# HG changeset patch # User haftmann # Date 1366533678 -7200 # Node ID b3e599b5ecc8b43b6cdee3e6e2cb7d7826159e46 # Parent 7c1bc02633763ab881068cc8076265edb70e8da4 reflection as official HOL tool diff -r 7c1bc0263376 -r b3e599b5ecc8 src/HOL/Library/Reflection.thy --- a/src/HOL/Library/Reflection.thy Sun Apr 21 10:41:18 2013 +0200 +++ b/src/HOL/Library/Reflection.thy Sun Apr 21 10:41:18 2013 +0200 @@ -8,7 +8,7 @@ imports Main begin -ML_file "reflection.ML" +ML_file "~~/src/HOL/Tools/reflection.ML" method_setup reify = {* Attrib.thms -- diff -r 7c1bc0263376 -r b3e599b5ecc8 src/HOL/Library/reflection.ML --- a/src/HOL/Library/reflection.ML Sun Apr 21 10:41:18 2013 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,356 +0,0 @@ -(* Title: HOL/Library/reflection.ML - Author: Amine Chaieb, TU Muenchen - -A trial for automatical reification. -*) - -signature REFLECTION = -sig - val gen_reify: Proof.context -> thm list -> term -> thm - val gen_reify_tac: Proof.context -> thm list -> term option -> int -> tactic - val gen_reflection_tac: Proof.context -> (cterm -> thm) - -> thm list -> thm list -> term option -> int -> tactic - val get_default: Proof.context -> { reification_eqs: thm list, correctness_thms: thm list } - val add_reification_eq: attribute - val del_reification_eq: attribute - val add_correctness_thm: attribute - val del_correctness_thm: attribute - val default_reify_tac: Proof.context -> thm list -> term option -> int -> tactic - val default_reflection_tac: Proof.context -> thm list -> thm list -> term option -> int -> tactic -end; - -structure Reflection : REFLECTION = -struct - -val FWD = curry (op OF); - -fun dest_listT (Type (@{type_name "list"}, [T])) = T; - - -(* Make a congruence rule out of a defining equation for the interpretation - - th is one defining equation of f, - i.e. th is "f (Cp ?t1 ... ?tn) = P(f ?t1, .., f ?tn)" - Cp is a constructor pattern and P is a pattern - - The result is: - [|?A1 = f ?t1 ; .. ; ?An= f ?tn |] ==> P (?A1, .., ?An) = f (Cp ?t1 .. ?tn) - + the a list of names of the A1 .. An, Those are fresh in the ctxt *) - -fun mk_congeq ctxt fs th = - let - val Const (fN, _) = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq - |> fst |> strip_comb |> fst; - val thy = Proof_Context.theory_of ctxt; - val cert = Thm.cterm_of thy; - val ((_, [th']), ctxt') = Variable.import true [th] ctxt; - val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of th')); - fun add_fterms (t as t1 $ t2) = - if exists (fn f => Term.could_unify (t |> strip_comb |> fst, f)) fs - then insert (op aconv) t - else add_fterms t1 #> add_fterms t2 - | add_fterms (t as Abs _) = - if exists_Const (fn (c, _) => c = fN) t - then K [t] - else K [] - | add_fterms _ = I; - val fterms = add_fterms rhs []; - val (xs, ctxt'') = Variable.variant_fixes (replicate (length fterms) "x") ctxt'; - val tys = map fastype_of fterms; - val vs = map Free (xs ~~ tys); - val env = fterms ~~ vs; (*FIXME*) - fun replace_fterms (t as t1 $ t2) = - (case AList.lookup (op aconv) env t of - SOME v => v - | NONE => replace_fterms t1 $ replace_fterms t2) - | replace_fterms t = - (case AList.lookup (op aconv) env t of - SOME v => v - | NONE => t); - fun mk_def (Abs (x, xT, t), v) = - HOLogic.mk_Trueprop (HOLogic.all_const xT $ Abs (x, xT, HOLogic.mk_eq (v $ Bound 0, t))) - | mk_def (t, v) = HOLogic.mk_Trueprop (HOLogic.mk_eq (v, t)); - fun tryext x = - (x RS @{lemma "(\x. f x = g x) \ f = g" by blast} handle THM _ => x); - val cong = - (Goal.prove ctxt'' [] (map mk_def env) - (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, replace_fterms rhs))) - (fn {context, prems, ...} => - Local_Defs.unfold_tac context (map tryext prems) THEN rtac th' 1)) RS sym; - val (cong' :: vars') = - Variable.export ctxt'' ctxt (cong :: map (Drule.mk_term o cert) vs); - val vs' = map (fst o fst o Term.dest_Var o Thm.term_of o Drule.dest_term) vars'; - - in (vs', cong') end; - -(* congs is a list of pairs (P,th) where th is a theorem for - [| f p1 = A1; ...; f pn = An|] ==> f (C p1 .. pn) = P *) - -fun rearrange congs = - let - fun P (_, th) = - let val @{term "Trueprop"} $ (Const (@{const_name HOL.eq}, _) $ l $ _) = concl_of th - in can dest_Var l end; - val (yes, no) = List.partition P congs; - in no @ yes end; - -fun gen_reify ctxt eqs t = - let - 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_genreif da cgns (t, ctxt) bds = - let - val thy = Proof_Context.theory_of ctxt; - val cert = cterm_of thy; - fun tryabsdecomp (s, ctxt) bds = - (case s 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 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 (([(ta, ctxt')], - fn ([th], bds) => - (hd (Variable.export ctxt' ctxt [(Thm.forall_intr (cert x) 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 (s, ctxt) bds) - in - (case cgns of - [] => tryabsdecomp (t, ctxt) bds - | ((vns, cong) :: congs) => - (let - val cert = cterm_of thy; - val certy = ctyp_of thy; - val (tyenv, tmenv) = - Pattern.match thy - ((fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) (concl_of cong), t) - (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)) => (certy (TVar((vn, vi), s)), certy ty)) (Vartab.dest tyenv); - in - ((fts ~~ replicate (length fts) ctxt, - apfst (FWD (Drule.instantiate_normalize (ctyenv, its) cong))), bds) - end handle Pattern.MATCH => decomp_genreif da congs (t,ctxt) bds)) - end; - - (* looks for the atoms equation and instantiates it with the right number *) - fun mk_decompatom eqs (t, ctxt) bds = (([], fn (_, bds) => - let - val tT = fastype_of t; - fun isat eq = - 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 acc = - case t of - Const(@{const_name "List.nth"}, _) $ vs $ n => insert (fn ((a, _), (b, _)) => a aconv b) (t, (vs, n)) acc - | t1 $ t2 => get_nths t1 (get_nths t2 acc) - | Abs (_ ,_ ,t') => get_nths t' acc - | _ => acc; - - fun tryeqs [] bds = error "Can not find the atoms equation" - | tryeqs (eq :: eqs) bds = (( - 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, t) (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 (fn (v, t) => (ih v, ih t)) (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); - - (* 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 thy = Proof_Context.theory_of ctxt'; - val cert = cterm_of thy; - val vstys = map (fn (t, v) => (t, SOME (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 (fn (v as Var (_, t)) => - (cert v, (the o the) (AList.lookup (op =) vstys t))) (filter is_Var 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 (congs, bds) = mk_congs ctxt eqs; - val congs = rearrange congs; - val (th, bds) = divide_and_conquer' (decomp_genreif (mk_decompatom eqs) congs) (t,ctxt) bds; - fun is_listVar (Var (_, t)) = can dest_listT t - | is_listVar _ = false; - val vars = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd - |> strip_comb |> snd |> filter is_listVar; - val cert = cterm_of (Proof_Context.theory_of ctxt); - val cvs = map (fn (v as Var(_, t)) => (cert v, - the (AList.lookup Type.could_unify bds t) |> snd |> HOLogic.mk_list (dest_listT t) |> cert)) vars; - val th' = Drule.instantiate_normalize ([], cvs) th; - val t' = (fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) th'; - val th'' = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq (t, t'))) - (fn _ => simp_tac ctxt 1) - in FWD trans [th'',th'] end; - -fun gen_reflect ctxt conv corr_thms eqs t = - let - val reify_thm = gen_reify ctxt eqs t; - fun try_corr thm = - SOME (FWD trans [reify_thm, thm RS sym]) handle THM _ => NONE; - val thm = case get_first try_corr corr_thms - of NONE => error "No suitable correctness theorem found" - | SOME thm => thm; - val ft = (Thm.dest_arg1 o Thm.dest_arg o Thm.dest_arg o cprop_of) thm; - val rth = conv ft; - in - thm - |> simplify (put_simpset HOL_basic_ss ctxt addsimps [rth]) - |> simplify (put_simpset HOL_basic_ss ctxt addsimps eqs addsimps @{thms nth_Cons_0 nth_Cons_Suc}) - end; - -fun tac_of_thm mk_thm to = SUBGOAL (fn (goal, i) => - let - val t = (case to of NONE => HOLogic.dest_Trueprop goal | SOME t => t) - val thm = mk_thm t RS ssubst; - in rtac thm i end); - -fun gen_reify_tac ctxt eqs = tac_of_thm (gen_reify ctxt eqs); - -(*Reflection calls reification and uses the correctness theorem assumed to be the head of the list*) -fun gen_reflection_tac ctxt conv corr_thms eqs = - tac_of_thm (gen_reflect ctxt conv corr_thms eqs); - -structure Data = Generic_Data -( - type T = thm list * thm list; - val empty = ([], []); - val extend = I; - fun merge ((ths1, rths1), (ths2, rths2)) = - (Thm.merge_thms (ths1, ths2), Thm.merge_thms (rths1, rths2)); -); - -fun get_default ctxt = - let - val (reification_eqs, correctness_thms) = Data.get (Context.Proof ctxt); - in { reification_eqs = reification_eqs, correctness_thms = correctness_thms } end; - -val add_reification_eq = Thm.declaration_attribute (Data.map o apfst o Thm.add_thm); -val del_reification_eq = Thm.declaration_attribute (Data.map o apfst o Thm.del_thm); -val add_correctness_thm = Thm.declaration_attribute (Data.map o apsnd o Thm.add_thm); -val del_correctness_thm = Thm.declaration_attribute (Data.map o apsnd o Thm.del_thm); - -val _ = Context.>> (Context.map_theory - (Attrib.setup @{binding reify} - (Attrib.add_del add_reification_eq del_reification_eq) "declare reification equations" #> - Attrib.setup @{binding reflection} - (Attrib.add_del add_correctness_thm del_correctness_thm) "declare reflection correctness theorems")); - -fun default_reify_tac ctxt user_eqs = - let - val { reification_eqs = default_eqs, correctness_thms = _ } = - get_default ctxt; - val eqs = fold Thm.add_thm user_eqs default_eqs; - in gen_reify_tac ctxt eqs end; - -fun default_reflection_tac ctxt user_thms user_eqs = - let - val { reification_eqs = default_eqs, correctness_thms = default_thms } = - get_default ctxt; - val corr_thms = fold Thm.add_thm user_thms default_thms; - val eqs = fold Thm.add_thm user_eqs default_eqs; - val conv = Code_Evaluation.dynamic_conv (Proof_Context.theory_of ctxt); - (*FIXME why Code_Evaluation.dynamic_conv? very specific*) - in gen_reflection_tac ctxt conv corr_thms eqs end; - - -end diff -r 7c1bc0263376 -r b3e599b5ecc8 src/HOL/Tools/reflection.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/reflection.ML Sun Apr 21 10:41:18 2013 +0200 @@ -0,0 +1,356 @@ +(* Title: HOL/Tools/reflection.ML + Author: Amine Chaieb, TU Muenchen + +A trial for automatical reification. +*) + +signature REFLECTION = +sig + val gen_reify: Proof.context -> thm list -> term -> thm + val gen_reify_tac: Proof.context -> thm list -> term option -> int -> tactic + val gen_reflection_tac: Proof.context -> (cterm -> thm) + -> thm list -> thm list -> term option -> int -> tactic + val get_default: Proof.context -> { reification_eqs: thm list, correctness_thms: thm list } + val add_reification_eq: attribute + val del_reification_eq: attribute + val add_correctness_thm: attribute + val del_correctness_thm: attribute + val default_reify_tac: Proof.context -> thm list -> term option -> int -> tactic + val default_reflection_tac: Proof.context -> thm list -> thm list -> term option -> int -> tactic +end; + +structure Reflection : REFLECTION = +struct + +val FWD = curry (op OF); + +fun dest_listT (Type (@{type_name "list"}, [T])) = T; + + +(* Make a congruence rule out of a defining equation for the interpretation + + th is one defining equation of f, + i.e. th is "f (Cp ?t1 ... ?tn) = P(f ?t1, .., f ?tn)" + Cp is a constructor pattern and P is a pattern + + The result is: + [|?A1 = f ?t1 ; .. ; ?An= f ?tn |] ==> P (?A1, .., ?An) = f (Cp ?t1 .. ?tn) + + the a list of names of the A1 .. An, Those are fresh in the ctxt *) + +fun mk_congeq ctxt fs th = + let + val Const (fN, _) = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq + |> fst |> strip_comb |> fst; + val thy = Proof_Context.theory_of ctxt; + val cert = Thm.cterm_of thy; + val ((_, [th']), ctxt') = Variable.import true [th] ctxt; + val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of th')); + fun add_fterms (t as t1 $ t2) = + if exists (fn f => Term.could_unify (t |> strip_comb |> fst, f)) fs + then insert (op aconv) t + else add_fterms t1 #> add_fterms t2 + | add_fterms (t as Abs _) = + if exists_Const (fn (c, _) => c = fN) t + then K [t] + else K [] + | add_fterms _ = I; + val fterms = add_fterms rhs []; + val (xs, ctxt'') = Variable.variant_fixes (replicate (length fterms) "x") ctxt'; + val tys = map fastype_of fterms; + val vs = map Free (xs ~~ tys); + val env = fterms ~~ vs; (*FIXME*) + fun replace_fterms (t as t1 $ t2) = + (case AList.lookup (op aconv) env t of + SOME v => v + | NONE => replace_fterms t1 $ replace_fterms t2) + | replace_fterms t = + (case AList.lookup (op aconv) env t of + SOME v => v + | NONE => t); + fun mk_def (Abs (x, xT, t), v) = + HOLogic.mk_Trueprop (HOLogic.all_const xT $ Abs (x, xT, HOLogic.mk_eq (v $ Bound 0, t))) + | mk_def (t, v) = HOLogic.mk_Trueprop (HOLogic.mk_eq (v, t)); + fun tryext x = + (x RS @{lemma "(\x. f x = g x) \ f = g" by blast} handle THM _ => x); + val cong = + (Goal.prove ctxt'' [] (map mk_def env) + (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, replace_fterms rhs))) + (fn {context, prems, ...} => + Local_Defs.unfold_tac context (map tryext prems) THEN rtac th' 1)) RS sym; + val (cong' :: vars') = + Variable.export ctxt'' ctxt (cong :: map (Drule.mk_term o cert) vs); + val vs' = map (fst o fst o Term.dest_Var o Thm.term_of o Drule.dest_term) vars'; + + in (vs', cong') end; + +(* congs is a list of pairs (P,th) where th is a theorem for + [| f p1 = A1; ...; f pn = An|] ==> f (C p1 .. pn) = P *) + +fun rearrange congs = + let + fun P (_, th) = + let val @{term "Trueprop"} $ (Const (@{const_name HOL.eq}, _) $ l $ _) = concl_of th + in can dest_Var l end; + val (yes, no) = List.partition P congs; + in no @ yes end; + +fun gen_reify ctxt eqs t = + let + 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_genreif da cgns (t, ctxt) bds = + let + val thy = Proof_Context.theory_of ctxt; + val cert = cterm_of thy; + fun tryabsdecomp (s, ctxt) bds = + (case s 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 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 (([(ta, ctxt')], + fn ([th], bds) => + (hd (Variable.export ctxt' ctxt [(Thm.forall_intr (cert x) 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 (s, ctxt) bds) + in + (case cgns of + [] => tryabsdecomp (t, ctxt) bds + | ((vns, cong) :: congs) => + (let + val cert = cterm_of thy; + val certy = ctyp_of thy; + val (tyenv, tmenv) = + Pattern.match thy + ((fst o HOLogic.dest_eq o HOLogic.dest_Trueprop) (concl_of cong), t) + (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)) => (certy (TVar((vn, vi), s)), certy ty)) (Vartab.dest tyenv); + in + ((fts ~~ replicate (length fts) ctxt, + apfst (FWD (Drule.instantiate_normalize (ctyenv, its) cong))), bds) + end handle Pattern.MATCH => decomp_genreif da congs (t,ctxt) bds)) + end; + + (* looks for the atoms equation and instantiates it with the right number *) + fun mk_decompatom eqs (t, ctxt) bds = (([], fn (_, bds) => + let + val tT = fastype_of t; + fun isat eq = + 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 acc = + case t of + Const(@{const_name "List.nth"}, _) $ vs $ n => insert (fn ((a, _), (b, _)) => a aconv b) (t, (vs, n)) acc + | t1 $ t2 => get_nths t1 (get_nths t2 acc) + | Abs (_ ,_ ,t') => get_nths t' acc + | _ => acc; + + fun tryeqs [] bds = error "Can not find the atoms equation" + | tryeqs (eq :: eqs) bds = (( + 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, t) (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 (fn (v, t) => (ih v, ih t)) (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); + + (* 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 thy = Proof_Context.theory_of ctxt'; + val cert = cterm_of thy; + val vstys = map (fn (t, v) => (t, SOME (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 (fn (v as Var (_, t)) => + (cert v, (the o the) (AList.lookup (op =) vstys t))) (filter is_Var 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 (congs, bds) = mk_congs ctxt eqs; + val congs = rearrange congs; + val (th, bds) = divide_and_conquer' (decomp_genreif (mk_decompatom eqs) congs) (t,ctxt) bds; + fun is_listVar (Var (_, t)) = can dest_listT t + | is_listVar _ = false; + val vars = th |> prop_of |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> snd + |> strip_comb |> snd |> filter is_listVar; + val cert = cterm_of (Proof_Context.theory_of ctxt); + val cvs = map (fn (v as Var(_, t)) => (cert v, + the (AList.lookup Type.could_unify bds t) |> snd |> HOLogic.mk_list (dest_listT t) |> cert)) vars; + val th' = Drule.instantiate_normalize ([], cvs) th; + val t' = (fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) th'; + val th'' = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq (t, t'))) + (fn _ => simp_tac ctxt 1) + in FWD trans [th'',th'] end; + +fun gen_reflect ctxt conv corr_thms eqs t = + let + val reify_thm = gen_reify ctxt eqs t; + fun try_corr thm = + SOME (FWD trans [reify_thm, thm RS sym]) handle THM _ => NONE; + val thm = case get_first try_corr corr_thms + of NONE => error "No suitable correctness theorem found" + | SOME thm => thm; + val ft = (Thm.dest_arg1 o Thm.dest_arg o Thm.dest_arg o cprop_of) thm; + val rth = conv ft; + in + thm + |> simplify (put_simpset HOL_basic_ss ctxt addsimps [rth]) + |> simplify (put_simpset HOL_basic_ss ctxt addsimps eqs addsimps @{thms nth_Cons_0 nth_Cons_Suc}) + end; + +fun tac_of_thm mk_thm to = SUBGOAL (fn (goal, i) => + let + val t = (case to of NONE => HOLogic.dest_Trueprop goal | SOME t => t) + val thm = mk_thm t RS ssubst; + in rtac thm i end); + +fun gen_reify_tac ctxt eqs = tac_of_thm (gen_reify ctxt eqs); + +(*Reflection calls reification and uses the correctness theorem assumed to be the head of the list*) +fun gen_reflection_tac ctxt conv corr_thms eqs = + tac_of_thm (gen_reflect ctxt conv corr_thms eqs); + +structure Data = Generic_Data +( + type T = thm list * thm list; + val empty = ([], []); + val extend = I; + fun merge ((ths1, rths1), (ths2, rths2)) = + (Thm.merge_thms (ths1, ths2), Thm.merge_thms (rths1, rths2)); +); + +fun get_default ctxt = + let + val (reification_eqs, correctness_thms) = Data.get (Context.Proof ctxt); + in { reification_eqs = reification_eqs, correctness_thms = correctness_thms } end; + +val add_reification_eq = Thm.declaration_attribute (Data.map o apfst o Thm.add_thm); +val del_reification_eq = Thm.declaration_attribute (Data.map o apfst o Thm.del_thm); +val add_correctness_thm = Thm.declaration_attribute (Data.map o apsnd o Thm.add_thm); +val del_correctness_thm = Thm.declaration_attribute (Data.map o apsnd o Thm.del_thm); + +val _ = Context.>> (Context.map_theory + (Attrib.setup @{binding reify} + (Attrib.add_del add_reification_eq del_reification_eq) "declare reification equations" #> + Attrib.setup @{binding reflection} + (Attrib.add_del add_correctness_thm del_correctness_thm) "declare reflection correctness theorems")); + +fun default_reify_tac ctxt user_eqs = + let + val { reification_eqs = default_eqs, correctness_thms = _ } = + get_default ctxt; + val eqs = fold Thm.add_thm user_eqs default_eqs; + in gen_reify_tac ctxt eqs end; + +fun default_reflection_tac ctxt user_thms user_eqs = + let + val { reification_eqs = default_eqs, correctness_thms = default_thms } = + get_default ctxt; + val corr_thms = fold Thm.add_thm user_thms default_thms; + val eqs = fold Thm.add_thm user_eqs default_eqs; + val conv = Code_Evaluation.dynamic_conv (Proof_Context.theory_of ctxt); + (*FIXME why Code_Evaluation.dynamic_conv? very specific*) + in gen_reflection_tac ctxt conv corr_thms eqs end; + + +end