--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOLP/simp.ML Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,611 @@
+(* Title: FOLP/simp
+ ID: $Id$
+ Author: Tobias Nipkow
+ Copyright 1993 University of Cambridge
+
+FOLP version of...
+
+Generic simplifier, suitable for most logics. (from Provers)
+
+This version allows instantiation of Vars in the subgoal, since the proof
+term must change.
+*)
+
+signature SIMP_DATA =
+sig
+ val case_splits : (thm * string) list
+ val dest_red : term -> term * term * term
+ val mk_rew_rules : thm -> thm list
+ val norm_thms : (thm*thm) list (* [(?x>>norm(?x), norm(?x)>>?x), ...] *)
+ val red1 : thm (* ?P>>?Q ==> ?P ==> ?Q *)
+ val red2 : thm (* ?P>>?Q ==> ?Q ==> ?P *)
+ val refl_thms : thm list
+ val subst_thms : thm list (* [ ?a>>?b ==> ?P(?a) ==> ?P(?b), ...] *)
+ val trans_thms : thm list
+end;
+
+
+infix 4 addrews addcongs delrews delcongs setauto;
+
+signature SIMP =
+sig
+ type simpset
+ val empty_ss : simpset
+ val addcongs : simpset * thm list -> simpset
+ val addrews : simpset * thm list -> simpset
+ val delcongs : simpset * thm list -> simpset
+ val delrews : simpset * thm list -> simpset
+ val dest_ss : simpset -> thm list * thm list
+ val print_ss : simpset -> unit
+ val setauto : simpset * (int -> tactic) -> simpset
+ val ASM_SIMP_CASE_TAC : simpset -> int -> tactic
+ val ASM_SIMP_TAC : simpset -> int -> tactic
+ val CASE_TAC : simpset -> int -> tactic
+ val SIMP_CASE2_TAC : simpset -> int -> tactic
+ val SIMP_THM : simpset -> thm -> thm
+ val SIMP_TAC : simpset -> int -> tactic
+ val SIMP_CASE_TAC : simpset -> int -> tactic
+ val mk_congs : theory -> string list -> thm list
+ val mk_typed_congs : theory -> (string * string) list -> thm list
+(* temporarily disabled:
+ val extract_free_congs : unit -> thm list
+*)
+ val tracing : bool ref
+end;
+
+functor SimpFun (Simp_data: SIMP_DATA) : SIMP =
+struct
+
+local open Simp_data Logic in
+
+(*For taking apart reductions into left, right hand sides*)
+val lhs_of = #2 o dest_red;
+val rhs_of = #3 o dest_red;
+
+(*** Indexing and filtering of theorems ***)
+
+fun eq_brl ((b1,th1),(b2,th2)) = b1=b2 andalso eq_thm(th1,th2);
+
+(*insert a thm in a discrimination net by its lhs*)
+fun lhs_insert_thm (th,net) =
+ Net.insert_term((lhs_of (concl_of th), (false,th)), net, eq_brl)
+ handle Net.INSERT => net;
+
+(*match subgoal i against possible theorems in the net.
+ Similar to match_from_nat_tac, but the net does not contain numbers;
+ rewrite rules are not ordered.*)
+fun net_tac net =
+ SUBGOAL(fn (prem,i) =>
+ resolve_tac (Net.unify_term net (strip_assums_concl prem)) i);
+
+(*match subgoal i against possible theorems indexed by lhs in the net*)
+fun lhs_net_tac net =
+ SUBGOAL(fn (prem,i) =>
+ biresolve_tac (Net.unify_term net
+ (lhs_of (strip_assums_concl prem))) i);
+
+fun nth_subgoal i thm = nth_elem(i-1,prems_of thm);
+
+fun goal_concl i thm = strip_assums_concl(nth_subgoal i thm);
+
+fun lhs_of_eq i thm = lhs_of(goal_concl i thm)
+and rhs_of_eq i thm = rhs_of(goal_concl i thm);
+
+fun var_lhs(thm,i) =
+let fun var(Var _) = true
+ | var(Abs(_,_,t)) = var t
+ | var(f$_) = var f
+ | var _ = false;
+in var(lhs_of_eq i thm) end;
+
+fun contains_op opns =
+ let fun contains(Const(s,_)) = s mem opns |
+ contains(s$t) = contains s orelse contains t |
+ contains(Abs(_,_,t)) = contains t |
+ contains _ = false;
+ in contains end;
+
+fun may_match(match_ops,i) = contains_op match_ops o lhs_of_eq i;
+
+val (normI_thms,normE_thms) = split_list norm_thms;
+
+(*Get the norm constants from norm_thms*)
+val norms =
+ let fun norm thm =
+ case lhs_of(concl_of thm) of
+ Const(n,_)$_ => n
+ | _ => (prths normE_thms; error"No constant in lhs of a norm_thm")
+ in map norm normE_thms end;
+
+fun lhs_is_NORM(thm,i) = case lhs_of_eq i thm of
+ Const(s,_)$_ => s mem norms | _ => false;
+
+val refl_tac = resolve_tac refl_thms;
+
+fun find_res thms thm =
+ let fun find [] = (prths thms; error"Check Simp_Data")
+ | find(th::thms) = thm RS th handle _ => find thms
+ in find thms end;
+
+val mk_trans = find_res trans_thms;
+
+fun mk_trans2 thm =
+let fun mk[] = error"Check transitivity"
+ | mk(t::ts) = (thm RSN (2,t)) handle _ => mk ts
+in mk trans_thms end;
+
+(*Applies tactic and returns the first resulting state, FAILS if none!*)
+fun one_result(tac,thm) = case Sequence.pull(tapply(tac,thm)) of
+ Some(thm',_) => thm'
+ | None => raise THM("Simplifier: could not continue", 0, [thm]);
+
+fun res1(thm,thms,i) = one_result(resolve_tac thms i,thm);
+
+
+(**** Adding "NORM" tags ****)
+
+(*get name of the constant from conclusion of a congruence rule*)
+fun cong_const cong =
+ case head_of (lhs_of (concl_of cong)) of
+ Const(c,_) => c
+ | _ => "" (*a placeholder distinct from const names*);
+
+(*true if the term is an atomic proposition (no ==> signs) *)
+val atomic = null o strip_assums_hyp;
+
+(*ccs contains the names of the constants possessing congruence rules*)
+fun add_hidden_vars ccs =
+ let fun add_hvars(tm,hvars) = case tm of
+ Abs(_,_,body) => add_term_vars(body,hvars)
+ | _$_ => let val (f,args) = strip_comb tm
+ in case f of
+ Const(c,T) =>
+ if c mem ccs
+ then foldr add_hvars (args,hvars)
+ else add_term_vars(tm,hvars)
+ | _ => add_term_vars(tm,hvars)
+ end
+ | _ => hvars;
+ in add_hvars end;
+
+fun add_new_asm_vars new_asms =
+ let fun itf((tm,at),vars) =
+ if at then vars else add_term_vars(tm,vars)
+ fun add_list(tm,al,vars) = let val (_,tml) = strip_comb tm
+ in if length(tml)=length(al)
+ then foldr itf (tml~~al,vars)
+ else vars
+ end
+ fun add_vars (tm,vars) = case tm of
+ Abs (_,_,body) => add_vars(body,vars)
+ | r$s => (case head_of tm of
+ Const(c,T) => (case assoc(new_asms,c) of
+ None => add_vars(r,add_vars(s,vars))
+ | Some(al) => add_list(tm,al,vars))
+ | _ => add_vars(r,add_vars(s,vars)))
+ | _ => vars
+ in add_vars end;
+
+
+fun add_norms(congs,ccs,new_asms) thm =
+let val thm' = mk_trans2 thm;
+(* thm': [?z -> l; Prems; r -> ?t] ==> ?z -> ?t *)
+ val nops = nprems_of thm'
+ val lhs = rhs_of_eq 1 thm'
+ val rhs = lhs_of_eq nops thm'
+ val asms = tl(rev(tl(prems_of thm')))
+ val hvars = foldr (add_hidden_vars ccs) (lhs::rhs::asms,[])
+ val hvars = add_new_asm_vars new_asms (rhs,hvars)
+ fun it_asms (asm,hvars) =
+ if atomic asm then add_new_asm_vars new_asms (asm,hvars)
+ else add_term_frees(asm,hvars)
+ val hvars = foldr it_asms (asms,hvars)
+ val hvs = map (#1 o dest_Var) hvars
+ val refl1_tac = refl_tac 1
+ val add_norm_tac = DEPTH_FIRST (has_fewer_prems nops)
+ (STATE(fn thm =>
+ case head_of(rhs_of_eq 1 thm) of
+ Var(ixn,_) => if ixn mem hvs then refl1_tac
+ else resolve_tac normI_thms 1 ORELSE refl1_tac
+ | Const _ => resolve_tac normI_thms 1 ORELSE
+ resolve_tac congs 1 ORELSE refl1_tac
+ | Free _ => resolve_tac congs 1 ORELSE refl1_tac
+ | _ => refl1_tac))
+ val Some(thm'',_) = Sequence.pull(tapply(add_norm_tac,thm'))
+in thm'' end;
+
+fun add_norm_tags congs =
+ let val ccs = map cong_const congs
+ val new_asms = filter (exists not o #2)
+ (ccs ~~ (map (map atomic o prems_of) congs));
+ in add_norms(congs,ccs,new_asms) end;
+
+fun normed_rews congs =
+ let val add_norms = add_norm_tags congs;
+ in fn thm => map (varifyT o add_norms o mk_trans) (mk_rew_rules(freezeT thm))
+ end;
+
+fun NORM norm_lhs_tac = EVERY'[resolve_tac [red2], norm_lhs_tac, refl_tac];
+
+val trans_norms = map mk_trans normE_thms;
+
+
+(* SIMPSET *)
+
+datatype simpset =
+ SS of {auto_tac: int -> tactic,
+ congs: thm list,
+ cong_net: thm Net.net,
+ mk_simps: thm -> thm list,
+ simps: (thm * thm list) list,
+ simp_net: thm Net.net}
+
+val empty_ss = SS{auto_tac= K no_tac, congs=[], cong_net=Net.empty,
+ mk_simps=normed_rews[], simps=[], simp_net=Net.empty};
+
+(** Insertion of congruences and rewrites **)
+
+(*insert a thm in a thm net*)
+fun insert_thm_warn (th,net) =
+ Net.insert_term((concl_of th, th), net, eq_thm)
+ handle Net.INSERT =>
+ (writeln"\nDuplicate rewrite or congruence rule:"; print_thm th;
+ net);
+
+val insert_thms = foldr insert_thm_warn;
+
+fun addrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) =
+let val thms = mk_simps thm
+in SS{auto_tac=auto_tac,congs=congs, cong_net=cong_net, mk_simps=mk_simps,
+ simps = (thm,thms)::simps, simp_net = insert_thms(thms,simp_net)}
+end;
+
+val op addrews = foldl addrew;
+
+fun op addcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
+let val congs' = thms @ congs;
+in SS{auto_tac=auto_tac, congs= congs',
+ cong_net= insert_thms (map mk_trans thms,cong_net),
+ mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
+end;
+
+(** Deletion of congruences and rewrites **)
+
+(*delete a thm from a thm net*)
+fun delete_thm_warn (th,net) =
+ Net.delete_term((concl_of th, th), net, eq_thm)
+ handle Net.DELETE =>
+ (writeln"\nNo such rewrite or congruence rule:"; print_thm th;
+ net);
+
+val delete_thms = foldr delete_thm_warn;
+
+fun op delcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thms) =
+let val congs' = foldl (gen_rem eq_thm) (congs,thms)
+in SS{auto_tac=auto_tac, congs= congs',
+ cong_net= delete_thms(map mk_trans thms,cong_net),
+ mk_simps= normed_rews congs', simps=simps, simp_net=simp_net}
+end;
+
+fun delrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net}, thm) =
+let fun find((p as (th,ths))::ps',ps) =
+ if eq_thm(thm,th) then (ths,ps@ps') else find(ps',p::ps)
+ | find([],simps') = (writeln"\nNo such rewrite or congruence rule:";
+ print_thm thm;
+ ([],simps'))
+ val (thms,simps') = find(simps,[])
+in SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
+ simps = simps', simp_net = delete_thms(thms,simp_net)}
+end;
+
+val op delrews = foldl delrew;
+
+
+fun op setauto(SS{congs,cong_net,mk_simps,simps,simp_net,...}, auto_tac) =
+ SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
+ simps=simps, simp_net=simp_net};
+
+
+(** Inspection of a simpset **)
+
+fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
+
+fun print_ss(SS{congs,simps,...}) =
+ (writeln"Congruences:"; prths congs;
+ writeln"Rewrite Rules:"; prths (map #1 simps); ());
+
+
+(* Rewriting with conditionals *)
+
+val (case_thms,case_consts) = split_list case_splits;
+val case_rews = map mk_trans case_thms;
+
+fun if_rewritable ifc i thm =
+ let val tm = goal_concl i thm
+ fun nobound(Abs(_,_,tm),j,k) = nobound(tm,j,k+1)
+ | nobound(s$t,j,k) = nobound(s,j,k) andalso nobound(t,j,k)
+ | nobound(Bound n,j,k) = n < k orelse k+j <= n
+ | nobound(_) = true;
+ fun check_args(al,j) = forall (fn t => nobound(t,j,0)) al
+ fun find_if(Abs(_,_,tm),j) = find_if(tm,j+1)
+ | find_if(tm as s$t,j) = let val (f,al) = strip_comb tm in
+ case f of Const(c,_) => if c=ifc then check_args(al,j)
+ else find_if(s,j) orelse find_if(t,j)
+ | _ => find_if(s,j) orelse find_if(t,j) end
+ | find_if(_) = false;
+ in find_if(tm,0) end;
+
+fun IF1_TAC cong_tac i =
+ let fun seq_try (ifth::ifths,ifc::ifcs) thm = tapply(
+ COND (if_rewritable ifc i) (DETERM(resolve_tac[ifth]i))
+ (Tactic(seq_try(ifths,ifcs))), thm)
+ | seq_try([],_) thm = tapply(no_tac,thm)
+ and try_rew thm = tapply(Tactic(seq_try(case_rews,case_consts))
+ ORELSE Tactic one_subt, thm)
+ and one_subt thm =
+ let val test = has_fewer_prems (nprems_of thm + 1)
+ fun loop thm = tapply(COND test no_tac
+ ((Tactic try_rew THEN DEPTH_FIRST test (refl_tac i))
+ ORELSE (refl_tac i THEN Tactic loop)), thm)
+ in tapply(cong_tac THEN Tactic loop, thm) end
+ in COND (may_match(case_consts,i)) (Tactic try_rew) no_tac end;
+
+fun CASE_TAC (SS{cong_net,...}) i =
+let val cong_tac = net_tac cong_net i
+in NORM (IF1_TAC cong_tac) i end;
+
+(* Rewriting Automaton *)
+
+datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
+ | PROVE | POP_CS | POP_ARTR | IF;
+(*
+fun pr_cntrl c = case c of STOP => prs("STOP") | MK_EQ => prs("MK_EQ") |
+ASMS i => print_int i | POP_ARTR => prs("POP_ARTR") |
+SIMP_LHS => prs("SIMP_LHS") | REW => prs("REW") | REFL => prs("REFL") |
+TRUE => prs("TRUE") | PROVE => prs("PROVE") | POP_CS => prs("POP_CS") | IF
+=> prs("IF");
+*)
+fun simp_refl([],_,ss) = ss
+ | simp_refl(a'::ns,a,ss) = if a'=a then simp_refl(ns,a,SIMP_LHS::REFL::ss)
+ else simp_refl(ns,a,ASMS(a)::SIMP_LHS::REFL::POP_ARTR::ss);
+
+(** Tracing **)
+
+val tracing = ref false;
+
+(*Replace parameters by Free variables in P*)
+fun variants_abs ([],P) = P
+ | variants_abs ((a,T)::aTs, P) =
+ variants_abs (aTs, #2 (variant_abs(a,T,P)));
+
+(*Select subgoal i from proof state; substitute parameters, for printing*)
+fun prepare_goal i st =
+ let val subgi = nth_subgoal i st
+ val params = rev(strip_params subgi)
+ in variants_abs (params, strip_assums_concl subgi) end;
+
+(*print lhs of conclusion of subgoal i*)
+fun pr_goal_lhs i st =
+ writeln (Sign.string_of_term (#sign(rep_thm st))
+ (lhs_of (prepare_goal i st)));
+
+(*print conclusion of subgoal i*)
+fun pr_goal_concl i st =
+ writeln (Sign.string_of_term (#sign(rep_thm st)) (prepare_goal i st))
+
+(*print subgoals i to j (inclusive)*)
+fun pr_goals (i,j) st =
+ if i>j then ()
+ else (pr_goal_concl i st; pr_goals (i+1,j) st);
+
+(*Print rewrite for tracing; i=subgoal#, n=number of new subgoals,
+ thm=old state, thm'=new state *)
+fun pr_rew (i,n,thm,thm',not_asms) =
+ if !tracing
+ then (if not_asms then () else writeln"Assumption used in";
+ pr_goal_lhs i thm; writeln"->"; pr_goal_lhs (i+n) thm';
+ if n>0 then (writeln"Conditions:"; pr_goals (i, i+n-1) thm')
+ else ();
+ writeln"" )
+ else ();
+
+(* Skip the first n hyps of a goal, and return the rest in generalized form *)
+fun strip_varify(Const("==>", _) $ H $ B, n, vs) =
+ if n=0 then subst_bounds(vs,H)::strip_varify(B,0,vs)
+ else strip_varify(B,n-1,vs)
+ | strip_varify(Const("all",_)$Abs(_,T,t), n, vs) =
+ strip_varify(t,n,Var(("?",length vs),T)::vs)
+ | strip_varify _ = [];
+
+fun execute(ss,if_fl,auto_tac,cong_tac,net,i,thm) = let
+
+fun simp_lhs(thm,ss,anet,ats,cs) =
+ if var_lhs(thm,i) then (ss,thm,anet,ats,cs) else
+ if lhs_is_NORM(thm,i) then (ss, res1(thm,trans_norms,i), anet,ats,cs)
+ else case Sequence.pull(tapply(cong_tac i,thm)) of
+ Some(thm',_) =>
+ let val ps = prems_of thm and ps' = prems_of thm';
+ val n = length(ps')-length(ps);
+ val a = length(strip_assums_hyp(nth_elem(i-1,ps)))
+ val l = map (fn p => length(strip_assums_hyp(p)))
+ (take(n,drop(i-1,ps')));
+ in (simp_refl(rev(l),a,REW::ss),thm',anet,ats,cs) end
+ | None => (REW::ss,thm,anet,ats,cs);
+
+(*NB: the "Adding rewrites:" trace will look strange because assumptions
+ are represented by rules, generalized over their parameters*)
+fun add_asms(ss,thm,a,anet,ats,cs) =
+ let val As = strip_varify(nth_subgoal i thm, a, []);
+ val thms = map (trivial o Sign.cterm_of(#sign(rep_thm(thm))))As;
+ val new_rws = flat(map mk_rew_rules thms);
+ val rwrls = map mk_trans (flat(map mk_rew_rules thms));
+ val anet' = foldr lhs_insert_thm (rwrls,anet)
+ in if !tracing andalso not(null new_rws)
+ then (writeln"Adding rewrites:"; prths new_rws; ())
+ else ();
+ (ss,thm,anet',anet::ats,cs)
+ end;
+
+fun rew(seq,thm,ss,anet,ats,cs, more) = case Sequence.pull seq of
+ Some(thm',seq') =>
+ let val n = (nprems_of thm') - (nprems_of thm)
+ in pr_rew(i,n,thm,thm',more);
+ if n=0 then (SIMP_LHS::ss, thm', anet, ats, cs)
+ else ((replicate n PROVE) @ (POP_CS::SIMP_LHS::ss),
+ thm', anet, ats, (ss,thm,anet,ats,seq',more)::cs)
+ end
+ | None => if more
+ then rew(tapply(lhs_net_tac anet i THEN assume_tac i,thm),
+ thm,ss,anet,ats,cs,false)
+ else (ss,thm,anet,ats,cs);
+
+fun try_true(thm,ss,anet,ats,cs) =
+ case Sequence.pull(tapply(auto_tac i,thm)) of
+ Some(thm',_) => (ss,thm',anet,ats,cs)
+ | None => let val (ss0,thm0,anet0,ats0,seq,more)::cs0 = cs
+ in if !tracing
+ then (writeln"*** Failed to prove precondition. Normal form:";
+ pr_goal_concl i thm; writeln"")
+ else ();
+ rew(seq,thm0,ss0,anet0,ats0,cs0,more)
+ end;
+
+fun if_exp(thm,ss,anet,ats,cs) =
+ case Sequence.pull(tapply(IF1_TAC (cong_tac i) i,thm)) of
+ Some(thm',_) => (SIMP_LHS::IF::ss,thm',anet,ats,cs)
+ | None => (ss,thm,anet,ats,cs);
+
+fun step(s::ss, thm, anet, ats, cs) = case s of
+ MK_EQ => (ss, res1(thm,[red2],i), anet, ats, cs)
+ | ASMS(a) => add_asms(ss,thm,a,anet,ats,cs)
+ | SIMP_LHS => simp_lhs(thm,ss,anet,ats,cs)
+ | REW => rew(tapply(net_tac net i,thm),thm,ss,anet,ats,cs,true)
+ | REFL => (ss, res1(thm,refl_thms,i), anet, ats, cs)
+ | TRUE => try_true(res1(thm,refl_thms,i),ss,anet,ats,cs)
+ | PROVE => (if if_fl then MK_EQ::SIMP_LHS::IF::TRUE::ss
+ else MK_EQ::SIMP_LHS::TRUE::ss, thm, anet, ats, cs)
+ | POP_ARTR => (ss,thm,hd ats,tl ats,cs)
+ | POP_CS => (ss,thm,anet,ats,tl cs)
+ | IF => if_exp(thm,ss,anet,ats,cs);
+
+fun exec(state as (s::ss, thm, _, _, _)) =
+ if s=STOP then thm else exec(step(state));
+
+in exec(ss, thm, Net.empty, [], []) end;
+
+
+fun EXEC_TAC(ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
+let val cong_tac = net_tac cong_net
+in fn i => Tactic(fn thm =>
+ if i <= 0 orelse nprems_of thm < i then Sequence.null
+ else Sequence.single(execute(ss,fl,auto_tac,cong_tac,simp_net,i,thm)))
+ THEN TRY(auto_tac i)
+end;
+
+val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,REFL,STOP],false);
+val SIMP_CASE_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
+
+val ASM_SIMP_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,REFL,STOP],false);
+val ASM_SIMP_CASE_TAC = EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,IF,REFL,STOP],false);
+
+val SIMP_CASE2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,IF,REFL,STOP],true);
+
+fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,...}) =
+let val cong_tac = net_tac cong_net
+in fn thm => let val state = thm RSN (2,red1)
+ in execute(ss,fl,auto_tac,cong_tac,simp_net,1,state) end
+end;
+
+val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,IF,REFL,STOP],false);
+
+
+(* Compute Congruence rules for individual constants using the substition
+ rules *)
+
+val subst_thms = map standard subst_thms;
+
+
+fun exp_app(0,t) = t
+ | exp_app(i,t) = exp_app(i-1,t $ Bound (i-1));
+
+fun exp_abs(Type("fun",[T1,T2]),t,i) =
+ Abs("x"^string_of_int i,T1,exp_abs(T2,t,i+1))
+ | exp_abs(T,t,i) = exp_app(i,t);
+
+fun eta_Var(ixn,T) = exp_abs(T,Var(ixn,T),0);
+
+
+fun Pinst(f,fT,(eq,eqT),k,i,T,yik,Ts) =
+let fun xn_list(x,n) =
+ let val ixs = map (fn i => (x^(radixstring(26,"a",i)),0)) (0 upto n);
+ in map eta_Var (ixs ~~ (take(n+1,Ts))) end
+ val lhs = list_comb(f,xn_list("X",k-1))
+ val rhs = list_comb(f,xn_list("X",i-1) @ [Bound 0] @ yik)
+in Abs("", T, Const(eq,[fT,fT]--->eqT) $ lhs $ rhs) end;
+
+fun find_subst tsig T =
+let fun find (thm::thms) =
+ let val (Const(_,cT), va, vb) = dest_red(hd(prems_of thm));
+ val [P] = add_term_vars(concl_of thm,[]) \\ [va,vb]
+ val eqT::_ = binder_types cT
+ in if Type.typ_instance(tsig,T,eqT) then Some(thm,va,vb,P)
+ else find thms
+ end
+ | find [] = None
+in find subst_thms end;
+
+fun mk_cong sg (f,aTs,rT) (refl,eq) =
+let val tsig = #tsig(Sign.rep_sg sg);
+ val k = length aTs;
+ fun ri((subst,va as Var(_,Ta),vb as Var(_,Tb),P),i,si,T,yik) =
+ let val ca = Sign.cterm_of sg va
+ and cx = Sign.cterm_of sg (eta_Var(("X"^si,0),T))
+ val cb = Sign.cterm_of sg vb
+ and cy = Sign.cterm_of sg (eta_Var(("Y"^si,0),T))
+ val cP = Sign.cterm_of sg P
+ and cp = Sign.cterm_of sg (Pinst(f,rT,eq,k,i,T,yik,aTs))
+ in cterm_instantiate [(ca,cx),(cb,cy),(cP,cp)] subst end;
+ fun mk(c,T::Ts,i,yik) =
+ let val si = radixstring(26,"a",i)
+ in case find_subst tsig T of
+ None => mk(c,Ts,i-1,eta_Var(("X"^si,0),T)::yik)
+ | Some s => let val c' = c RSN (2,ri(s,i,si,T,yik))
+ in mk(c',Ts,i-1,eta_Var(("Y"^si,0),T)::yik) end
+ end
+ | mk(c,[],_,_) = c;
+in mk(refl,rev aTs,k-1,[]) end;
+
+fun mk_cong_type sg (f,T) =
+let val (aTs,rT) = strip_type T;
+ val tsig = #tsig(Sign.rep_sg sg);
+ fun find_refl(r::rs) =
+ let val (Const(eq,eqT),_,_) = dest_red(concl_of r)
+ in if Type.typ_instance(tsig, rT, hd(binder_types eqT))
+ then Some(r,(eq,body_type eqT)) else find_refl rs
+ end
+ | find_refl([]) = None;
+in case find_refl refl_thms of
+ None => [] | Some(refl) => [mk_cong sg (f,aTs,rT) refl]
+end;
+
+fun mk_cong_thy thy f =
+let val sg = sign_of thy;
+ val T = case Sign.Symtab.lookup(#const_tab(Sign.rep_sg sg),f) of
+ None => error(f^" not declared") | Some(T) => T;
+ val T' = incr_tvar 9 T;
+in mk_cong_type sg (Const(f,T'),T') end;
+
+fun mk_congs thy = flat o map (mk_cong_thy thy);
+
+fun mk_typed_congs thy =
+let val sg = sign_of thy;
+ val S0 = Type.defaultS(#tsig(Sign.rep_sg sg))
+ fun readfT(f,s) =
+ let val T = incr_tvar 9 (Sign.read_typ(sg,K(Some(S0))) s);
+ val t = case Sign.Symtab.lookup(#const_tab(Sign.rep_sg sg),f) of
+ Some(_) => Const(f,T) | None => Free(f,T)
+ in (t,T) end
+in flat o map (mk_cong_type sg o readfT) end;
+
+end (* local *)
+end (* SIMP *);