haftmann@37744: (* Title: HOL/Tools/Quotient/quotient_term.ML kaliszyk@35222: Author: Cezary Kaliszyk and Christian Urban kaliszyk@35222: wenzelm@35788: Constructs terms corresponding to goals from lifting theorems to wenzelm@35788: quotient types. kaliszyk@35222: *) kaliszyk@35222: kaliszyk@35222: signature QUOTIENT_TERM = kaliszyk@35222: sig kaliszyk@35222: exception LIFT_MATCH of string kaliszyk@35222: kaliszyk@35222: datatype flag = AbsF | RepF kaliszyk@35222: kaliszyk@35222: val absrep_fun: flag -> Proof.context -> typ * typ -> term kaliszyk@35222: val absrep_fun_chk: flag -> Proof.context -> typ * typ -> term kaliszyk@35222: kaliszyk@35222: (* Allows Nitpick to represent quotient types as single elements from raw type *) kaliszyk@35222: val absrep_const_chk: flag -> Proof.context -> string -> term kaliszyk@35222: kaliszyk@35222: val equiv_relation: Proof.context -> typ * typ -> term kaliszyk@35222: val equiv_relation_chk: Proof.context -> typ * typ -> term kaliszyk@35222: kaliszyk@35222: val regularize_trm: Proof.context -> term * term -> term kaliszyk@35222: val regularize_trm_chk: Proof.context -> term * term -> term kaliszyk@35222: kaliszyk@35222: val inj_repabs_trm: Proof.context -> term * term -> term kaliszyk@35222: val inj_repabs_trm_chk: Proof.context -> term * term -> term kaliszyk@35222: urbanc@37592: val derive_qtyp: typ list -> typ -> Proof.context -> typ urbanc@37592: val derive_qtrm: typ list -> term -> Proof.context -> term urbanc@37592: val derive_rtyp: typ list -> typ -> Proof.context -> typ urbanc@37592: val derive_rtrm: typ list -> term -> Proof.context -> term kaliszyk@35222: end; kaliszyk@35222: kaliszyk@35222: structure Quotient_Term: QUOTIENT_TERM = kaliszyk@35222: struct kaliszyk@35222: kaliszyk@35222: open Quotient_Info; kaliszyk@35222: kaliszyk@35222: exception LIFT_MATCH of string kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (*** Aggregate Rep/Abs Function ***) kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (* The flag RepF is for types in negative position; AbsF is for types kaliszyk@35222: in positive position. Because of this, function types need to be kaliszyk@35222: treated specially, since there the polarity changes. kaliszyk@35222: *) kaliszyk@35222: kaliszyk@35222: datatype flag = AbsF | RepF kaliszyk@35222: kaliszyk@35222: fun negF AbsF = RepF kaliszyk@35222: | negF RepF = AbsF kaliszyk@35222: haftmann@37677: fun is_identity (Const (@{const_name id}, _)) = true kaliszyk@35222: | is_identity _ = false kaliszyk@35222: haftmann@37677: fun mk_identity ty = Const (@{const_name id}, ty --> ty) kaliszyk@35222: kaliszyk@35222: fun mk_fun_compose flag (trm1, trm2) = kaliszyk@35222: case flag of haftmann@37677: AbsF => Const (@{const_name comp}, dummyT) $ trm1 $ trm2 haftmann@37677: | RepF => Const (@{const_name comp}, dummyT) $ trm2 $ trm1 kaliszyk@35222: kaliszyk@35222: fun get_mapfun ctxt s = kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: val exn = LIFT_MATCH ("No map function for type " ^ quote s ^ " found.") kaliszyk@35222: val mapfun = #mapfun (maps_lookup thy s) handle Quotient_Info.NotFound => raise exn kaliszyk@35222: in kaliszyk@35222: Const (mapfun, dummyT) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* makes a Free out of a TVar *) kaliszyk@35222: fun mk_Free (TVar ((x, i), _)) = Free (unprefix "'" x ^ string_of_int i, dummyT) kaliszyk@35222: kaliszyk@35222: (* produces an aggregate map function for the kaliszyk@35222: rty-part of a quotient definition; abstracts kaliszyk@35222: over all variables listed in vs (these variables kaliszyk@35222: correspond to the type variables in rty) kaliszyk@35222: kaliszyk@35222: for example for: (?'a list * ?'b) kaliszyk@35222: it produces: %a b. prod_map (map a) b kaliszyk@35222: *) kaliszyk@35222: fun mk_mapfun ctxt vs rty = kaliszyk@35222: let urbanc@37530: val vs' = map mk_Free vs kaliszyk@35222: kaliszyk@35222: fun mk_mapfun_aux rty = kaliszyk@35222: case rty of kaliszyk@35222: TVar _ => mk_Free rty kaliszyk@35222: | Type (_, []) => mk_identity rty kaliszyk@35222: | Type (s, tys) => list_comb (get_mapfun ctxt s, map mk_mapfun_aux tys) kaliszyk@35222: | _ => raise LIFT_MATCH "mk_mapfun (default)" kaliszyk@35222: in kaliszyk@35222: fold_rev Term.lambda vs' (mk_mapfun_aux rty) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* looks up the (varified) rty and qty for kaliszyk@35222: a quotient definition kaliszyk@35222: *) kaliszyk@35222: fun get_rty_qty ctxt s = kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: val exn = LIFT_MATCH ("No quotient type " ^ quote s ^ " found.") urbanc@37530: val qdata = quotdata_lookup thy s handle Quotient_Info.NotFound => raise exn kaliszyk@35222: in kaliszyk@35222: (#rtyp qdata, #qtyp qdata) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* takes two type-environments and looks kaliszyk@35222: up in both of them the variable v, which kaliszyk@35222: must be listed in the environment kaliszyk@35222: *) kaliszyk@35222: fun double_lookup rtyenv qtyenv v = kaliszyk@35222: let kaliszyk@35222: val v' = fst (dest_TVar v) kaliszyk@35222: in kaliszyk@35222: (snd (the (Vartab.lookup rtyenv v')), snd (the (Vartab.lookup qtyenv v'))) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* matches a type pattern with a type *) kaliszyk@35222: fun match ctxt err ty_pat ty = kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: in kaliszyk@35222: Sign.typ_match thy (ty_pat, ty) Vartab.empty kaliszyk@35222: handle MATCH_TYPE => err ctxt ty_pat ty kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* produces the rep or abs constant for a qty *) kaliszyk@35222: fun absrep_const flag ctxt qty_str = kaliszyk@35222: let kaliszyk@35222: val qty_name = Long_Name.base_name qty_str kaliszyk@35843: val qualifier = Long_Name.qualifier qty_str kaliszyk@35222: in kaliszyk@35222: case flag of kaliszyk@35843: AbsF => Const (Long_Name.qualify qualifier ("abs_" ^ qty_name), dummyT) kaliszyk@35843: | RepF => Const (Long_Name.qualify qualifier ("rep_" ^ qty_name), dummyT) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* Lets Nitpick represent elements of quotient types as elements of the raw type *) kaliszyk@35222: fun absrep_const_chk flag ctxt qty_str = kaliszyk@35222: Syntax.check_term ctxt (absrep_const flag ctxt qty_str) kaliszyk@35222: kaliszyk@35222: fun absrep_match_err ctxt ty_pat ty = kaliszyk@35222: let kaliszyk@35222: val ty_pat_str = Syntax.string_of_typ ctxt ty_pat kaliszyk@35222: val ty_str = Syntax.string_of_typ ctxt ty kaliszyk@35222: in kaliszyk@35222: raise LIFT_MATCH (space_implode " " kaliszyk@35222: ["absrep_fun (Types ", quote ty_pat_str, "and", quote ty_str, " do not match.)"]) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (** generation of an aggregate absrep function **) kaliszyk@35222: kaliszyk@35222: (* - In case of equal types we just return the identity. kaliszyk@35222: kaliszyk@35222: - In case of TFrees we also return the identity. kaliszyk@35222: kaliszyk@35222: - In case of function types we recurse taking kaliszyk@35222: the polarity change into account. kaliszyk@35222: kaliszyk@35222: - If the type constructors are equal, we recurse for the kaliszyk@35222: arguments and build the appropriate map function. kaliszyk@35222: kaliszyk@35222: - If the type constructors are unequal, there must be an kaliszyk@35222: instance of quotient types: kaliszyk@35222: kaliszyk@35222: - we first look up the corresponding rty_pat and qty_pat kaliszyk@35222: from the quotient definition; the arguments of qty_pat kaliszyk@35222: must be some distinct TVars kaliszyk@35222: - we then match the rty_pat with rty and qty_pat with qty; kaliszyk@35222: if matching fails the types do not correspond -> error kaliszyk@35222: - the matching produces two environments; we look up the kaliszyk@35222: assignments for the qty_pat variables and recurse on the kaliszyk@35222: assignments kaliszyk@35222: - we prefix the aggregate map function for the rty_pat, kaliszyk@35222: which is an abstraction over all type variables kaliszyk@35222: - finally we compose the result with the appropriate kaliszyk@35222: absrep function in case at least one argument produced kaliszyk@35222: a non-identity function / kaliszyk@35222: otherwise we just return the appropriate absrep kaliszyk@35222: function kaliszyk@35222: kaliszyk@35222: The composition is necessary for types like kaliszyk@35222: kaliszyk@35222: ('a list) list / ('a foo) foo kaliszyk@35222: kaliszyk@35222: The matching is necessary for types like kaliszyk@35222: kaliszyk@35222: ('a * 'a) list / 'a bar kaliszyk@35222: kaliszyk@35222: The test is necessary in order to eliminate superfluous kaliszyk@35222: identity maps. kaliszyk@35222: *) kaliszyk@35222: kaliszyk@35222: fun absrep_fun flag ctxt (rty, qty) = kaliszyk@35222: if rty = qty kaliszyk@35222: then mk_identity rty kaliszyk@35222: else kaliszyk@35222: case (rty, qty) of kaliszyk@35222: (Type ("fun", [ty1, ty2]), Type ("fun", [ty1', ty2'])) => kaliszyk@35222: let kaliszyk@35222: val arg1 = absrep_fun (negF flag) ctxt (ty1, ty1') kaliszyk@35222: val arg2 = absrep_fun flag ctxt (ty2, ty2') kaliszyk@35222: in kaliszyk@35222: list_comb (get_mapfun ctxt "fun", [arg1, arg2]) kaliszyk@35222: end kaliszyk@35222: | (Type (s, tys), Type (s', tys')) => kaliszyk@35222: if s = s' kaliszyk@35222: then kaliszyk@35222: let kaliszyk@35222: val args = map (absrep_fun flag ctxt) (tys ~~ tys') kaliszyk@35222: in kaliszyk@35222: list_comb (get_mapfun ctxt s, args) kaliszyk@35222: end kaliszyk@35222: else kaliszyk@35222: let kaliszyk@35222: val (rty_pat, qty_pat as Type (_, vs)) = get_rty_qty ctxt s' kaliszyk@35222: val rtyenv = match ctxt absrep_match_err rty_pat rty kaliszyk@35222: val qtyenv = match ctxt absrep_match_err qty_pat qty kaliszyk@35222: val args_aux = map (double_lookup rtyenv qtyenv) vs kaliszyk@35222: val args = map (absrep_fun flag ctxt) args_aux kaliszyk@35222: val map_fun = mk_mapfun ctxt vs rty_pat kaliszyk@35222: val result = list_comb (map_fun, args) kaliszyk@35222: in kaliszyk@35222: if forall is_identity args kaliszyk@35222: then absrep_const flag ctxt s' kaliszyk@35222: else mk_fun_compose flag (absrep_const flag ctxt s', result) kaliszyk@35222: end kaliszyk@35222: | (TFree x, TFree x') => kaliszyk@35222: if x = x' kaliszyk@35222: then mk_identity rty kaliszyk@35222: else raise (LIFT_MATCH "absrep_fun (frees)") kaliszyk@35222: | (TVar _, TVar _) => raise (LIFT_MATCH "absrep_fun (vars)") kaliszyk@35222: | _ => raise (LIFT_MATCH "absrep_fun (default)") kaliszyk@35222: kaliszyk@35222: fun absrep_fun_chk flag ctxt (rty, qty) = kaliszyk@35222: absrep_fun flag ctxt (rty, qty) kaliszyk@35222: |> Syntax.check_term ctxt kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (*** Aggregate Equivalence Relation ***) kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (* works very similar to the absrep generation, kaliszyk@35222: except there is no need for polarities kaliszyk@35222: *) kaliszyk@35222: kaliszyk@35222: (* instantiates TVars so that the term is of type ty *) kaliszyk@35222: fun force_typ ctxt trm ty = kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: val trm_ty = fastype_of trm kaliszyk@35222: val ty_inst = Sign.typ_match thy (trm_ty, ty) Vartab.empty kaliszyk@35222: in kaliszyk@35222: map_types (Envir.subst_type ty_inst) trm kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: fun is_eq (Const (@{const_name "op ="}, _)) = true kaliszyk@35222: | is_eq _ = false kaliszyk@35222: kaliszyk@35222: fun mk_rel_compose (trm1, trm2) = wenzelm@35402: Const (@{const_abbrev "rel_conj"}, dummyT) $ trm1 $ trm2 kaliszyk@35222: kaliszyk@35222: fun get_relmap ctxt s = kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: val exn = LIFT_MATCH ("get_relmap (no relation map function found for type " ^ s ^ ")") kaliszyk@35222: val relmap = #relmap (maps_lookup thy s) handle Quotient_Info.NotFound => raise exn kaliszyk@35222: in kaliszyk@35222: Const (relmap, dummyT) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: fun mk_relmap ctxt vs rty = kaliszyk@35222: let kaliszyk@35222: val vs' = map (mk_Free) vs kaliszyk@35222: kaliszyk@35222: fun mk_relmap_aux rty = kaliszyk@35222: case rty of kaliszyk@35222: TVar _ => mk_Free rty kaliszyk@35222: | Type (_, []) => HOLogic.eq_const rty kaliszyk@35222: | Type (s, tys) => list_comb (get_relmap ctxt s, map mk_relmap_aux tys) kaliszyk@35222: | _ => raise LIFT_MATCH ("mk_relmap (default)") kaliszyk@35222: in kaliszyk@35222: fold_rev Term.lambda vs' (mk_relmap_aux rty) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: fun get_equiv_rel ctxt s = kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: val exn = LIFT_MATCH ("get_quotdata (no quotient found for type " ^ s ^ ")") kaliszyk@35222: in kaliszyk@35222: #equiv_rel (quotdata_lookup thy s) handle Quotient_Info.NotFound => raise exn kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: fun equiv_match_err ctxt ty_pat ty = kaliszyk@35222: let kaliszyk@35222: val ty_pat_str = Syntax.string_of_typ ctxt ty_pat kaliszyk@35222: val ty_str = Syntax.string_of_typ ctxt ty kaliszyk@35222: in kaliszyk@35222: raise LIFT_MATCH (space_implode " " kaliszyk@35222: ["equiv_relation (Types ", quote ty_pat_str, "and", quote ty_str, " do not match.)"]) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* builds the aggregate equivalence relation kaliszyk@35222: that will be the argument of Respects kaliszyk@35222: *) kaliszyk@35222: fun equiv_relation ctxt (rty, qty) = kaliszyk@35222: if rty = qty kaliszyk@35222: then HOLogic.eq_const rty kaliszyk@35222: else kaliszyk@35222: case (rty, qty) of kaliszyk@35222: (Type (s, tys), Type (s', tys')) => kaliszyk@35222: if s = s' kaliszyk@35222: then kaliszyk@35222: let kaliszyk@35222: val args = map (equiv_relation ctxt) (tys ~~ tys') kaliszyk@35222: in kaliszyk@35222: list_comb (get_relmap ctxt s, args) kaliszyk@35222: end kaliszyk@35222: else kaliszyk@35222: let kaliszyk@35222: val (rty_pat, qty_pat as Type (_, vs)) = get_rty_qty ctxt s' kaliszyk@35222: val rtyenv = match ctxt equiv_match_err rty_pat rty kaliszyk@35222: val qtyenv = match ctxt equiv_match_err qty_pat qty kaliszyk@35222: val args_aux = map (double_lookup rtyenv qtyenv) vs kaliszyk@35222: val args = map (equiv_relation ctxt) args_aux kaliszyk@35222: val rel_map = mk_relmap ctxt vs rty_pat kaliszyk@35222: val result = list_comb (rel_map, args) kaliszyk@35222: val eqv_rel = get_equiv_rel ctxt s' kaliszyk@35222: val eqv_rel' = force_typ ctxt eqv_rel ([rty, rty] ---> @{typ bool}) kaliszyk@35222: in kaliszyk@35222: if forall is_eq args kaliszyk@35222: then eqv_rel' kaliszyk@35222: else mk_rel_compose (result, eqv_rel') kaliszyk@35222: end kaliszyk@35222: | _ => HOLogic.eq_const rty kaliszyk@35222: kaliszyk@35222: fun equiv_relation_chk ctxt (rty, qty) = kaliszyk@35222: equiv_relation ctxt (rty, qty) kaliszyk@35222: |> Syntax.check_term ctxt kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (*** Regularization ***) kaliszyk@35222: kaliszyk@35222: (* Regularizing an rtrm means: kaliszyk@35222: kaliszyk@35222: - Quantifiers over types that need lifting are replaced kaliszyk@35222: by bounded quantifiers, for example: kaliszyk@35222: kaliszyk@35222: All P ----> All (Respects R) P kaliszyk@35222: kaliszyk@35222: where the aggregate relation R is given by the rty and qty; kaliszyk@35222: kaliszyk@35222: - Abstractions over types that need lifting are replaced kaliszyk@35222: by bounded abstractions, for example: kaliszyk@35222: kaliszyk@35222: %x. P ----> Ball (Respects R) %x. P kaliszyk@35222: kaliszyk@35222: - Equalities over types that need lifting are replaced by kaliszyk@35222: corresponding equivalence relations, for example: kaliszyk@35222: kaliszyk@35222: A = B ----> R A B kaliszyk@35222: kaliszyk@35222: or kaliszyk@35222: kaliszyk@35222: A = B ----> (R ===> R) A B kaliszyk@35222: kaliszyk@35222: for more complicated types of A and B kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: The regularize_trm accepts raw theorems in which equalities kaliszyk@35222: and quantifiers match exactly the ones in the lifted theorem kaliszyk@35222: but also accepts partially regularized terms. kaliszyk@35222: kaliszyk@35222: This means that the raw theorems can have: kaliszyk@35222: Ball (Respects R), Bex (Respects R), Bex1_rel (Respects R), Babs, R kaliszyk@35222: in the places where: kaliszyk@35222: All, Ex, Ex1, %, (op =) kaliszyk@35222: is required the lifted theorem. kaliszyk@35222: kaliszyk@35222: *) kaliszyk@35222: kaliszyk@35222: val mk_babs = Const (@{const_name Babs}, dummyT) kaliszyk@35222: val mk_ball = Const (@{const_name Ball}, dummyT) kaliszyk@35222: val mk_bex = Const (@{const_name Bex}, dummyT) kaliszyk@35222: val mk_bex1_rel = Const (@{const_name Bex1_rel}, dummyT) kaliszyk@35222: val mk_resp = Const (@{const_name Respects}, dummyT) kaliszyk@35222: kaliszyk@35222: (* - applies f to the subterm of an abstraction, kaliszyk@35222: otherwise to the given term, kaliszyk@35222: - used by regularize, therefore abstracted kaliszyk@35222: variables do not have to be treated specially kaliszyk@35222: *) kaliszyk@35222: fun apply_subt f (trm1, trm2) = kaliszyk@35222: case (trm1, trm2) of kaliszyk@35222: (Abs (x, T, t), Abs (_ , _, t')) => Abs (x, T, f (t, t')) kaliszyk@35222: | _ => f (trm1, trm2) kaliszyk@35222: kaliszyk@35222: fun term_mismatch str ctxt t1 t2 = kaliszyk@35222: let kaliszyk@35222: val t1_str = Syntax.string_of_term ctxt t1 kaliszyk@35222: val t2_str = Syntax.string_of_term ctxt t2 kaliszyk@35222: val t1_ty_str = Syntax.string_of_typ ctxt (fastype_of t1) kaliszyk@35222: val t2_ty_str = Syntax.string_of_typ ctxt (fastype_of t2) kaliszyk@35222: in kaliszyk@35222: raise LIFT_MATCH (cat_lines [str, t1_str ^ "::" ^ t1_ty_str, t2_str ^ "::" ^ t2_ty_str]) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: (* the major type of All and Ex quantifiers *) kaliszyk@35222: fun qnt_typ ty = domain_type (domain_type ty) kaliszyk@35222: kaliszyk@35222: (* Checks that two types match, for example: kaliszyk@35222: rty -> rty matches qty -> qty *) kaliszyk@35222: fun matches_typ thy rT qT = kaliszyk@35222: if rT = qT then true else kaliszyk@35222: case (rT, qT) of kaliszyk@35222: (Type (rs, rtys), Type (qs, qtys)) => kaliszyk@35222: if rs = qs then kaliszyk@35222: if length rtys <> length qtys then false else kaliszyk@35222: forall (fn x => x = true) (map2 (matches_typ thy) rtys qtys) kaliszyk@35222: else kaliszyk@35222: (case Quotient_Info.quotdata_lookup_raw thy qs of kaliszyk@35222: SOME quotinfo => Sign.typ_instance thy (rT, #rtyp quotinfo) kaliszyk@35222: | NONE => false) kaliszyk@35222: | _ => false kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (* produces a regularized version of rtrm kaliszyk@35222: kaliszyk@35222: - the result might contain dummyTs kaliszyk@35222: kaliszyk@35222: - for regularisation we do not need any kaliszyk@35222: special treatment of bound variables kaliszyk@35222: *) kaliszyk@35222: fun regularize_trm ctxt (rtrm, qtrm) = kaliszyk@35222: case (rtrm, qtrm) of kaliszyk@35222: (Abs (x, ty, t), Abs (_, ty', t')) => kaliszyk@35222: let kaliszyk@35222: val subtrm = Abs(x, ty, regularize_trm ctxt (t, t')) kaliszyk@35222: in kaliszyk@35222: if ty = ty' then subtrm kaliszyk@35222: else mk_babs $ (mk_resp $ equiv_relation ctxt (ty, ty')) $ subtrm kaliszyk@35222: end haftmann@37677: | (Const (@{const_name Babs}, T) $ resrel $ (t as (Abs (_, ty, _))), t' as (Abs (_, ty', _))) => kaliszyk@35222: let kaliszyk@35222: val subtrm = regularize_trm ctxt (t, t') kaliszyk@35222: val needres = mk_resp $ equiv_relation_chk ctxt (ty, ty') kaliszyk@35222: in kaliszyk@35222: if resrel <> needres kaliszyk@35222: then term_mismatch "regularize (Babs)" ctxt resrel needres kaliszyk@35222: else mk_babs $ resrel $ subtrm kaliszyk@35222: end kaliszyk@35222: haftmann@37677: | (Const (@{const_name All}, ty) $ t, Const (@{const_name All}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t, t') kaliszyk@35222: in haftmann@37677: if ty = ty' then Const (@{const_name All}, ty) $ subtrm kaliszyk@35222: else mk_ball $ (mk_resp $ equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm kaliszyk@35222: end kaliszyk@35222: haftmann@37677: | (Const (@{const_name Ex}, ty) $ t, Const (@{const_name Ex}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t, t') kaliszyk@35222: in haftmann@37677: if ty = ty' then Const (@{const_name Ex}, ty) $ subtrm kaliszyk@35222: else mk_bex $ (mk_resp $ equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm kaliszyk@35222: end kaliszyk@35222: haftmann@37677: | (Const (@{const_name Ex1}, ty) $ (Abs (_, _, haftmann@37677: (Const (@{const_name "op &"}, _) $ (Const (@{const_name Set.member}, _) $ _ $ haftmann@37677: (Const (@{const_name Respects}, _) $ resrel)) $ (t $ _)))), haftmann@37677: Const (@{const_name Ex1}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val t_ = incr_boundvars (~1) t kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t_, t') kaliszyk@35222: val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty') kaliszyk@35222: in kaliszyk@35222: if resrel <> needrel kaliszyk@35222: then term_mismatch "regularize (Bex1)" ctxt resrel needrel kaliszyk@35222: else mk_bex1_rel $ resrel $ subtrm kaliszyk@35222: end kaliszyk@35222: haftmann@38558: | (Const (@{const_name Ex1}, ty) $ t, Const (@{const_name Ex1}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t, t') kaliszyk@35222: in haftmann@38558: if ty = ty' then Const (@{const_name Ex1}, ty) $ subtrm kaliszyk@35222: else mk_bex1_rel $ (equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | (Const (@{const_name "Ball"}, ty) $ (Const (@{const_name "Respects"}, _) $ resrel) $ t, haftmann@38558: Const (@{const_name All}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t, t') kaliszyk@35222: val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty') kaliszyk@35222: in kaliszyk@35222: if resrel <> needrel kaliszyk@35222: then term_mismatch "regularize (Ball)" ctxt resrel needrel kaliszyk@35222: else mk_ball $ (mk_resp $ resrel) $ subtrm kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | (Const (@{const_name "Bex"}, ty) $ (Const (@{const_name "Respects"}, _) $ resrel) $ t, haftmann@38558: Const (@{const_name Ex}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t, t') kaliszyk@35222: val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty') kaliszyk@35222: in kaliszyk@35222: if resrel <> needrel kaliszyk@35222: then term_mismatch "regularize (Bex)" ctxt resrel needrel kaliszyk@35222: else mk_bex $ (mk_resp $ resrel) $ subtrm kaliszyk@35222: end kaliszyk@35222: haftmann@38558: | (Const (@{const_name "Bex1_rel"}, ty) $ resrel $ t, Const (@{const_name Ex1}, ty') $ t') => kaliszyk@35222: let kaliszyk@35222: val subtrm = apply_subt (regularize_trm ctxt) (t, t') kaliszyk@35222: val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty') kaliszyk@35222: in kaliszyk@35222: if resrel <> needrel kaliszyk@35222: then term_mismatch "regularize (Bex1_res)" ctxt resrel needrel kaliszyk@35222: else mk_bex1_rel $ resrel $ subtrm kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | (* equalities need to be replaced by appropriate equivalence relations *) kaliszyk@35222: (Const (@{const_name "op ="}, ty), Const (@{const_name "op ="}, ty')) => kaliszyk@35222: if ty = ty' then rtrm kaliszyk@35222: else equiv_relation ctxt (domain_type ty, domain_type ty') kaliszyk@35222: kaliszyk@35222: | (* in this case we just check whether the given equivalence relation is correct *) kaliszyk@35222: (rel, Const (@{const_name "op ="}, ty')) => kaliszyk@35222: let kaliszyk@35222: val rel_ty = fastype_of rel kaliszyk@35222: val rel' = equiv_relation_chk ctxt (domain_type rel_ty, domain_type ty') kaliszyk@35222: in kaliszyk@35222: if rel' aconv rel then rtrm kaliszyk@35222: else term_mismatch "regularise (relation mismatch)" ctxt rel rel' kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | (_, Const _) => kaliszyk@35222: let kaliszyk@35222: val thy = ProofContext.theory_of ctxt kaliszyk@35222: fun same_const (Const (s, T)) (Const (s', T')) = (s = s') andalso matches_typ thy T T' kaliszyk@35222: | same_const _ _ = false kaliszyk@35222: in kaliszyk@35222: if same_const rtrm qtrm then rtrm kaliszyk@35222: else kaliszyk@35222: let kaliszyk@35222: val rtrm' = #rconst (qconsts_lookup thy qtrm) kaliszyk@35222: handle Quotient_Info.NotFound => term_mismatch "regularize(constant notfound)" ctxt rtrm qtrm kaliszyk@35222: in kaliszyk@35222: if Pattern.matches thy (rtrm', rtrm) kaliszyk@35222: then rtrm else term_mismatch "regularize(constant mismatch)" ctxt rtrm qtrm kaliszyk@35222: end kaliszyk@35222: end kaliszyk@35222: haftmann@37591: | (((t1 as Const (@{const_name prod_case}, _)) $ Abs (v1, ty, Abs(v1', ty', s1))), haftmann@37591: ((t2 as Const (@{const_name prod_case}, _)) $ Abs (v2, _ , Abs(v2', _ , s2)))) => kaliszyk@35222: regularize_trm ctxt (t1, t2) $ Abs (v1, ty, Abs (v1', ty', regularize_trm ctxt (s1, s2))) kaliszyk@35222: haftmann@37591: | (((t1 as Const (@{const_name prod_case}, _)) $ Abs (v1, ty, s1)), haftmann@37591: ((t2 as Const (@{const_name prod_case}, _)) $ Abs (v2, _ , s2))) => kaliszyk@35222: regularize_trm ctxt (t1, t2) $ Abs (v1, ty, regularize_trm ctxt (s1, s2)) kaliszyk@35222: kaliszyk@35222: | (t1 $ t2, t1' $ t2') => kaliszyk@35222: regularize_trm ctxt (t1, t1') $ regularize_trm ctxt (t2, t2') kaliszyk@35222: kaliszyk@35222: | (Bound i, Bound i') => kaliszyk@35222: if i = i' then rtrm kaliszyk@35222: else raise (LIFT_MATCH "regularize (bounds mismatch)") kaliszyk@35222: kaliszyk@35222: | _ => kaliszyk@35222: let kaliszyk@35222: val rtrm_str = Syntax.string_of_term ctxt rtrm kaliszyk@35222: val qtrm_str = Syntax.string_of_term ctxt qtrm kaliszyk@35222: in kaliszyk@35222: raise (LIFT_MATCH ("regularize failed (default: " ^ rtrm_str ^ "," ^ qtrm_str ^ ")")) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: fun regularize_trm_chk ctxt (rtrm, qtrm) = kaliszyk@35222: regularize_trm ctxt (rtrm, qtrm) kaliszyk@35222: |> Syntax.check_term ctxt kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (*** Rep/Abs Injection ***) kaliszyk@35222: kaliszyk@35222: (* kaliszyk@35222: Injection of Rep/Abs means: kaliszyk@35222: kaliszyk@35222: For abstractions: kaliszyk@35222: kaliszyk@35222: * If the type of the abstraction needs lifting, then we add Rep/Abs kaliszyk@35222: around the abstraction; otherwise we leave it unchanged. kaliszyk@35222: kaliszyk@35222: For applications: kaliszyk@35222: kaliszyk@35222: * If the application involves a bounded quantifier, we recurse on kaliszyk@35222: the second argument. If the application is a bounded abstraction, kaliszyk@35222: we always put an Rep/Abs around it (since bounded abstractions kaliszyk@35222: are assumed to always need lifting). Otherwise we recurse on both kaliszyk@35222: arguments. kaliszyk@35222: kaliszyk@35222: For constants: kaliszyk@35222: kaliszyk@35222: * If the constant is (op =), we leave it always unchanged. kaliszyk@35222: Otherwise the type of the constant needs lifting, we put kaliszyk@35222: and Rep/Abs around it. kaliszyk@35222: kaliszyk@35222: For free variables: kaliszyk@35222: kaliszyk@35222: * We put a Rep/Abs around it if the type needs lifting. kaliszyk@35222: kaliszyk@35222: Vars case cannot occur. kaliszyk@35222: *) kaliszyk@35222: kaliszyk@35222: fun mk_repabs ctxt (T, T') trm = kaliszyk@35222: absrep_fun RepF ctxt (T, T') $ (absrep_fun AbsF ctxt (T, T') $ trm) kaliszyk@35222: kaliszyk@35222: fun inj_repabs_err ctxt msg rtrm qtrm = kaliszyk@35222: let kaliszyk@35222: val rtrm_str = Syntax.string_of_term ctxt rtrm kaliszyk@35222: val qtrm_str = Syntax.string_of_term ctxt qtrm kaliszyk@35222: in kaliszyk@35222: raise LIFT_MATCH (space_implode " " [msg, quote rtrm_str, "and", quote qtrm_str]) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (* bound variables need to be treated properly, kaliszyk@35222: as the type of subterms needs to be calculated *) kaliszyk@35222: fun inj_repabs_trm ctxt (rtrm, qtrm) = kaliszyk@35222: case (rtrm, qtrm) of haftmann@38558: (Const (@{const_name "Ball"}, T) $ r $ t, Const (@{const_name All}, _) $ t') => kaliszyk@35222: Const (@{const_name "Ball"}, T) $ r $ (inj_repabs_trm ctxt (t, t')) kaliszyk@35222: haftmann@38558: | (Const (@{const_name "Bex"}, T) $ r $ t, Const (@{const_name Ex}, _) $ t') => kaliszyk@35222: Const (@{const_name "Bex"}, T) $ r $ (inj_repabs_trm ctxt (t, t')) kaliszyk@35222: kaliszyk@35222: | (Const (@{const_name "Babs"}, T) $ r $ t, t' as (Abs _)) => kaliszyk@35222: let kaliszyk@35222: val rty = fastype_of rtrm kaliszyk@35222: val qty = fastype_of qtrm kaliszyk@35222: in kaliszyk@35222: mk_repabs ctxt (rty, qty) (Const (@{const_name "Babs"}, T) $ r $ (inj_repabs_trm ctxt (t, t'))) kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | (Abs (x, T, t), Abs (x', T', t')) => kaliszyk@35222: let kaliszyk@35222: val rty = fastype_of rtrm kaliszyk@35222: val qty = fastype_of qtrm kaliszyk@35222: val (y, s) = Term.dest_abs (x, T, t) kaliszyk@35222: val (_, s') = Term.dest_abs (x', T', t') kaliszyk@35222: val yvar = Free (y, T) kaliszyk@35222: val result = Term.lambda_name (y, yvar) (inj_repabs_trm ctxt (s, s')) kaliszyk@35222: in kaliszyk@35222: if rty = qty then result kaliszyk@35222: else mk_repabs ctxt (rty, qty) result kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | (t $ s, t' $ s') => kaliszyk@35222: (inj_repabs_trm ctxt (t, t')) $ (inj_repabs_trm ctxt (s, s')) kaliszyk@35222: kaliszyk@35222: | (Free (_, T), Free (_, T')) => kaliszyk@35222: if T = T' then rtrm kaliszyk@35222: else mk_repabs ctxt (T, T') rtrm kaliszyk@35222: kaliszyk@35222: | (_, Const (@{const_name "op ="}, _)) => rtrm kaliszyk@35222: kaliszyk@35222: | (_, Const (_, T')) => kaliszyk@35222: let kaliszyk@35222: val rty = fastype_of rtrm kaliszyk@35222: in kaliszyk@35222: if rty = T' then rtrm kaliszyk@35222: else mk_repabs ctxt (rty, T') rtrm kaliszyk@35222: end kaliszyk@35222: kaliszyk@35222: | _ => inj_repabs_err ctxt "injection (default):" rtrm qtrm kaliszyk@35222: kaliszyk@35222: fun inj_repabs_trm_chk ctxt (rtrm, qtrm) = kaliszyk@35222: inj_repabs_trm ctxt (rtrm, qtrm) kaliszyk@35222: |> Syntax.check_term ctxt kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: kaliszyk@35222: (*** Wrapper for automatically transforming an rthm into a qthm ***) kaliszyk@35222: urbanc@37592: (* substitutions functions for r/q-types and urbanc@37592: r/q-constants, respectively urbanc@37560: *) urbanc@37592: fun subst_typ ctxt ty_subst rty = urbanc@37560: case rty of urbanc@37560: Type (s, rtys) => urbanc@37560: let urbanc@37560: val thy = ProofContext.theory_of ctxt urbanc@37592: val rty' = Type (s, map (subst_typ ctxt ty_subst) rtys) urbanc@37560: urbanc@37560: fun matches [] = rty' urbanc@37560: | matches ((rty, qty)::tail) = urbanc@37560: case try (Sign.typ_match thy (rty, rty')) Vartab.empty of urbanc@37560: NONE => matches tail urbanc@37560: | SOME inst => Envir.subst_type inst qty urbanc@37560: in urbanc@37560: matches ty_subst urbanc@37560: end urbanc@37560: | _ => rty urbanc@37560: urbanc@37592: fun subst_trm ctxt ty_subst trm_subst rtrm = urbanc@37560: case rtrm of urbanc@37592: t1 $ t2 => (subst_trm ctxt ty_subst trm_subst t1) $ (subst_trm ctxt ty_subst trm_subst t2) urbanc@37592: | Abs (x, ty, t) => Abs (x, subst_typ ctxt ty_subst ty, subst_trm ctxt ty_subst trm_subst t) urbanc@37592: | Free(n, ty) => Free(n, subst_typ ctxt ty_subst ty) urbanc@37592: | Var(n, ty) => Var(n, subst_typ ctxt ty_subst ty) urbanc@37560: | Bound i => Bound i urbanc@37560: | Const (a, ty) => urbanc@37560: let urbanc@37560: val thy = ProofContext.theory_of ctxt kaliszyk@35222: urbanc@37592: fun matches [] = Const (a, subst_typ ctxt ty_subst ty) urbanc@37560: | matches ((rconst, qconst)::tail) = urbanc@37560: case try (Pattern.match thy (rconst, rtrm)) (Vartab.empty, Vartab.empty) of urbanc@37560: NONE => matches tail urbanc@37560: | SOME inst => Envir.subst_term inst qconst urbanc@37560: in urbanc@37560: matches trm_subst urbanc@37560: end urbanc@37560: urbanc@37592: (* generate type and term substitutions out of the urbanc@37592: qtypes involved in a quotient; the direction flag urbanc@37609: indicates in which direction the substitutions work: urbanc@37592: urbanc@37592: true: quotient -> raw urbanc@37592: false: raw -> quotient urbanc@37560: *) urbanc@37592: fun mk_ty_subst qtys direction ctxt = urbanc@37560: Quotient_Info.quotdata_dest ctxt urbanc@37560: |> map (fn x => (#rtyp x, #qtyp x)) urbanc@37560: |> filter (fn (_, qty) => member (op =) qtys qty) urbanc@37592: |> map (if direction then swap else I) kaliszyk@35222: urbanc@37592: fun mk_trm_subst qtys direction ctxt = kaliszyk@37563: let urbanc@37592: val subst_typ' = subst_typ ctxt (mk_ty_subst qtys direction ctxt) urbanc@37609: fun proper (t1, t2) = subst_typ' (fastype_of t1) = fastype_of t2 kaliszyk@37563: urbanc@37560: val const_substs = urbanc@37560: Quotient_Info.qconsts_dest ctxt kaliszyk@37563: |> map (fn x => (#rconst x, #qconst x)) urbanc@37592: |> map (if direction then swap else I) urbanc@37560: kaliszyk@37563: val rel_substs = urbanc@37560: Quotient_Info.quotdata_dest ctxt urbanc@37560: |> map (fn x => (#equiv_rel x, HOLogic.eq_const (#qtyp x))) urbanc@37592: |> map (if direction then swap else I) kaliszyk@35222: in urbanc@37560: filter proper (const_substs @ rel_substs) kaliszyk@35222: end kaliszyk@35222: urbanc@37592: urbanc@37560: (* derives a qtyp and qtrm out of a rtyp and rtrm, urbanc@37560: respectively urbanc@37560: *) urbanc@37592: fun derive_qtyp qtys rty ctxt = urbanc@37592: subst_typ ctxt (mk_ty_subst qtys false ctxt) rty urbanc@37592: urbanc@37592: fun derive_qtrm qtys rtrm ctxt = urbanc@37592: subst_trm ctxt (mk_ty_subst qtys false ctxt) (mk_trm_subst qtys false ctxt) rtrm kaliszyk@35222: urbanc@37592: (* derives a rtyp and rtrm out of a qtyp and qtrm, urbanc@37592: respectively urbanc@37592: *) urbanc@37592: fun derive_rtyp qtys qty ctxt = urbanc@37592: subst_typ ctxt (mk_ty_subst qtys true ctxt) qty urbanc@37592: urbanc@37592: fun derive_rtrm qtys qtrm ctxt = urbanc@37592: subst_trm ctxt (mk_ty_subst qtys true ctxt) (mk_trm_subst qtys true ctxt) qtrm urbanc@37560: kaliszyk@35222: kaliszyk@35222: end; (* structure *)