--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/Quot/quotient_term.ML Thu Feb 25 07:57:17 2010 +0100
@@ -0,0 +1,786 @@
+(* Title: quotient_term.thy
+ Author: Cezary Kaliszyk and Christian Urban
+
+ Constructs terms corresponding to goals from
+ lifting theorems to quotient types.
+*)
+
+signature QUOTIENT_TERM =
+sig
+ exception LIFT_MATCH of string
+
+ datatype flag = AbsF | RepF
+
+ val absrep_fun: flag -> Proof.context -> typ * typ -> term
+ val absrep_fun_chk: flag -> Proof.context -> typ * typ -> term
+
+ (* Allows Nitpick to represent quotient types as single elements from raw type *)
+ val absrep_const_chk: flag -> Proof.context -> string -> term
+
+ val equiv_relation: Proof.context -> typ * typ -> term
+ val equiv_relation_chk: Proof.context -> typ * typ -> term
+
+ val regularize_trm: Proof.context -> term * term -> term
+ val regularize_trm_chk: Proof.context -> term * term -> term
+
+ val inj_repabs_trm: Proof.context -> term * term -> term
+ val inj_repabs_trm_chk: Proof.context -> term * term -> term
+
+ val quotient_lift_const: string * term -> local_theory -> term
+ val quotient_lift_all: Proof.context -> term -> term
+end;
+
+structure Quotient_Term: QUOTIENT_TERM =
+struct
+
+open Quotient_Info;
+
+exception LIFT_MATCH of string
+
+
+
+(*** Aggregate Rep/Abs Function ***)
+
+
+(* The flag RepF is for types in negative position; AbsF is for types
+ in positive position. Because of this, function types need to be
+ treated specially, since there the polarity changes.
+*)
+
+datatype flag = AbsF | RepF
+
+fun negF AbsF = RepF
+ | negF RepF = AbsF
+
+fun is_identity (Const (@{const_name "id"}, _)) = true
+ | is_identity _ = false
+
+fun mk_identity ty = Const (@{const_name "id"}, ty --> ty)
+
+fun mk_fun_compose flag (trm1, trm2) =
+ case flag of
+ AbsF => Const (@{const_name "comp"}, dummyT) $ trm1 $ trm2
+ | RepF => Const (@{const_name "comp"}, dummyT) $ trm2 $ trm1
+
+fun get_mapfun ctxt s =
+let
+ val thy = ProofContext.theory_of ctxt
+ val exn = LIFT_MATCH ("No map function for type " ^ quote s ^ " found.")
+ val mapfun = #mapfun (maps_lookup thy s) handle Quotient_Info.NotFound => raise exn
+in
+ Const (mapfun, dummyT)
+end
+
+(* makes a Free out of a TVar *)
+fun mk_Free (TVar ((x, i), _)) = Free (unprefix "'" x ^ string_of_int i, dummyT)
+
+(* produces an aggregate map function for the
+ rty-part of a quotient definition; abstracts
+ over all variables listed in vs (these variables
+ correspond to the type variables in rty)
+
+ for example for: (?'a list * ?'b)
+ it produces: %a b. prod_map (map a) b
+*)
+fun mk_mapfun ctxt vs rty =
+let
+ val vs' = map (mk_Free) vs
+
+ fun mk_mapfun_aux rty =
+ case rty of
+ TVar _ => mk_Free rty
+ | Type (_, []) => mk_identity rty
+ | Type (s, tys) => list_comb (get_mapfun ctxt s, map mk_mapfun_aux tys)
+ | _ => raise LIFT_MATCH "mk_mapfun (default)"
+in
+ fold_rev Term.lambda vs' (mk_mapfun_aux rty)
+end
+
+(* looks up the (varified) rty and qty for
+ a quotient definition
+*)
+fun get_rty_qty ctxt s =
+let
+ val thy = ProofContext.theory_of ctxt
+ val exn = LIFT_MATCH ("No quotient type " ^ quote s ^ " found.")
+ val qdata = (quotdata_lookup thy s) handle Quotient_Info.NotFound => raise exn
+in
+ (#rtyp qdata, #qtyp qdata)
+end
+
+(* takes two type-environments and looks
+ up in both of them the variable v, which
+ must be listed in the environment
+*)
+fun double_lookup rtyenv qtyenv v =
+let
+ val v' = fst (dest_TVar v)
+in
+ (snd (the (Vartab.lookup rtyenv v')), snd (the (Vartab.lookup qtyenv v')))
+end
+
+(* matches a type pattern with a type *)
+fun match ctxt err ty_pat ty =
+let
+ val thy = ProofContext.theory_of ctxt
+in
+ Sign.typ_match thy (ty_pat, ty) Vartab.empty
+ handle MATCH_TYPE => err ctxt ty_pat ty
+end
+
+(* produces the rep or abs constant for a qty *)
+fun absrep_const flag ctxt qty_str =
+let
+ val thy = ProofContext.theory_of ctxt
+ val qty_name = Long_Name.base_name qty_str
+in
+ case flag of
+ AbsF => Const (Sign.full_bname thy ("abs_" ^ qty_name), dummyT)
+ | RepF => Const (Sign.full_bname thy ("rep_" ^ qty_name), dummyT)
+end
+
+(* Lets Nitpick represent elements of quotient types as elements of the raw type *)
+fun absrep_const_chk flag ctxt qty_str =
+ Syntax.check_term ctxt (absrep_const flag ctxt qty_str)
+
+fun absrep_match_err ctxt ty_pat ty =
+let
+ val ty_pat_str = Syntax.string_of_typ ctxt ty_pat
+ val ty_str = Syntax.string_of_typ ctxt ty
+in
+ raise LIFT_MATCH (space_implode " "
+ ["absrep_fun (Types ", quote ty_pat_str, "and", quote ty_str, " do not match.)"])
+end
+
+
+(** generation of an aggregate absrep function **)
+
+(* - In case of equal types we just return the identity.
+
+ - In case of TFrees we also return the identity.
+
+ - In case of function types we recurse taking
+ the polarity change into account.
+
+ - If the type constructors are equal, we recurse for the
+ arguments and build the appropriate map function.
+
+ - If the type constructors are unequal, there must be an
+ instance of quotient types:
+
+ - we first look up the corresponding rty_pat and qty_pat
+ from the quotient definition; the arguments of qty_pat
+ must be some distinct TVars
+ - we then match the rty_pat with rty and qty_pat with qty;
+ if matching fails the types do not correspond -> error
+ - the matching produces two environments; we look up the
+ assignments for the qty_pat variables and recurse on the
+ assignments
+ - we prefix the aggregate map function for the rty_pat,
+ which is an abstraction over all type variables
+ - finally we compose the result with the appropriate
+ absrep function in case at least one argument produced
+ a non-identity function /
+ otherwise we just return the appropriate absrep
+ function
+
+ The composition is necessary for types like
+
+ ('a list) list / ('a foo) foo
+
+ The matching is necessary for types like
+
+ ('a * 'a) list / 'a bar
+
+ The test is necessary in order to eliminate superfluous
+ identity maps.
+*)
+
+fun absrep_fun flag ctxt (rty, qty) =
+ if rty = qty
+ then mk_identity rty
+ else
+ case (rty, qty) of
+ (Type ("fun", [ty1, ty2]), Type ("fun", [ty1', ty2'])) =>
+ let
+ val arg1 = absrep_fun (negF flag) ctxt (ty1, ty1')
+ val arg2 = absrep_fun flag ctxt (ty2, ty2')
+ in
+ list_comb (get_mapfun ctxt "fun", [arg1, arg2])
+ end
+ | (Type (s, tys), Type (s', tys')) =>
+ if s = s'
+ then
+ let
+ val args = map (absrep_fun flag ctxt) (tys ~~ tys')
+ in
+ list_comb (get_mapfun ctxt s, args)
+ end
+ else
+ let
+ val (rty_pat, qty_pat as Type (_, vs)) = get_rty_qty ctxt s'
+ val rtyenv = match ctxt absrep_match_err rty_pat rty
+ val qtyenv = match ctxt absrep_match_err qty_pat qty
+ val args_aux = map (double_lookup rtyenv qtyenv) vs
+ val args = map (absrep_fun flag ctxt) args_aux
+ val map_fun = mk_mapfun ctxt vs rty_pat
+ val result = list_comb (map_fun, args)
+ in
+ if forall is_identity args
+ then absrep_const flag ctxt s'
+ else mk_fun_compose flag (absrep_const flag ctxt s', result)
+ end
+ | (TFree x, TFree x') =>
+ if x = x'
+ then mk_identity rty
+ else raise (LIFT_MATCH "absrep_fun (frees)")
+ | (TVar _, TVar _) => raise (LIFT_MATCH "absrep_fun (vars)")
+ | _ => raise (LIFT_MATCH "absrep_fun (default)")
+
+fun absrep_fun_chk flag ctxt (rty, qty) =
+ absrep_fun flag ctxt (rty, qty)
+ |> Syntax.check_term ctxt
+
+
+
+
+(*** Aggregate Equivalence Relation ***)
+
+
+(* works very similar to the absrep generation,
+ except there is no need for polarities
+*)
+
+(* instantiates TVars so that the term is of type ty *)
+fun force_typ ctxt trm ty =
+let
+ val thy = ProofContext.theory_of ctxt
+ val trm_ty = fastype_of trm
+ val ty_inst = Sign.typ_match thy (trm_ty, ty) Vartab.empty
+in
+ map_types (Envir.subst_type ty_inst) trm
+end
+
+fun is_eq (Const (@{const_name "op ="}, _)) = true
+ | is_eq _ = false
+
+fun mk_rel_compose (trm1, trm2) =
+ Const (@{const_name "rel_conj"}, dummyT) $ trm1 $ trm2
+
+fun get_relmap ctxt s =
+let
+ val thy = ProofContext.theory_of ctxt
+ val exn = LIFT_MATCH ("get_relmap (no relation map function found for type " ^ s ^ ")")
+ val relmap = #relmap (maps_lookup thy s) handle Quotient_Info.NotFound => raise exn
+in
+ Const (relmap, dummyT)
+end
+
+fun mk_relmap ctxt vs rty =
+let
+ val vs' = map (mk_Free) vs
+
+ fun mk_relmap_aux rty =
+ case rty of
+ TVar _ => mk_Free rty
+ | Type (_, []) => HOLogic.eq_const rty
+ | Type (s, tys) => list_comb (get_relmap ctxt s, map mk_relmap_aux tys)
+ | _ => raise LIFT_MATCH ("mk_relmap (default)")
+in
+ fold_rev Term.lambda vs' (mk_relmap_aux rty)
+end
+
+fun get_equiv_rel ctxt s =
+let
+ val thy = ProofContext.theory_of ctxt
+ val exn = LIFT_MATCH ("get_quotdata (no quotient found for type " ^ s ^ ")")
+in
+ #equiv_rel (quotdata_lookup thy s) handle Quotient_Info.NotFound => raise exn
+end
+
+fun equiv_match_err ctxt ty_pat ty =
+let
+ val ty_pat_str = Syntax.string_of_typ ctxt ty_pat
+ val ty_str = Syntax.string_of_typ ctxt ty
+in
+ raise LIFT_MATCH (space_implode " "
+ ["equiv_relation (Types ", quote ty_pat_str, "and", quote ty_str, " do not match.)"])
+end
+
+(* builds the aggregate equivalence relation
+ that will be the argument of Respects
+*)
+fun equiv_relation ctxt (rty, qty) =
+ if rty = qty
+ then HOLogic.eq_const rty
+ else
+ case (rty, qty) of
+ (Type (s, tys), Type (s', tys')) =>
+ if s = s'
+ then
+ let
+ val args = map (equiv_relation ctxt) (tys ~~ tys')
+ in
+ list_comb (get_relmap ctxt s, args)
+ end
+ else
+ let
+ val (rty_pat, qty_pat as Type (_, vs)) = get_rty_qty ctxt s'
+ val rtyenv = match ctxt equiv_match_err rty_pat rty
+ val qtyenv = match ctxt equiv_match_err qty_pat qty
+ val args_aux = map (double_lookup rtyenv qtyenv) vs
+ val args = map (equiv_relation ctxt) args_aux
+ val rel_map = mk_relmap ctxt vs rty_pat
+ val result = list_comb (rel_map, args)
+ val eqv_rel = get_equiv_rel ctxt s'
+ val eqv_rel' = force_typ ctxt eqv_rel ([rty, rty] ---> @{typ bool})
+ in
+ if forall is_eq args
+ then eqv_rel'
+ else mk_rel_compose (result, eqv_rel')
+ end
+ | _ => HOLogic.eq_const rty
+
+fun equiv_relation_chk ctxt (rty, qty) =
+ equiv_relation ctxt (rty, qty)
+ |> Syntax.check_term ctxt
+
+
+
+(*** Regularization ***)
+
+(* Regularizing an rtrm means:
+
+ - Quantifiers over types that need lifting are replaced
+ by bounded quantifiers, for example:
+
+ All P ----> All (Respects R) P
+
+ where the aggregate relation R is given by the rty and qty;
+
+ - Abstractions over types that need lifting are replaced
+ by bounded abstractions, for example:
+
+ %x. P ----> Ball (Respects R) %x. P
+
+ - Equalities over types that need lifting are replaced by
+ corresponding equivalence relations, for example:
+
+ A = B ----> R A B
+
+ or
+
+ A = B ----> (R ===> R) A B
+
+ for more complicated types of A and B
+
+
+ The regularize_trm accepts raw theorems in which equalities
+ and quantifiers match exactly the ones in the lifted theorem
+ but also accepts partially regularized terms.
+
+ This means that the raw theorems can have:
+ Ball (Respects R), Bex (Respects R), Bex1_rel (Respects R), Babs, R
+ in the places where:
+ All, Ex, Ex1, %, (op =)
+ is required the lifted theorem.
+
+*)
+
+val mk_babs = Const (@{const_name Babs}, dummyT)
+val mk_ball = Const (@{const_name Ball}, dummyT)
+val mk_bex = Const (@{const_name Bex}, dummyT)
+val mk_bex1_rel = Const (@{const_name Bex1_rel}, dummyT)
+val mk_resp = Const (@{const_name Respects}, dummyT)
+
+(* - applies f to the subterm of an abstraction,
+ otherwise to the given term,
+ - used by regularize, therefore abstracted
+ variables do not have to be treated specially
+*)
+fun apply_subt f (trm1, trm2) =
+ case (trm1, trm2) of
+ (Abs (x, T, t), Abs (_ , _, t')) => Abs (x, T, f (t, t'))
+ | _ => f (trm1, trm2)
+
+fun term_mismatch str ctxt t1 t2 =
+let
+ val t1_str = Syntax.string_of_term ctxt t1
+ val t2_str = Syntax.string_of_term ctxt t2
+ val t1_ty_str = Syntax.string_of_typ ctxt (fastype_of t1)
+ val t2_ty_str = Syntax.string_of_typ ctxt (fastype_of t2)
+in
+ raise LIFT_MATCH (cat_lines [str, t1_str ^ "::" ^ t1_ty_str, t2_str ^ "::" ^ t2_ty_str])
+end
+
+(* the major type of All and Ex quantifiers *)
+fun qnt_typ ty = domain_type (domain_type ty)
+
+(* Checks that two types match, for example:
+ rty -> rty matches qty -> qty *)
+fun matches_typ thy rT qT =
+ if rT = qT then true else
+ case (rT, qT) of
+ (Type (rs, rtys), Type (qs, qtys)) =>
+ if rs = qs then
+ if length rtys <> length qtys then false else
+ forall (fn x => x = true) (map2 (matches_typ thy) rtys qtys)
+ else
+ (case Quotient_Info.quotdata_lookup_raw thy qs of
+ SOME quotinfo => Sign.typ_instance thy (rT, #rtyp quotinfo)
+ | NONE => false)
+ | _ => false
+
+
+(* produces a regularized version of rtrm
+
+ - the result might contain dummyTs
+
+ - for regularisation we do not need any
+ special treatment of bound variables
+*)
+fun regularize_trm ctxt (rtrm, qtrm) =
+ case (rtrm, qtrm) of
+ (Abs (x, ty, t), Abs (_, ty', t')) =>
+ let
+ val subtrm = Abs(x, ty, regularize_trm ctxt (t, t'))
+ in
+ if ty = ty' then subtrm
+ else mk_babs $ (mk_resp $ equiv_relation ctxt (ty, ty')) $ subtrm
+ end
+ | (Const (@{const_name "Babs"}, T) $ resrel $ (t as (Abs (_, ty, _))), t' as (Abs (_, ty', _))) =>
+ let
+ val subtrm = regularize_trm ctxt (t, t')
+ val needres = mk_resp $ equiv_relation_chk ctxt (ty, ty')
+ in
+ if resrel <> needres
+ then term_mismatch "regularize (Babs)" ctxt resrel needres
+ else mk_babs $ resrel $ subtrm
+ end
+
+ | (Const (@{const_name "All"}, ty) $ t, Const (@{const_name "All"}, ty') $ t') =>
+ let
+ val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+ in
+ if ty = ty' then Const (@{const_name "All"}, ty) $ subtrm
+ else mk_ball $ (mk_resp $ equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm
+ end
+
+ | (Const (@{const_name "Ex"}, ty) $ t, Const (@{const_name "Ex"}, ty') $ t') =>
+ let
+ val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+ in
+ if ty = ty' then Const (@{const_name "Ex"}, ty) $ subtrm
+ else mk_bex $ (mk_resp $ equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm
+ end
+
+ | (Const (@{const_name "Ex1"}, ty) $ (Abs (_, _,
+ (Const (@{const_name "op &"}, _) $ (Const (@{const_name "op :"}, _) $ _ $
+ (Const (@{const_name "Respects"}, _) $ resrel)) $ (t $ _)))),
+ Const (@{const_name "Ex1"}, ty') $ t') =>
+ let
+ val t_ = incr_boundvars (~1) t
+ val subtrm = apply_subt (regularize_trm ctxt) (t_, t')
+ val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty')
+ in
+ if resrel <> needrel
+ then term_mismatch "regularize (Bex1)" ctxt resrel needrel
+ else mk_bex1_rel $ resrel $ subtrm
+ end
+
+ | (Const (@{const_name "Ex1"}, ty) $ t, Const (@{const_name "Ex1"}, ty') $ t') =>
+ let
+ val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+ in
+ if ty = ty' then Const (@{const_name "Ex1"}, ty) $ subtrm
+ else mk_bex1_rel $ (equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm
+ end
+
+ | (Const (@{const_name "Ball"}, ty) $ (Const (@{const_name "Respects"}, _) $ resrel) $ t,
+ Const (@{const_name "All"}, ty') $ t') =>
+ let
+ val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+ val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty')
+ in
+ if resrel <> needrel
+ then term_mismatch "regularize (Ball)" ctxt resrel needrel
+ else mk_ball $ (mk_resp $ resrel) $ subtrm
+ end
+
+ | (Const (@{const_name "Bex"}, ty) $ (Const (@{const_name "Respects"}, _) $ resrel) $ t,
+ Const (@{const_name "Ex"}, ty') $ t') =>
+ let
+ val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+ val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty')
+ in
+ if resrel <> needrel
+ then term_mismatch "regularize (Bex)" ctxt resrel needrel
+ else mk_bex $ (mk_resp $ resrel) $ subtrm
+ end
+
+ | (Const (@{const_name "Bex1_rel"}, ty) $ resrel $ t, Const (@{const_name "Ex1"}, ty') $ t') =>
+ let
+ val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+ val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty')
+ in
+ if resrel <> needrel
+ then term_mismatch "regularize (Bex1_res)" ctxt resrel needrel
+ else mk_bex1_rel $ resrel $ subtrm
+ end
+
+ | (* equalities need to be replaced by appropriate equivalence relations *)
+ (Const (@{const_name "op ="}, ty), Const (@{const_name "op ="}, ty')) =>
+ if ty = ty' then rtrm
+ else equiv_relation ctxt (domain_type ty, domain_type ty')
+
+ | (* in this case we just check whether the given equivalence relation is correct *)
+ (rel, Const (@{const_name "op ="}, ty')) =>
+ let
+ val rel_ty = fastype_of rel
+ val rel' = equiv_relation_chk ctxt (domain_type rel_ty, domain_type ty')
+ in
+ if rel' aconv rel then rtrm
+ else term_mismatch "regularise (relation mismatch)" ctxt rel rel'
+ end
+
+ | (_, Const _) =>
+ let
+ val thy = ProofContext.theory_of ctxt
+ fun same_const (Const (s, T)) (Const (s', T')) = (s = s') andalso matches_typ thy T T'
+ | same_const _ _ = false
+ in
+ if same_const rtrm qtrm then rtrm
+ else
+ let
+ val rtrm' = #rconst (qconsts_lookup thy qtrm)
+ handle Quotient_Info.NotFound => term_mismatch "regularize(constant notfound)" ctxt rtrm qtrm
+ in
+ if Pattern.matches thy (rtrm', rtrm)
+ then rtrm else term_mismatch "regularize(constant mismatch)" ctxt rtrm qtrm
+ end
+ end
+
+ | (((t1 as Const (@{const_name "split"}, _)) $ Abs (v1, ty, Abs(v1', ty', s1))),
+ ((t2 as Const (@{const_name "split"}, _)) $ Abs (v2, _ , Abs(v2', _ , s2)))) =>
+ regularize_trm ctxt (t1, t2) $ Abs (v1, ty, Abs (v1', ty', regularize_trm ctxt (s1, s2)))
+
+ | (((t1 as Const (@{const_name "split"}, _)) $ Abs (v1, ty, s1)),
+ ((t2 as Const (@{const_name "split"}, _)) $ Abs (v2, _ , s2))) =>
+ regularize_trm ctxt (t1, t2) $ Abs (v1, ty, regularize_trm ctxt (s1, s2))
+
+ | (t1 $ t2, t1' $ t2') =>
+ regularize_trm ctxt (t1, t1') $ regularize_trm ctxt (t2, t2')
+
+ | (Bound i, Bound i') =>
+ if i = i' then rtrm
+ else raise (LIFT_MATCH "regularize (bounds mismatch)")
+
+ | _ =>
+ let
+ val rtrm_str = Syntax.string_of_term ctxt rtrm
+ val qtrm_str = Syntax.string_of_term ctxt qtrm
+ in
+ raise (LIFT_MATCH ("regularize failed (default: " ^ rtrm_str ^ "," ^ qtrm_str ^ ")"))
+ end
+
+fun regularize_trm_chk ctxt (rtrm, qtrm) =
+ regularize_trm ctxt (rtrm, qtrm)
+ |> Syntax.check_term ctxt
+
+
+
+(*** Rep/Abs Injection ***)
+
+(*
+Injection of Rep/Abs means:
+
+ For abstractions:
+
+ * If the type of the abstraction needs lifting, then we add Rep/Abs
+ around the abstraction; otherwise we leave it unchanged.
+
+ For applications:
+
+ * If the application involves a bounded quantifier, we recurse on
+ the second argument. If the application is a bounded abstraction,
+ we always put an Rep/Abs around it (since bounded abstractions
+ are assumed to always need lifting). Otherwise we recurse on both
+ arguments.
+
+ For constants:
+
+ * If the constant is (op =), we leave it always unchanged.
+ Otherwise the type of the constant needs lifting, we put
+ and Rep/Abs around it.
+
+ For free variables:
+
+ * We put a Rep/Abs around it if the type needs lifting.
+
+ Vars case cannot occur.
+*)
+
+fun mk_repabs ctxt (T, T') trm =
+ absrep_fun RepF ctxt (T, T') $ (absrep_fun AbsF ctxt (T, T') $ trm)
+
+fun inj_repabs_err ctxt msg rtrm qtrm =
+let
+ val rtrm_str = Syntax.string_of_term ctxt rtrm
+ val qtrm_str = Syntax.string_of_term ctxt qtrm
+in
+ raise LIFT_MATCH (space_implode " " [msg, quote rtrm_str, "and", quote qtrm_str])
+end
+
+
+(* bound variables need to be treated properly,
+ as the type of subterms needs to be calculated *)
+fun inj_repabs_trm ctxt (rtrm, qtrm) =
+ case (rtrm, qtrm) of
+ (Const (@{const_name "Ball"}, T) $ r $ t, Const (@{const_name "All"}, _) $ t') =>
+ Const (@{const_name "Ball"}, T) $ r $ (inj_repabs_trm ctxt (t, t'))
+
+ | (Const (@{const_name "Bex"}, T) $ r $ t, Const (@{const_name "Ex"}, _) $ t') =>
+ Const (@{const_name "Bex"}, T) $ r $ (inj_repabs_trm ctxt (t, t'))
+
+ | (Const (@{const_name "Babs"}, T) $ r $ t, t' as (Abs _)) =>
+ let
+ val rty = fastype_of rtrm
+ val qty = fastype_of qtrm
+ in
+ mk_repabs ctxt (rty, qty) (Const (@{const_name "Babs"}, T) $ r $ (inj_repabs_trm ctxt (t, t')))
+ end
+
+ | (Abs (x, T, t), Abs (x', T', t')) =>
+ let
+ val rty = fastype_of rtrm
+ val qty = fastype_of qtrm
+ val (y, s) = Term.dest_abs (x, T, t)
+ val (_, s') = Term.dest_abs (x', T', t')
+ val yvar = Free (y, T)
+ val result = Term.lambda_name (y, yvar) (inj_repabs_trm ctxt (s, s'))
+ in
+ if rty = qty then result
+ else mk_repabs ctxt (rty, qty) result
+ end
+
+ | (t $ s, t' $ s') =>
+ (inj_repabs_trm ctxt (t, t')) $ (inj_repabs_trm ctxt (s, s'))
+
+ | (Free (_, T), Free (_, T')) =>
+ if T = T' then rtrm
+ else mk_repabs ctxt (T, T') rtrm
+
+ | (_, Const (@{const_name "op ="}, _)) => rtrm
+
+ | (_, Const (_, T')) =>
+ let
+ val rty = fastype_of rtrm
+ in
+ if rty = T' then rtrm
+ else mk_repabs ctxt (rty, T') rtrm
+ end
+
+ | _ => inj_repabs_err ctxt "injection (default):" rtrm qtrm
+
+fun inj_repabs_trm_chk ctxt (rtrm, qtrm) =
+ inj_repabs_trm ctxt (rtrm, qtrm)
+ |> Syntax.check_term ctxt
+
+
+
+(*** Wrapper for automatically transforming an rthm into a qthm ***)
+
+(* subst_tys takes a list of (rty, qty) substitution pairs
+ and replaces all occurences of rty in the given type
+ by appropriate qty, with substitution *)
+fun subst_ty thy ty (rty, qty) r =
+ if r <> NONE then r else
+ case try (Sign.typ_match thy (rty, ty)) Vartab.empty of
+ SOME inst => SOME (Envir.subst_type inst qty)
+ | NONE => NONE
+fun subst_tys thy substs ty =
+ case fold (subst_ty thy ty) substs NONE of
+ SOME ty => ty
+ | NONE =>
+ (case ty of
+ Type (s, tys) => Type (s, map (subst_tys thy substs) tys)
+ | x => x)
+
+(* subst_trms takes a list of (rtrm, qtrm) substitution pairs
+ and if the given term matches any of the raw terms it
+ returns the appropriate qtrm instantiated. If none of
+ them matched it returns NONE. *)
+fun subst_trm thy t (rtrm, qtrm) s =
+ if s <> NONE then s else
+ case try (Pattern.match thy (rtrm, t)) (Vartab.empty, Vartab.empty) of
+ SOME inst => SOME (Envir.subst_term inst qtrm)
+ | NONE => NONE;
+fun subst_trms thy substs t = fold (subst_trm thy t) substs NONE
+
+(* prepares type and term substitution pairs to be used by above
+ functions that let replace all raw constructs by appropriate
+ lifted counterparts. *)
+fun get_ty_trm_substs ctxt =
+let
+ val thy = ProofContext.theory_of ctxt
+ val quot_infos = Quotient_Info.quotdata_dest ctxt
+ val const_infos = Quotient_Info.qconsts_dest ctxt
+ val ty_substs = map (fn ri => (#rtyp ri, #qtyp ri)) quot_infos
+ val const_substs = map (fn ci => (#rconst ci, #qconst ci)) const_infos
+ fun rel_eq rel = HOLogic.eq_const (subst_tys thy ty_substs (domain_type (fastype_of rel)))
+ val rel_substs = map (fn ri => (#equiv_rel ri, rel_eq (#equiv_rel ri))) quot_infos
+in
+ (ty_substs, const_substs @ rel_substs)
+end
+
+fun quotient_lift_const (b, t) ctxt =
+let
+ val thy = ProofContext.theory_of ctxt
+ val (ty_substs, _) = get_ty_trm_substs ctxt;
+ val (_, ty) = dest_Const t;
+ val nty = subst_tys thy ty_substs ty;
+in
+ Free(b, nty)
+end
+
+(*
+Takes a term and
+
+* replaces raw constants by the quotient constants
+
+* replaces equivalence relations by equalities
+
+* replaces raw types by the quotient types
+
+*)
+
+fun quotient_lift_all ctxt t =
+let
+ val thy = ProofContext.theory_of ctxt
+ val (ty_substs, substs) = get_ty_trm_substs ctxt
+ fun lift_aux t =
+ case subst_trms thy substs t of
+ SOME x => x
+ | NONE =>
+ (case t of
+ a $ b => lift_aux a $ lift_aux b
+ | Abs(a, ty, s) =>
+ let
+ val (y, s') = Term.dest_abs (a, ty, s)
+ val nty = subst_tys thy ty_substs ty
+ in
+ Abs(y, nty, abstract_over (Free (y, nty), lift_aux s'))
+ end
+ | Free(n, ty) => Free(n, subst_tys thy ty_substs ty)
+ | Var(n, ty) => Var(n, subst_tys thy ty_substs ty)
+ | Bound i => Bound i
+ | Const(s, ty) => Const(s, subst_tys thy ty_substs ty))
+in
+ lift_aux t
+end
+
+
+end; (* structure *)
+
+
+