--- a/Quot/quotient_term.ML Thu Feb 25 07:48:57 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,786 +0,0 @@
-(* 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 *)
-
-
-