signature TFL =
sig
structure Prim : TFL_sig
val tgoalw : theory -> thm list -> thm list -> thm list
val tgoal: theory -> thm list -> thm list
val WF_TAC : thm list -> tactic
val simplifier : thm -> thm
val std_postprocessor : theory
-> {induction:thm, rules:thm, TCs:term list list}
-> {induction:thm, rules:thm, nested_tcs:thm list}
val define_i : theory -> term -> term -> theory * (thm * Prim.pattern list)
val define : theory -> string -> string list -> theory * Prim.pattern list
val simplify_defn : theory * (string * Prim.pattern list)
-> {rules:thm list, induct:thm, tcs:term list}
(*-------------------------------------------------------------------------
val function : theory -> term -> {theory:theory, eq_ind : thm}
val lazyR_def: theory -> term -> {theory:theory, eqns : thm}
*-------------------------------------------------------------------------*)
val tflcongs : theory -> thm list
end;
structure Tfl: TFL =
struct
structure Prim = Prim
structure S = Prim.USyntax
(*---------------------------------------------------------------------------
* Extract termination goals so that they can be put it into a goalstack, or
* have a tactic directly applied to them.
*--------------------------------------------------------------------------*)
fun termination_goals rules =
map (Logic.freeze_vars o S.drop_Trueprop)
(foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));
(*---------------------------------------------------------------------------
* Finds the termination conditions in (highly massaged) definition and
* puts them into a goalstack.
*--------------------------------------------------------------------------*)
fun tgoalw thy defs rules =
let val L = termination_goals rules
open USyntax
val g = cterm_of (sign_of thy) (mk_prop(list_mk_conj L))
in goalw_cterm defs g
end;
val tgoal = Utils.C tgoalw [];
(*---------------------------------------------------------------------------
* Simple wellfoundedness prover.
*--------------------------------------------------------------------------*)
fun WF_TAC thms = REPEAT(FIRST1(map rtac thms))
val WFtac = WF_TAC[wf_measure, wf_inv_image, wf_lex_prod, wf_less_than,
wf_pred_nat, wf_pred_list, wf_trancl];
val terminator = simp_tac(!simpset addsimps [less_than_def, pred_nat_def,
pred_list_def]) 1
THEN TRY(best_tac
(!claset addSDs [not0_implies_Suc]
addIs [r_into_trancl,
trans_trancl RS transD]
addss (!simpset)) 1);
val simpls = [less_eq RS eq_reflection,
lex_prod_def, rprod_def, measure_def, inv_image_def];
(*---------------------------------------------------------------------------
* Does some standard things with the termination conditions of a definition:
* attempts to prove wellfoundedness of the given relation; simplifies the
* non-proven termination conditions; and finally attempts to prove the
* simplified termination conditions.
*--------------------------------------------------------------------------*)
val std_postprocessor = Prim.postprocess{WFtac = WFtac,
terminator = terminator,
simplifier = Prim.Rules.simpl_conv simpls};
val simplifier = rewrite_rule (simpls @ #simps(rep_ss (!simpset)) @
[less_than_def, pred_nat_def, pred_list_def]);
fun tflcongs thy = Prim.Context.read() @ (#case_congs(Thry.extract_info thy));
val concl = #2 o Prim.Rules.dest_thm;
(*---------------------------------------------------------------------------
* Defining a function with an associated termination relation.
*---------------------------------------------------------------------------*)
fun define_i thy R eqs =
let val dummy = require_thy thy "WF_Rel" "recursive function definitions";
val {functional,pats} = Prim.mk_functional thy eqs
val (thm,thry) = Prim.wfrec_definition0 thy R functional
in (thry,(thm,pats))
end;
(*lcp's version: takes strings; doesn't return "thm"
(whose signature is a draft and therefore useless) *)
fun define thy R eqs =
let fun read thy = readtm (sign_of thy) (TVar(("DUMMY",0),[]))
val (thy',(_,pats)) =
define_i thy (read thy R)
(fold_bal (app Ind_Syntax.conj) (map (read thy) eqs))
in (thy',pats) end
handle Utils.ERR {mesg,...} => error mesg;
(*---------------------------------------------------------------------------
* Postprocess a definition made by "define". This is a separate stage of
* processing from the definition stage.
*---------------------------------------------------------------------------*)
local
structure R = Prim.Rules
structure U = Utils
(* The rest of these local definitions are for the tricky nested case *)
val solved = not o U.can S.dest_eq o #2 o S.strip_forall o concl
fun id_thm th =
let val {lhs,rhs} = S.dest_eq(#2(S.strip_forall(#2 (R.dest_thm th))))
in S.aconv lhs rhs
end handle _ => false
fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
fun mk_meta_eq r = case concl_of r of
Const("==",_)$_$_ => r
| _$(Const("op =",_)$_$_) => r RS eq_reflection
| _ => r RS P_imp_P_eq_True
fun rewrite L = rewrite_rule (map mk_meta_eq (Utils.filter(not o id_thm) L))
fun reducer thl = rewrite (map standard thl @ #simps(rep_ss HOL_ss))
fun join_assums th =
let val {sign,...} = rep_thm th
val tych = cterm_of sign
val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
val cntxtl = (#1 o S.strip_imp) lhs (* cntxtl should = cntxtr *)
val cntxtr = (#1 o S.strip_imp) rhs (* but union is solider *)
val cntxt = U.union S.aconv cntxtl cntxtr
in
R.GEN_ALL
(R.DISCH_ALL
(rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
end
val gen_all = S.gen_all
in
(*---------------------------------------------------------------------------
* The "reducer" argument is
* (fn thl => rewrite (map standard thl @ #simps(rep_ss HOL_ss)));
*---------------------------------------------------------------------------*)
fun proof_stage theory reducer {f, R, rules, full_pats_TCs, TCs} =
let val dummy = output(std_out, "Proving induction theorem.. ")
val ind = Prim.mk_induction theory f R full_pats_TCs
val dummy = output(std_out, "Proved induction theorem.\n")
val pp = std_postprocessor theory
val dummy = output(std_out, "Postprocessing.. ")
val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs}
in
case nested_tcs
of [] => (output(std_out, "Postprocessing done.\n");
{induction=induction, rules=rules,tcs=[]})
| L => let val dummy = output(std_out, "Simplifying nested TCs.. ")
val (solved,simplified,stubborn) =
U.itlist (fn th => fn (So,Si,St) =>
if (id_thm th) then (So, Si, th::St) else
if (solved th) then (th::So, Si, St)
else (So, th::Si, St)) nested_tcs ([],[],[])
val simplified' = map join_assums simplified
val induction' = reducer (solved@simplified') induction
val rules' = reducer (solved@simplified') rules
val dummy = output(std_out, "Postprocessing done.\n")
in
{induction = induction',
rules = rules',
tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
(simplified@stubborn)}
end
end handle (e as Utils.ERR _) => Utils.Raise e
| e => print_exn e;
(*lcp: put a theorem into Isabelle form, using meta-level connectives*)
val meta_outer =
standard o rule_by_tactic (REPEAT_FIRST (resolve_tac [allI, impI, conjI]));
(*Strip off the outer !P*)
val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
fun simplify_defn (thy,(id,pats)) =
let val dummy = deny (id mem map ! (stamps_of_thy thy))
("Recursive definition " ^ id ^
" would clash with the theory of the same name!")
val def = freezeT(get_def thy id RS meta_eq_to_obj_eq)
val {theory,rules,TCs,full_pats_TCs,patterns} =
Prim.post_definition (thy,(def,pats))
val {lhs=f,rhs} = S.dest_eq(concl def)
val (_,[R,_]) = S.strip_comb rhs
val {induction, rules, tcs} =
proof_stage theory reducer
{f = f, R = R, rules = rules,
full_pats_TCs = full_pats_TCs,
TCs = TCs}
val rules' = map (standard o normalize_thm [RSmp]) (R.CONJUNCTS rules)
in {induct = meta_outer
(normalize_thm [RSspec,RSmp] (induction RS spec')),
rules = rules',
tcs = (termination_goals rules') @ tcs}
end
handle Utils.ERR {mesg,...} => error mesg
end;
(*---------------------------------------------------------------------------
*
* Definitions with synthesized termination relation temporarily
* deleted -- it's not clear how to integrate this facility with
* the Isabelle theory file scheme, which restricts
* inference at theory-construction time.
*
local structure R = Prim.Rules
in
fun function theory eqs =
let val dummy = prs "Making definition.. "
val {rules,R,theory,full_pats_TCs,...} = Prim.lazyR_def theory eqs
val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules))
val dummy = prs "Definition made.\n"
val dummy = prs "Proving induction theorem.. "
val induction = Prim.mk_induction theory f R full_pats_TCs
val dummy = prs "Induction theorem proved.\n"
in {theory = theory,
eq_ind = standard (induction RS (rules RS conjI))}
end
handle (e as Utils.ERR _) => Utils.Raise e
| e => print_exn e
end;
fun lazyR_def theory eqs =
let val {rules,theory, ...} = Prim.lazyR_def theory eqs
in {eqns=rules, theory=theory}
end
handle (e as Utils.ERR _) => Utils.Raise e
| e => print_exn e;
*
*
*---------------------------------------------------------------------------*)
(*---------------------------------------------------------------------------
* Install the basic context notions. Others (for nat and list and prod)
* have already been added in thry.sml
*---------------------------------------------------------------------------*)
val () = Prim.Context.write[Thms.LET_CONG, Thms.COND_CONG];
end;