# HG changeset patch # User haftmann # Date 1370163441 -7200 # Node ID ca4932dad084b84b97f785bd69b7813436c9fb81 # Parent 7e54c4d964e7085436e2034635900493ffc8ada1 denesting of functions diff -r 7e54c4d964e7 -r ca4932dad084 src/HOL/Tools/reification.ML --- 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);