(* Title: Provers/simp
Author: Tobias Nipkow
Copyright 1993 University of Cambridge
Generic simplifier, suitable for most logics. The only known exception is
Constructive Type Theory. The reflexivity axiom must be unconditional,
namely a=a not a:A ==> a=a:A. Used typedsimp.ML otherwise.
*)
signature SIMP_DATA =
sig
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 addsplits 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 addsplits : 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 * (thm list -> int -> tactic) -> simpset
val ASM_SIMP_TAC : simpset -> int -> tactic
val SPLIT_TAC : simpset -> int -> tactic
val SIMP_SPLIT2_TAC : simpset -> int -> tactic
val SIMP_THM : simpset -> thm -> thm
val SIMP_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) =>
match_tac (Net.match_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) =>
bimatch_tac (Net.match_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 Seq.pull(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
fun norm_step_tac st = st |>
(case head_of(rhs_of_eq 1 st) 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 add_norm_tac = DEPTH_FIRST (has_fewer_prems nops) norm_step_tac
val Some(thm'',_) = Seq.pull(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: thm list -> 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,
splits: thm list,
split_consts: string list}
val empty_ss = SS{auto_tac= K (K no_tac), congs=[], cong_net=Net.empty,
mk_simps=normed_rews[], simps=[], simp_net=Net.empty,
splits=[], split_consts=[]};
(** Insertion of congruences, rewrites and case splits **)
(*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,
splits,split_consts}, 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),
splits=splits,split_consts=split_consts}
end;
val op addrews = foldl addrew;
fun op addcongs(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net,
splits,split_consts}, 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,
splits=splits,split_consts=split_consts}
end;
fun split_err() = error("split rule not of the form ?P(c(...)) = ...");
fun split_const(_ $ t) =
(case head_of t of Const(a,_) => a | _ => split_err())
| split_const _ = split_err();
fun addsplit(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net,
splits,split_consts}, thm) =
let val a = split_const(lhs_of(concl_of thm))
in SS{auto_tac=auto_tac,congs=congs,cong_net=cong_net,
mk_simps=mk_simps,simps=simps,simp_net=simp_net,
splits=splits@[mk_trans thm],split_consts=split_consts@[a]} end;
val op addsplits = foldl addsplit;
(** 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,
splits,split_consts}, 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,
splits=splits,split_consts=split_consts}
end;
fun delrew(SS{auto_tac,congs,cong_net,mk_simps,simps,simp_net,
splits,split_consts}, 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),
splits=splits,split_consts=split_consts}
end;
val op delrews = foldl delrew;
fun op setauto(SS{congs,cong_net,mk_simps,simps,simp_net,
splits,split_consts,...}, auto_tac) =
SS{auto_tac=auto_tac, congs=congs, cong_net=cong_net, mk_simps=mk_simps,
simps=simps, simp_net=simp_net,splits=splits,split_consts=split_consts};
(** Inspection of a simpset **)
fun dest_ss(SS{congs,simps,...}) = (congs, map #1 simps);
fun print_ss(SS{congs,simps,splits,...}) =
(writeln"Congruences:"; prths congs;
writeln"Case Splits"; prths splits;
writeln"Rewrite Rules:"; prths (map #1 simps); ());
(* Rewriting with case splits *)
fun splittable a 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=a 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 split_tac (cong_tac,splits,split_consts) i =
let fun seq_try (split::splits,a::bs) thm = tapply(
COND (splittable a i) (DETERM(resolve_tac[split]i))
((seq_try(splits,bs))), thm)
| seq_try([],_) thm = no_tac thm
and try_rew thm = tapply((seq_try(splits,split_consts))
ORELSE 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
((try_rew THEN DEPTH_FIRST test (refl_tac i))
ORELSE (refl_tac i THEN loop)), thm)
in (cong_tac THEN loop) thm end
in if null splits then no_tac
else COND (may_match(split_consts,i)) try_rew no_tac
end;
fun SPLIT_TAC (SS{cong_net,splits,split_consts,...}) i =
let val cong_tac = net_tac cong_net i
in NORM (split_tac (cong_tac,splits,split_consts)) i end;
(* Rewriting Automaton *)
datatype cntrl = STOP | MK_EQ | ASMS of int | SIMP_LHS | REW | REFL | TRUE
| PROVE | POP_CS | POP_ARTR | SPLIT;
(*
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") | SPLIT
=> prs("SPLIT");
*)
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,splits,split_consts,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 Seq.pull(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 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 Seq.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 Seq.pull(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 split(thm,ss,anet,ats,cs) =
case Seq.pull(tapply(split_tac
(cong_tac i,splits,split_consts) i,thm)) of
Some(thm',_) => (SIMP_LHS::SPLIT::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(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::SPLIT::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)
| SPLIT => split(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;
(*ss = list of commands (not simpset!);
fl = even use case splits to solve conditional rewrite rules;
addhyps = add hyps to simpset*)
fun EXEC_TAC (ss,fl,addhyps) simpset = METAHYPS
(fn hyps =>
case (if addhyps then simpset addrews hyps else simpset) of
(SS{auto_tac,cong_net,simp_net,splits,split_consts,...}) =>
PRIMITIVE(execute(ss,fl,auto_tac hyps,
net_tac cong_net,splits,split_consts,
simp_net, 1))
THEN TRY(auto_tac hyps 1));
val SIMP_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,SPLIT,REFL,STOP],false,false);
val ASM_SIMP_TAC =
EXEC_TAC([ASMS(0),MK_EQ,SIMP_LHS,SPLIT,REFL,STOP],false,true);
val SIMP_SPLIT2_TAC = EXEC_TAC([MK_EQ,SIMP_LHS,SPLIT,REFL,STOP],true,false);
fun REWRITE (ss,fl) (SS{auto_tac,cong_net,simp_net,splits,split_consts,...}) =
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,splits,split_consts,simp_net,1)state
end
end;
val SIMP_THM = REWRITE ([ASMS(0),SIMP_LHS,SPLIT,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 ListPair.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] = 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 = cterm_of sg va
and cx = cterm_of sg (eta_Var(("X"^si,0),T))
val cb = cterm_of sg vb
and cy = cterm_of sg (eta_Var(("Y"^si,0),T))
val cP = cterm_of sg P
and cp = 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.const_type 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 = filter_out is_fact o 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.const_type 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;
(* This code is fishy, esp the "let val T' = ..."
fun extract_free_congs() =
let val {prop,sign,...} = rep_thm(topthm());
val frees = add_term_frees(prop,[]);
fun filter(Free(a,T as Type("fun",_))) =
let val T' = incr_tvar 9 (Type.varifyT T)
in [(Free(a,T),T)] end
| filter _ = []
in flat(map (mk_cong_type sign) (flat (map filter frees))) end;
*)
end (* local *)
end (* SIMP *);