var ((n, _), _), ts) => fold_map trans ts #>> app n
+ | (u as Const (c as (n, T)), ts) =>
+ if member (op =) unmarked_builtins n then
+ (case B.builtin_fun ctxt c ts of
+ SOME (((m, _), _), us, _) => fold_map trans us #>> app m
+ | NONE => raise TERM ("not a built-in symbol", [t]))
+ else transs u T ts
+ | (u as Free (_, T), ts) => transs u T ts
| (Bound i, []) => pair (SVar i)
- | (Abs (_, _, t1 $ Bound 0), []) =>
- if not (loose_bvar1 (t1, 0)) then trans t1 (* eta-reduce on the fly *)
- else raise TERM ("smt_translate", [t])
- | _ => raise TERM ("smt_translate", [t]))
-
+ | _ => raise TERM ("bad SMT term", [t]))
+
and transs t T ts =
let val (Us, U) = U.dest_funT (length ts) T
in
fold_map transT Us ##>> transT U #-> (fn Up =>
- fresh_fun func_prefix t (SOME Up) ##>> fold_map trans ts #>> SApp)
+ add_fun t (SOME Up) ##>> fold_map trans ts #>> SApp)
end
+
+ val (us, trx') = fold_map trans ts trx
+ in ((sign_of (header ts) dtyps trx', us), trx') end
+
+
+
+(* translation *)
+
+structure Configs = Generic_Data
+(
+ type T = (Proof.context -> config) U.dict
+ val empty = []
+ val extend = I
+ val merge = U.dict_merge fst
+)
+
+fun add_config (cs, cfg) = Configs.map (U.dict_update (cs, cfg))
+
+fun translate ctxt comments ithms =
+ let
+ val cs = SMT_Config.solver_class_of ctxt
+ val {prefixes, is_fol, header, has_datatypes, serialize} =
+ (case U.dict_get (Configs.get (Context.Proof ctxt)) cs of
+ SOME cfg => cfg ctxt
+ | NONE => error ("SMT: no translation configuration found " ^
+ "for solver class " ^ quote (U.string_of_class cs)))
+
+ val with_datatypes =
+ has_datatypes andalso Config.get ctxt SMT_Config.datatypes
+
+ fun no_dtyps (tr_context, ctxt) ts = (([], tr_context, ctxt), ts)
+
+ val (builtins, ts1) =
+ ithms
+ |> map (HOLogic.dest_Trueprop o Thm.prop_of o snd)
+ |> map (Envir.eta_contract o Envir.beta_norm)
+ |> mark_builtins ctxt
+
+ val ((dtyps, tr_context, ctxt1), ts2) =
+ ((make_tr_context prefixes, ctxt), ts1)
+ |-> (if with_datatypes then collect_datatypes_and_records else no_dtyps)
+
+ val (ctxt2, ts3) =
+ ts2
+ |> eta_expand
+ |> lift_lambdas ctxt1
+ ||> intro_explicit_application
+
+ val ((rewrite_rules, extra_thms), ts4) =
+ (if is_fol then folify ctxt2 builtins else pair ([], [])) ts3
+
+ val rewrite_rules' = fun_app_eq :: rewrite_rules
in
- (if is_fol then folify ctxt else relaxed) #>
- with_context (header ctxt) trans #>> uncurry (serialize comments)
+ (ts4, tr_context)
+ |-> intermediate header dtyps ctxt2
+ |>> uncurry (serialize comments)
+ ||> recon_of ctxt2 rewrite_rules' extra_thms ithms revert_typ revert_types
end
end