--- a/src/HOL/Tools/reification.ML Sun Jun 02 09:10:53 2013 +0200
+++ b/src/HOL/Tools/reification.ML Sun Jun 02 10:57:21 2013 +0200
@@ -103,179 +103,180 @@
fun dereify ctxt eqs =
rewrite_with ctxt (eqs @ @{thms nth_Cons_0 nth_Cons_Suc});
-fun conv ctxt eqs ct =
+fun index_of t bds =
+ let
+ val tt = HOLogic.listT (fastype_of t);
+ in
+ (case AList.lookup Type.could_unify bds tt of
+ NONE => error "index_of: type not found in environements!"
+ | SOME (tbs, tats) =>
+ let
+ val i = find_index (fn t' => t' = t) tats;
+ val j = find_index (fn t' => t' = t) tbs;
+ in
+ if j = ~1 then
+ if i = ~1
+ then (length tbs + length tats, AList.update Type.could_unify (tt, (tbs, tats @ [t])) bds)
+ else (i, bds)
+ else (j, bds)
+ end)
+ end;
+
+(* Generic decomp for reification : matches the actual term with the
+ rhs of one cong rule. The result of the matching guides the
+ proof synthesis: The matches of the introduced Variables A1 .. An are
+ processed recursively
+ The rest is instantiated in the cong rule,i.e. no reification is needed *)
+
+(* da is the decomposition for atoms, ie. it returns ([],g) where g
+ returns the right instance f (AtC n) = t , where AtC is the Atoms
+ constructor and n is the number of the atom corresponding to t *)
+fun decomp_reify da cgns (ct, ctxt) bds =
let
- fun index_of t bds =
+ val thy = Proof_Context.theory_of ctxt;
+ val cert = cterm_of thy;
+ val certT = ctyp_of thy;
+ fun tryabsdecomp (ct, ctxt) bds =
+ (case Thm.term_of ct of
+ Abs (_, xT, ta) =>
+ let
+ val ([raw_xn], ctxt') = Variable.variant_fixes ["x"] ctxt;
+ val (xn, ta) = Syntax_Trans.variant_abs (raw_xn, xT, ta); (* FIXME !? *)
+ val x = Free (xn, xT);
+ val cx = cert x;
+ val cta = cert ta;
+ val bds = (case AList.lookup Type.could_unify bds (HOLogic.listT xT) of
+ NONE => error "tryabsdecomp: Type not found in the Environement"
+ | SOME (bsT, atsT) => AList.update Type.could_unify (HOLogic.listT xT,
+ (x :: bsT, atsT)) bds);
+ in (([(cta, ctxt')],
+ fn ([th], bds) =>
+ (hd (Variable.export ctxt' ctxt [(Thm.forall_intr cx th) COMP allI]),
+ let
+ val (bsT, asT) = the (AList.lookup Type.could_unify bds (HOLogic.listT xT));
+ in
+ AList.update Type.could_unify (HOLogic.listT xT, (tl bsT, asT)) bds
+ end)),
+ bds)
+ end
+ | _ => da (ct, ctxt) bds)
+ in
+ (case cgns of
+ [] => tryabsdecomp (ct, ctxt) bds
+ | ((vns, cong) :: congs) =>
+ (let
+ val (tyenv, tmenv) =
+ Pattern.match thy
+ ((fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) (concl_of cong), Thm.term_of ct)
+ (Vartab.empty, Vartab.empty);
+ val (fnvs, invs) = List.partition (fn ((vn, _),_) => member (op =) vns vn) (Vartab.dest tmenv);
+ val (fts, its) =
+ (map (snd o snd) fnvs,
+ map (fn ((vn, vi), (tT, t)) => (cert (Var ((vn, vi), tT)), cert t)) invs);
+ val ctyenv = map (fn ((vn, vi), (s, ty)) => (certT (TVar((vn, vi), s)), certT ty)) (Vartab.dest tyenv);
+ in
+ ((map cert fts ~~ replicate (length fts) ctxt,
+ apfst (FWD (Drule.instantiate_normalize (ctyenv, its) cong))), bds)
+ end handle Pattern.MATCH => decomp_reify da congs (ct, ctxt) bds))
+ end;
+
+fun get_nths (t as (Const (@{const_name "List.nth"}, _) $ vs $ n)) =
+ AList.update (op aconv) (t, (vs, n))
+ | get_nths (t1 $ t2) = get_nths t1 #> get_nths t2
+ | get_nths (Abs (_, _, t')) = get_nths t'
+ | get_nths _ = I;
+
+fun tryeqs [] (ct, ctxt) bds = error "Cannot find the atoms equation"
+ | tryeqs (eq :: eqs) (ct, ctxt) bds = ((
let
- val tt = HOLogic.listT (fastype_of t);
- in
- (case AList.lookup Type.could_unify bds tt of
- NONE => error "index_of: type not found in environements!"
- | SOME (tbs, tats) =>
- let
- val i = find_index (fn t' => t' = t) tats;
- val j = find_index (fn t' => t' = t) tbs;
- in
- if j = ~1 then
- if i = ~1
- then (length tbs + length tats, AList.update Type.could_unify (tt, (tbs, tats @ [t])) bds)
- else (i, bds)
- else (j, bds)
- end)
- end;
-
- (* Generic decomp for reification : matches the actual term with the
- rhs of one cong rule. The result of the matching guides the
- proof synthesis: The matches of the introduced Variables A1 .. An are
- processed recursively
- The rest is instantiated in the cong rule,i.e. no reification is needed *)
-
- (* da is the decomposition for atoms, ie. it returns ([],g) where g
- returns the right instance f (AtC n) = t , where AtC is the Atoms
- constructor and n is the number of the atom corresponding to t *)
- fun decomp_reify da cgns (ct, ctxt) bds =
- let
- val thy = Proof_Context.theory_of ctxt;
+ val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd;
+ val nths = get_nths rhs [];
+ val (vss, _) = fold_rev (fn (_, (vs, n)) => fn (vss, ns) =>
+ (insert (op aconv) vs vss, insert (op aconv) n ns)) nths ([], []);
+ val (vsns, ctxt') = Variable.variant_fixes (replicate (length vss) "vs") ctxt;
+ val (xns, ctxt'') = Variable.variant_fixes (replicate (length nths) "x") ctxt';
+ val thy = Proof_Context.theory_of ctxt'';
val cert = cterm_of thy;
val certT = ctyp_of thy;
- fun tryabsdecomp (ct, ctxt) bds =
- (case Thm.term_of ct of
- Abs (_, xT, ta) =>
- let
- val ([raw_xn], ctxt') = Variable.variant_fixes ["x"] ctxt;
- val (xn, ta) = Syntax_Trans.variant_abs (raw_xn, xT, ta); (* FIXME !? *)
- val x = Free (xn, xT);
- val cx = cert x;
- val cta = cert ta;
- val bds = (case AList.lookup Type.could_unify bds (HOLogic.listT xT) of
- NONE => error "tryabsdecomp: Type not found in the Environement"
- | SOME (bsT, atsT) => AList.update Type.could_unify (HOLogic.listT xT,
- (x :: bsT, atsT)) bds);
- in (([(cta, ctxt')],
- fn ([th], bds) =>
- (hd (Variable.export ctxt' ctxt [(Thm.forall_intr cx th) COMP allI]),
- let
- val (bsT, asT) = the (AList.lookup Type.could_unify bds (HOLogic.listT xT));
- in
- AList.update Type.could_unify (HOLogic.listT xT, (tl bsT, asT)) bds
- end)),
- bds)
- end
- | _ => da (ct, ctxt) bds)
- in
- (case cgns of
- [] => tryabsdecomp (ct, ctxt) bds
- | ((vns, cong) :: congs) =>
- (let
- val (tyenv, tmenv) =
- Pattern.match thy
- ((fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) (concl_of cong), Thm.term_of ct)
- (Vartab.empty, Vartab.empty);
- val (fnvs, invs) = List.partition (fn ((vn, _),_) => member (op =) vns vn) (Vartab.dest tmenv);
- val (fts, its) =
- (map (snd o snd) fnvs,
- map (fn ((vn, vi), (tT, t)) => (cert (Var ((vn, vi), tT)), cert t)) invs);
- val ctyenv = map (fn ((vn, vi), (s, ty)) => (certT (TVar((vn, vi), s)), certT ty)) (Vartab.dest tyenv);
- in
- ((map cert fts ~~ replicate (length fts) ctxt,
- apfst (FWD (Drule.instantiate_normalize (ctyenv, its) cong))), bds)
- end handle Pattern.MATCH => decomp_reify da congs (ct, ctxt) bds))
- end;
-
- (* looks for the atoms equation and instantiates it with the right number *)
- fun mk_decompatom eqs (ct, ctxt) bds = (([], fn (_, bds) =>
- let
- val tT = fastype_of (Thm.term_of ct);
- fun isat eq =
+ val vsns_map = vss ~~ vsns;
+ val xns_map = fst (split_list nths) ~~ xns;
+ val subst = map (fn (nt, xn) => (nt, Var ((xn, 0), fastype_of nt))) xns_map;
+ val rhs_P = subst_free subst rhs;
+ val (tyenv, tmenv) = Pattern.match thy (rhs_P, Thm.term_of ct) (Vartab.empty, Vartab.empty);
+ val sbst = Envir.subst_term (tyenv, tmenv);
+ val sbsT = Envir.subst_type tyenv;
+ val subst_ty = map (fn (n, (s, t)) =>
+ (certT (TVar (n, s)), certT t)) (Vartab.dest tyenv)
+ val tml = Vartab.dest tmenv;
+ val (subst_ns, bds) = fold_map
+ (fn (Const _ $ _ $ n, Var (xn0, _)) => fn bds =>
+ let
+ val name = snd (the (AList.lookup (op =) tml xn0));
+ val (idx, bds) = index_of name bds;
+ in ((cert n, idx |> (HOLogic.mk_nat #> cert)), bds) end) subst bds;
+ val subst_vs =
let
- val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd;
- in exists_Const
- (fn (n, ty) => n = @{const_name "List.nth"}
- andalso AList.defined Type.could_unify bds (domain_type ty)) rhs
- andalso Type.could_unify (fastype_of rhs, tT)
- end;
-
- fun get_nths (t as (Const (@{const_name "List.nth"}, _) $ vs $ n)) =
- AList.update (op aconv) (t, (vs, n))
- | get_nths (t1 $ t2) = get_nths t1 #> get_nths t2
- | get_nths (Abs (_, _, t')) = get_nths t'
- | get_nths _ = I;
-
- fun tryeqs [] bds = error "Cannot find the atoms equation"
- | tryeqs (eq :: eqs) bds = ((
+ fun h (Const _ $ (vs as Var (_, lT)) $ _, Var (_, T)) =
let
- val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd;
- val nths = get_nths rhs [];
- val (vss, _) = fold_rev (fn (_, (vs, n)) => fn (vss, ns) =>
- (insert (op aconv) vs vss, insert (op aconv) n ns)) nths ([], []);
- val (vsns, ctxt') = Variable.variant_fixes (replicate (length vss) "vs") ctxt;
- val (xns, ctxt'') = Variable.variant_fixes (replicate (length nths) "x") ctxt';
- val thy = Proof_Context.theory_of ctxt'';
- val cert = cterm_of thy;
- val certT = ctyp_of thy;
- val vsns_map = vss ~~ vsns;
- val xns_map = fst (split_list nths) ~~ xns;
- val subst = map (fn (nt, xn) => (nt, Var ((xn, 0), fastype_of nt))) xns_map;
- val rhs_P = subst_free subst rhs;
- val (tyenv, tmenv) = Pattern.match thy (rhs_P, Thm.term_of ct) (Vartab.empty, Vartab.empty);
- val sbst = Envir.subst_term (tyenv, tmenv);
- val sbsT = Envir.subst_type tyenv;
- val subst_ty = map (fn (n, (s, t)) =>
- (certT (TVar (n, s)), certT t)) (Vartab.dest tyenv)
- val tml = Vartab.dest tmenv;
- val (subst_ns, bds) = fold_map
- (fn (Const _ $ _ $ n, Var (xn0, _)) => fn bds =>
- let
- val name = snd (the (AList.lookup (op =) tml xn0));
- val (idx, bds) = index_of name bds;
- in ((cert n, idx |> (HOLogic.mk_nat #> cert)), bds) end) subst bds;
- val subst_vs =
- let
- fun h (Const _ $ (vs as Var (_, lT)) $ _, Var (_, T)) =
- let
- val cns = sbst (Const (@{const_name "List.Cons"}, T --> lT --> lT));
- val lT' = sbsT lT;
- val (bsT, _) = the (AList.lookup Type.could_unify bds lT);
- val vsn = the (AList.lookup (op =) vsns_map vs);
- val cvs = cert (fold_rev (fn x => fn xs => cns $ x $xs) bsT (Free (vsn, lT')));
- in (cert vs, cvs) end;
- in map h subst end;
- val cts = map (fn ((vn, vi), (tT, t)) => (cert (Var ((vn, vi), tT)), cert t))
- (fold (AList.delete (fn (((a : string), _), (b, _)) => a = b))
- (map (fn n => (n, 0)) xns) tml);
- val substt =
- let
- val ih = Drule.cterm_rule (Thm.instantiate (subst_ty, []));
- in map (pairself ih) (subst_ns @ subst_vs @ cts) end;
- val th = (Drule.instantiate_normalize (subst_ty, substt) eq) RS sym;
- in (hd (Variable.export ctxt'' ctxt [th]), bds) end)
- handle Pattern.MATCH => tryeqs eqs bds)
- in tryeqs (filter isat eqs) bds end), bds);
+ val cns = sbst (Const (@{const_name "List.Cons"}, T --> lT --> lT));
+ val lT' = sbsT lT;
+ val (bsT, _) = the (AList.lookup Type.could_unify bds lT);
+ val vsn = the (AList.lookup (op =) vsns_map vs);
+ val cvs = cert (fold_rev (fn x => fn xs => cns $ x $xs) bsT (Free (vsn, lT')));
+ in (cert vs, cvs) end;
+ in map h subst end;
+ val cts = map (fn ((vn, vi), (tT, t)) => (cert (Var ((vn, vi), tT)), cert t))
+ (fold (AList.delete (fn (((a : string), _), (b, _)) => a = b))
+ (map (fn n => (n, 0)) xns) tml);
+ val substt =
+ let
+ val ih = Drule.cterm_rule (Thm.instantiate (subst_ty, []));
+ in map (pairself ih) (subst_ns @ subst_vs @ cts) end;
+ val th = (Drule.instantiate_normalize (subst_ty, substt) eq) RS sym;
+ in (hd (Variable.export ctxt'' ctxt [th]), bds) end)
+ handle Pattern.MATCH => tryeqs eqs (ct, ctxt) bds);
+
+(* looks for the atoms equation and instantiates it with the right number *)
- (* Generic reification procedure: *)
- (* creates all needed cong rules and then just uses the theorem synthesis *)
-
- fun mk_congs ctxt eqs =
+fun mk_decompatom eqs (ct, ctxt) bds = (([], fn (_, bds) =>
+ let
+ val tT = fastype_of (Thm.term_of ct);
+ fun isat eq =
let
- val fs = fold_rev (fn eq => insert (op =) (eq |> prop_of |> HOLogic.dest_Trueprop
- |> HOLogic.dest_eq |> fst |> strip_comb
- |> fst)) eqs [];
- val tys = fold_rev (fn f => fold (insert (op =)) (f |> fastype_of |> binder_types |> tl)) fs [];
- val (vs, ctxt') = Variable.variant_fixes (replicate (length tys) "vs") ctxt;
- val cert = cterm_of (Proof_Context.theory_of ctxt');
- val subst =
- the o AList.lookup (op =) (map2 (fn T => fn v => (T, cert (Free (v, T)))) tys vs);
- fun prep_eq eq =
- let
- val (_, _ :: vs) = eq |> prop_of |> HOLogic.dest_Trueprop
- |> HOLogic.dest_eq |> fst |> strip_comb;
- val subst = map_filter (fn (v as Var (_, T)) => SOME (cert v, subst T)
- | _ => NONE) vs;
- in Thm.instantiate ([], subst) eq end;
- val (ps, congs) = map_split (mk_congeq ctxt' fs o prep_eq) eqs;
- val bds = AList.make (K ([], [])) tys;
- in (ps ~~ Variable.export ctxt' ctxt congs, bds) end
+ val rhs = eq |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd;
+ in exists_Const
+ (fn (n, ty) => n = @{const_name "List.nth"}
+ andalso AList.defined Type.could_unify bds (domain_type ty)) rhs
+ andalso Type.could_unify (fastype_of rhs, tT)
+ end;
+ in tryeqs (filter isat eqs) (ct, ctxt) bds end), bds);
+
+(* Generic reification procedure: *)
+(* creates all needed cong rules and then just uses the theorem synthesis *)
+fun mk_congs ctxt eqs =
+ let
+ val fs = fold_rev (fn eq => insert (op =) (eq |> prop_of |> HOLogic.dest_Trueprop
+ |> HOLogic.dest_eq |> fst |> strip_comb
+ |> fst)) eqs [];
+ val tys = fold_rev (fn f => fold (insert (op =)) (f |> fastype_of |> binder_types |> tl)) fs [];
+ val (vs, ctxt') = Variable.variant_fixes (replicate (length tys) "vs") ctxt;
+ val cert = cterm_of (Proof_Context.theory_of ctxt');
+ val subst =
+ the o AList.lookup (op =) (map2 (fn T => fn v => (T, cert (Free (v, T)))) tys vs);
+ fun prep_eq eq =
+ let
+ val (_, _ :: vs) = eq |> prop_of |> HOLogic.dest_Trueprop
+ |> HOLogic.dest_eq |> fst |> strip_comb;
+ val subst = map_filter (fn (v as Var (_, T)) => SOME (cert v, subst T)
+ | _ => NONE) vs;
+ in Thm.instantiate ([], subst) eq end;
+ val (ps, congs) = map_split (mk_congeq ctxt' fs o prep_eq) eqs;
+ val bds = AList.make (K ([], [])) tys;
+ in (ps ~~ Variable.export ctxt' ctxt congs, bds) end
+
+fun conv ctxt eqs ct =
+ let
val (congs, bds) = mk_congs ctxt eqs;
val congs = rearrange congs;
val (th, bds') = apfst mk_eq (divide_and_conquer' (decomp_reify (mk_decompatom eqs) congs) (ct, ctxt) bds);