(* Title: Pure/logic.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Author: Makarius
Abstract syntax operations of the Pure meta-logic.
*)
signature LOGIC =
sig
val all_const: typ -> term
val all: term -> term -> term
val dependent_all_name: string * term -> term -> term
val is_all: term -> bool
val dest_all: term -> (string * typ) * term
val list_all: (string * typ) list * term -> term
val all_constraint: (string -> typ option) -> string * string -> term -> term
val dependent_all_constraint: (string -> typ option) -> string * string -> term -> term
val mk_equals: term * term -> term
val dest_equals: term -> term * term
val implies: term
val mk_implies: term * term -> term
val dest_implies: term -> term * term
val list_implies: term list * term -> term
val strip_imp_prems: term -> term list
val strip_imp_concl: term -> term
val strip_prems: int * term list * term -> term list * term
val count_prems: term -> int
val nth_prem: int * term -> term
val close_term: (string * term) list -> term -> term
val close_prop: (string * term) list -> term list -> term -> term
val close_prop_constraint: (string -> typ option) ->
(string * string) list -> term list -> term -> term
val true_prop: term
val conjunction: term
val mk_conjunction: term * term -> term
val mk_conjunction_list: term list -> term
val mk_conjunction_balanced: term list -> term
val dest_conjunction: term -> term * term
val dest_conjunction_list: term -> term list
val dest_conjunction_balanced: int -> term -> term list
val dest_conjunctions: term -> term list
val strip_horn: term -> term list * term
val mk_type: typ -> term
val dest_type: term -> typ
val type_map: (term -> term) -> typ -> typ
val const_of_class: class -> string
val class_of_const: string -> class
val mk_of_class: typ * class -> term
val dest_of_class: term -> typ * class
val mk_of_sort: typ * sort -> term list
val name_classrel: string * string -> string
val mk_classrel: class * class -> term
val dest_classrel: term -> class * class
val name_arities: arity -> string list
val name_arity: string * sort list * class -> string
val mk_arities: arity -> term list
val mk_arity: string * sort list * class -> term
val dest_arity: term -> string * sort list * class
val dummy_tfree: sort -> typ
type unconstrain_context =
{present_map: (typ * typ) list,
constraints_map: (sort * typ) list,
atyp_map: typ -> typ,
map_atyps: typ -> typ,
constraints: ((typ * class) * term) list,
outer_constraints: (typ * class) list};
val unconstrainT: sort list -> term -> unconstrain_context * term
val protectC: term
val protect: term -> term
val unprotect: term -> term
val mk_term: term -> term
val dest_term: term -> term
val occs: term * term -> bool
val close_form: term -> term
val combound: term * int * int -> term
val rlist_abs: (string * typ) list * term -> term
val incr_tvar_same: int -> typ Same.operation
val incr_tvar: int -> typ -> typ
val incr_indexes_same: string list * typ list * int -> term Same.operation
val incr_indexes: string list * typ list * int -> term -> term
val lift_abs: int -> term -> term -> term
val lift_all: int -> term -> term -> term
val strip_assums_hyp: term -> term list
val strip_assums_concl: term -> term
val strip_params: term -> (string * typ) list
val has_meta_prems: term -> bool
val flatten_params: int -> term -> term
val list_rename_params: string list -> term -> term
val assum_pairs: int * term -> (term * term) list
val assum_problems: int * term -> (term -> term) * term list * term
val bad_schematic: indexname -> string
val bad_fixed: string -> string
val varifyT_global: typ -> typ
val unvarifyT_global: typ -> typ
val varify_types_global: term -> term
val unvarify_types_global: term -> term
val varify_global: term -> term
val unvarify_global: term -> term
val get_goal: term -> int -> term
val goal_params: term -> int -> term * term list
val prems_of_goal: term -> int -> term list
val concl_of_goal: term -> int -> term
end;
structure Logic : LOGIC =
struct
(*** Abstract syntax operations on the meta-connectives ***)
(** all **)
fun all_const T = Const ("Pure.all", (T --> propT) --> propT);
fun all v t = all_const (Term.fastype_of v) $ lambda v t;
fun dependent_all_name (x, v) t =
let
val x' = if x = "" then Term.term_name v else x;
val T = Term.fastype_of v;
val t' = Term.abstract_over (v, t);
in if Term.is_dependent t' then all_const T $ Abs (x', T, t') else t end;
fun is_all (Const ("Pure.all", _) $ Abs _) = true
| is_all _ = false;
fun dest_all (Const ("Pure.all", _) $ Abs (abs as (_, T, _))) =
let val (x, b) = Term.dest_abs abs (*potentially slow*)
in ((x, T), b) end
| dest_all t = raise TERM ("dest_all", [t]);
fun list_all ([], t) = t
| list_all ((a, T) :: vars, t) = all_const T $ Abs (a, T, list_all (vars, t));
(* operations before type-inference *)
local
fun abs_body default_type z tm =
let
fun abs lev (Abs (x, T, b)) = Abs (x, T, abs (lev + 1) b)
| abs lev (t $ u) = abs lev t $ abs lev u
| abs lev (a as Free (x, T)) =
if x = z then
Type.constraint (the_default dummyT (default_type x))
(Type.constraint T (Bound lev))
else a
| abs _ a = a;
in abs 0 (Term.incr_boundvars 1 tm) end;
in
fun all_constraint default_type (y, z) t =
all_const dummyT $ Abs (y, dummyT, abs_body default_type z t);
fun dependent_all_constraint default_type (y, z) t =
let val t' = abs_body default_type z t
in if Term.is_dependent t' then all_const dummyT $ Abs (y, dummyT, t') else t end;
end;
(** equality **)
fun mk_equals (t, u) =
let val T = Term.fastype_of t
in Const ("Pure.eq", T --> T --> propT) $ t $ u end;
fun dest_equals (Const ("Pure.eq", _) $ t $ u) = (t, u)
| dest_equals t = raise TERM ("dest_equals", [t]);
(** implies **)
val implies = Const ("Pure.imp", propT --> propT --> propT);
fun mk_implies (A, B) = implies $ A $ B;
fun dest_implies (Const ("Pure.imp", _) $ A $ B) = (A, B)
| dest_implies A = raise TERM ("dest_implies", [A]);
(** nested implications **)
(* [A1,...,An], B goes to A1\<Longrightarrow>...An\<Longrightarrow>B *)
fun list_implies ([], B) = B
| list_implies (A::As, B) = implies $ A $ list_implies(As,B);
(* A1\<Longrightarrow>...An\<Longrightarrow>B goes to [A1,...,An], where B is not an implication *)
fun strip_imp_prems (Const("Pure.imp", _) $ A $ B) = A :: strip_imp_prems B
| strip_imp_prems _ = [];
(* A1\<Longrightarrow>...An\<Longrightarrow>B goes to B, where B is not an implication *)
fun strip_imp_concl (Const("Pure.imp", _) $ A $ B) = strip_imp_concl B
| strip_imp_concl A = A : term;
(*Strip and return premises: (i, [], A1\<Longrightarrow>...Ai\<Longrightarrow>B)
goes to ([Ai, A(i-1),...,A1] , B) (REVERSED)
if i<0 or else i too big then raises TERM*)
fun strip_prems (0, As, B) = (As, B)
| strip_prems (i, As, Const("Pure.imp", _) $ A $ B) =
strip_prems (i-1, A::As, B)
| strip_prems (_, As, A) = raise TERM("strip_prems", A::As);
(*Count premises -- quicker than (length o strip_prems) *)
fun count_prems (Const ("Pure.imp", _) $ _ $ B) = 1 + count_prems B
| count_prems _ = 0;
(*Select Ai from A1\<Longrightarrow>...Ai\<Longrightarrow>B*)
fun nth_prem (1, Const ("Pure.imp", _) $ A $ _) = A
| nth_prem (i, Const ("Pure.imp", _) $ _ $ B) = nth_prem (i - 1, B)
| nth_prem (_, A) = raise TERM ("nth_prem", [A]);
(*strip a proof state (Horn clause):
B1 \<Longrightarrow> ... Bn \<Longrightarrow> C goes to ([B1, ..., Bn], C) *)
fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);
(* close -- omit vacuous quantifiers *)
val close_term = fold_rev Term.dependent_lambda_name;
fun close_prop xs As B =
fold_rev dependent_all_name xs (list_implies (As, B));
fun close_prop_constraint default_type xs As B =
fold_rev (dependent_all_constraint default_type) xs (list_implies (As, B));
(** conjunction **)
val true_prop = all_const propT $ Abs ("dummy", propT, mk_implies (Bound 0, Bound 0));
val conjunction = Const ("Pure.conjunction", propT --> propT --> propT);
(*A &&& B*)
fun mk_conjunction (A, B) = conjunction $ A $ B;
(*A &&& B &&& C -- improper*)
fun mk_conjunction_list [] = true_prop
| mk_conjunction_list ts = foldr1 mk_conjunction ts;
(*(A &&& B) &&& (C &&& D) -- balanced*)
fun mk_conjunction_balanced [] = true_prop
| mk_conjunction_balanced ts = Balanced_Tree.make mk_conjunction ts;
(*A &&& B*)
fun dest_conjunction (Const ("Pure.conjunction", _) $ A $ B) = (A, B)
| dest_conjunction t = raise TERM ("dest_conjunction", [t]);
(*A &&& B &&& C -- improper*)
fun dest_conjunction_list t =
(case try dest_conjunction t of
NONE => [t]
| SOME (A, B) => A :: dest_conjunction_list B);
(*(A &&& B) &&& (C &&& D) -- balanced*)
fun dest_conjunction_balanced 0 _ = []
| dest_conjunction_balanced n t = Balanced_Tree.dest dest_conjunction n t;
(*((A &&& B) &&& C) &&& D &&& E -- flat*)
fun dest_conjunctions t =
(case try dest_conjunction t of
NONE => [t]
| SOME (A, B) => dest_conjunctions A @ dest_conjunctions B);
(** types as terms **)
fun mk_type ty = Const ("Pure.type", Term.itselfT ty);
fun dest_type (Const ("Pure.type", Type ("itself", [ty]))) = ty
| dest_type t = raise TERM ("dest_type", [t]);
fun type_map f = dest_type o f o mk_type;
(** type classes **)
(* const names *)
val classN = "_class";
val const_of_class = suffix classN;
fun class_of_const c = unsuffix classN c
handle Fail _ => raise TERM ("class_of_const: bad name " ^ quote c, []);
(* class/sort membership *)
fun mk_of_class (ty, c) =
Const (const_of_class c, Term.itselfT ty --> propT) $ mk_type ty;
fun dest_of_class (Const (c_class, _) $ ty) = (dest_type ty, class_of_const c_class)
| dest_of_class t = raise TERM ("dest_of_class", [t]);
fun mk_of_sort (ty, S) = map (fn c => mk_of_class (ty, c)) S;
(* class relations *)
fun name_classrel (c1, c2) =
Long_Name.base_name c1 ^ "_" ^ Long_Name.base_name c2;
fun mk_classrel (c1, c2) = mk_of_class (Term.aT [c1], c2);
fun dest_classrel tm =
(case dest_of_class tm of
(TVar (_, [c1]), c2) => (c1, c2)
| _ => raise TERM ("dest_classrel", [tm]));
(* type arities *)
fun name_arities (t, _, S) =
let val b = Long_Name.base_name t
in S |> map (fn c => Long_Name.base_name c ^ "_" ^ b) end;
fun name_arity (t, dom, c) = hd (name_arities (t, dom, [c]));
fun mk_arities (t, Ss, S) =
let val T = Type (t, ListPair.map TFree (Name.invent Name.context Name.aT (length Ss), Ss))
in map (fn c => mk_of_class (T, c)) S end;
fun mk_arity (t, Ss, c) = the_single (mk_arities (t, Ss, [c]));
fun dest_arity tm =
let
fun err () = raise TERM ("dest_arity", [tm]);
val (ty, c) = dest_of_class tm;
val (t, tvars) =
(case ty of
Type (t, tys) => (t, map dest_TVar tys handle TYPE _ => err ())
| _ => err ());
val Ss =
if has_duplicates (eq_fst (op =)) tvars then err ()
else map snd tvars;
in (t, Ss, c) end;
(* internalized sort constraints *)
fun dummy_tfree S = TFree ("'dummy", S);
type unconstrain_context =
{present_map: (typ * typ) list,
constraints_map: (sort * typ) list,
atyp_map: typ -> typ,
map_atyps: typ -> typ,
constraints: ((typ * class) * term) list,
outer_constraints: (typ * class) list};
fun unconstrainT shyps prop =
let
val present = rev ((fold_types o fold_atyps_sorts) (insert (eq_fst op =)) prop []);
val extra = fold (Sorts.remove_sort o #2) present shyps;
val n = length present;
val (names1, names2) = Name.invent Name.context Name.aT (n + length extra) |> chop n;
val present_map =
map2 (fn (T, S) => fn a => (T, TVar ((a, 0), S))) present names1;
val constraints_map =
map2 (fn (_, S) => fn a => (S, TVar ((a, 0), S))) present names1 @
map2 (fn S => fn a => (S, TVar ((a, 0), S))) extra names2;
fun atyp_map T =
(case AList.lookup (op =) present_map T of
SOME U => U
| NONE =>
(case AList.lookup (op =) constraints_map (Type.sort_of_atyp T) of
SOME U => U
| NONE => raise TYPE ("Dangling type variable ", [T], [prop])));
val map_atyps = Term.map_atyps (Type.strip_sorts o atyp_map);
val constraints =
constraints_map |> maps (fn (_, T as TVar (ai, S)) =>
map (fn c => ((T, c), mk_of_class (TVar (ai, []), c))) S);
val outer_constraints =
maps (fn (T, S) => map (pair T) S) (present @ map (`dummy_tfree) extra);
val ucontext =
{present_map = present_map,
constraints_map = constraints_map,
atyp_map = atyp_map,
map_atyps = map_atyps,
constraints = constraints,
outer_constraints = outer_constraints};
val prop' = prop
|> Term.map_types map_atyps
|> curry list_implies (map #2 constraints);
in (ucontext, prop') end;
(** protected propositions and embedded terms **)
val protectC = Const ("Pure.prop", propT --> propT);
fun protect t = protectC $ t;
fun unprotect (Const ("Pure.prop", _) $ t) = t
| unprotect t = raise TERM ("unprotect", [t]);
fun mk_term t = Const ("Pure.term", Term.fastype_of t --> propT) $ t;
fun dest_term (Const ("Pure.term", _) $ t) = t
| dest_term t = raise TERM ("dest_term", [t]);
(*** Low-level term operations ***)
(*Does t occur in u? Or is alpha-convertible to u?
The term t must contain no loose bound variables*)
fun occs (t, u) = exists_subterm (fn s => t aconv s) u;
(*Close up a formula over all free variables by quantification*)
fun close_form A = fold (all o Free) (Term.add_frees A []) A;
(*** Specialized operations for resolution... ***)
(*computes t(Bound(n+k-1),...,Bound(n)) *)
fun combound (t, n, k) =
if k>0 then combound (t,n+1,k-1) $ (Bound n) else t;
(* ([xn,...,x1], t) goes to \<lambda>x1 ... xn. t *)
fun rlist_abs ([], body) = body
| rlist_abs ((a,T)::pairs, body) = rlist_abs(pairs, Abs(a, T, body));
fun incr_tvar_same 0 = Same.same
| incr_tvar_same k = Term_Subst.map_atypsT_same
(fn TVar ((a, i), S) => TVar ((a, i + k), S)
| _ => raise Same.SAME);
fun incr_tvar k T = incr_tvar_same k T handle Same.SAME => T;
(*For all variables in the term, increment indexnames and lift over the Us
result is ?Gidx(B.(lev+n-1),...,B.lev) where lev is abstraction level *)
fun incr_indexes_same ([], [], 0) = Same.same
| incr_indexes_same (fixed, Ts, k) =
let
val n = length Ts;
val incrT = incr_tvar_same k;
fun incr lev (Var ((x, i), T)) =
combound (Var ((x, i + k), Ts ---> Same.commit incrT T), lev, n)
| incr lev (Free (x, T)) =
if member (op =) fixed x then
combound (Free (x, Ts ---> Same.commit incrT T), lev, n)
else Free (x, incrT T)
| incr lev (Abs (x, T, body)) =
(Abs (x, incrT T, incr (lev + 1) body handle Same.SAME => body)
handle Same.SAME => Abs (x, T, incr (lev + 1) body))
| incr lev (t $ u) =
(incr lev t $ (incr lev u handle Same.SAME => u)
handle Same.SAME => t $ incr lev u)
| incr _ (Const (c, T)) = Const (c, incrT T)
| incr _ (Bound _) = raise Same.SAME;
in incr 0 end;
fun incr_indexes arg t = incr_indexes_same arg t handle Same.SAME => t;
(* Lifting functions from subgoal and increment:
lift_abs operates on terms
lift_all operates on propositions *)
fun lift_abs inc =
let
fun lift Ts (Const ("Pure.imp", _) $ _ $ B) t = lift Ts B t
| lift Ts (Const ("Pure.all", _) $ Abs (a, T, B)) t = Abs (a, T, lift (T :: Ts) B t)
| lift Ts _ t = incr_indexes ([], rev Ts, inc) t;
in lift [] end;
fun lift_all inc =
let
fun lift Ts ((c as Const ("Pure.imp", _)) $ A $ B) t = c $ A $ lift Ts B t
| lift Ts ((c as Const ("Pure.all", _)) $ Abs (a, T, B)) t = c $ Abs (a, T, lift (T :: Ts) B t)
| lift Ts _ t = incr_indexes ([], rev Ts, inc) t;
in lift [] end;
(*Strips assumptions in goal, yielding list of hypotheses. *)
fun strip_assums_hyp B =
let
fun strip Hs (Const ("Pure.imp", _) $ H $ B) = strip (H :: Hs) B
| strip Hs (Const ("Pure.all", _) $ Abs (a, T, t)) =
strip (map (incr_boundvars 1) Hs) t
| strip Hs B = rev Hs
in strip [] B end;
(*Strips assumptions in goal, yielding conclusion. *)
fun strip_assums_concl (Const("Pure.imp", _) $ H $ B) = strip_assums_concl B
| strip_assums_concl (Const("Pure.all", _) $ Abs (a, T, t)) = strip_assums_concl t
| strip_assums_concl B = B;
(*Make a list of all the parameters in a subgoal, even if nested*)
fun strip_params (Const("Pure.imp", _) $ H $ B) = strip_params B
| strip_params (Const("Pure.all", _) $ Abs (a, T, t)) = (a, T) :: strip_params t
| strip_params B = [];
(*test for nested meta connectives in prems*)
val has_meta_prems =
let
fun is_meta (Const ("Pure.eq", _) $ _ $ _) = true
| is_meta (Const ("Pure.imp", _) $ _ $ _) = true
| is_meta (Const ("Pure.all", _) $ _) = true
| is_meta _ = false;
fun ex_meta (Const ("Pure.imp", _) $ A $ B) = is_meta A orelse ex_meta B
| ex_meta (Const ("Pure.all", _) $ Abs (_, _, B)) = ex_meta B
| ex_meta _ = false;
in ex_meta end;
(*Removes the parameters from a subgoal and renumber bvars in hypotheses,
where j is the total number of parameters (precomputed)
If n>0 then deletes assumption n. *)
fun remove_params j n A =
if j=0 andalso n<=0 then A (*nothing left to do...*)
else case A of
Const("Pure.imp", _) $ H $ B =>
if n=1 then (remove_params j (n-1) B)
else implies $ (incr_boundvars j H) $ (remove_params j (n-1) B)
| Const("Pure.all",_)$Abs(a,T,t) => remove_params (j-1) n t
| _ => if n>0 then raise TERM("remove_params", [A])
else A;
(*Move all parameters to the front of the subgoal, renaming them apart;
if n>0 then deletes assumption n. *)
fun flatten_params n A =
let val params = strip_params A;
val vars = ListPair.zip (Name.variant_list [] (map #1 params),
map #2 params)
in list_all (vars, remove_params (length vars) n A) end;
(*Makes parameters in a goal have the names supplied by the list cs.*)
fun list_rename_params cs (Const ("Pure.imp", _) $ A $ B) =
implies $ A $ list_rename_params cs B
| list_rename_params (c :: cs) ((a as Const ("Pure.all", _)) $ Abs (_, T, t)) =
a $ Abs (c, T, list_rename_params cs t)
| list_rename_params cs B = B;
(*** Treatment of "assume", "erule", etc. ***)
(*Strips assumptions in goal yielding
HS = [Hn,...,H1], params = [xm,...,x1], and B,
where x1...xm are the parameters. This version (21.1.2005) REQUIRES
the the parameters to be flattened, but it allows erule to work on
assumptions of the form \<And>x. phi. Any \<And> after the outermost string
will be regarded as belonging to the conclusion, and left untouched.
Used ONLY by assum_pairs.
Unless nasms<0, it can terminate the recursion early; that allows
erule to work on assumptions of the form P\<Longrightarrow>Q.*)
fun strip_assums_imp (0, Hs, B) = (Hs, B) (*recursion terminated by nasms*)
| strip_assums_imp (nasms, Hs, Const("Pure.imp", _) $ H $ B) =
strip_assums_imp (nasms-1, H::Hs, B)
| strip_assums_imp (_, Hs, B) = (Hs, B); (*recursion terminated by B*)
(*Strips OUTER parameters only.*)
fun strip_assums_all (params, Const("Pure.all",_)$Abs(a,T,t)) =
strip_assums_all ((a,T)::params, t)
| strip_assums_all (params, B) = (params, B);
(*Produces disagreement pairs, one for each assumption proof, in order.
A is the first premise of the lifted rule, and thus has the form
H1 \<Longrightarrow> ... Hk \<Longrightarrow> B and the pairs are (H1,B),...,(Hk,B).
nasms is the number of assumptions in the original subgoal, needed when B
has the form B1 \<Longrightarrow> B2: it stops B1 from being taken as an assumption. *)
fun assum_pairs(nasms,A) =
let val (params, A') = strip_assums_all ([],A)
val (Hs,B) = strip_assums_imp (nasms,[],A')
fun abspar t = rlist_abs(params, t)
val D = abspar B
fun pairrev ([], pairs) = pairs
| pairrev (H::Hs, pairs) = pairrev(Hs, (abspar H, D) :: pairs)
in pairrev (Hs,[])
end;
fun assum_problems (nasms, A) =
let
val (params, A') = strip_assums_all ([], A)
val (Hs, B) = strip_assums_imp (nasms, [], A')
fun abspar t = rlist_abs (params, t)
in (abspar, rev Hs, B) end;
(* global schematic variables *)
fun bad_schematic xi = "Illegal schematic variable: " ^ quote (Term.string_of_vname xi);
fun bad_fixed x = "Illegal fixed variable: " ^ quote x;
fun varifyT_global_same ty = ty
|> Term_Subst.map_atypsT_same
(fn TFree (a, S) => TVar ((a, 0), S)
| TVar (ai, _) => raise TYPE (bad_schematic ai, [ty], []));
fun unvarifyT_global_same ty = ty
|> Term_Subst.map_atypsT_same
(fn TVar ((a, 0), S) => TFree (a, S)
| TVar (ai, _) => raise TYPE (bad_schematic ai, [ty], [])
| TFree (a, _) => raise TYPE (bad_fixed a, [ty], []));
val varifyT_global = Same.commit varifyT_global_same;
val unvarifyT_global = Same.commit unvarifyT_global_same;
fun varify_types_global tm = tm
|> Same.commit (Term_Subst.map_types_same varifyT_global_same)
handle TYPE (msg, _, _) => raise TERM (msg, [tm]);
fun unvarify_types_global tm = tm
|> Same.commit (Term_Subst.map_types_same unvarifyT_global_same)
handle TYPE (msg, _, _) => raise TERM (msg, [tm]);
fun varify_global tm = tm
|> Same.commit (Term_Subst.map_aterms_same
(fn Free (x, T) => Var ((x, 0), T)
| Var (xi, _) => raise TERM (bad_schematic xi, [tm])
| _ => raise Same.SAME))
|> varify_types_global;
fun unvarify_global tm = tm
|> Same.commit (Term_Subst.map_aterms_same
(fn Var ((x, 0), T) => Free (x, T)
| Var (xi, _) => raise TERM (bad_schematic xi, [tm])
| Free (x, _) => raise TERM (bad_fixed x, [tm])
| _ => raise Same.SAME))
|> unvarify_types_global;
(* goal states *)
fun get_goal st i =
nth_prem (i, st) handle TERM _ =>
error ("Subgoal number " ^ string_of_int i ^ " out of range (a total of " ^
string_of_int (count_prems st) ^ " subgoals)");
(*reverses parameters for substitution*)
fun goal_params st i =
let val gi = get_goal st i
val rfrees = map Free (Term.rename_wrt_term gi (strip_params gi))
in (gi, rfrees) end;
fun concl_of_goal st i =
let val (gi, rfrees) = goal_params st i
val B = strip_assums_concl gi
in subst_bounds (rfrees, B) end;
fun prems_of_goal st i =
let val (gi, rfrees) = goal_params st i
val As = strip_assums_hyp gi
in map (fn A => subst_bounds (rfrees, A)) As end;
end;