(* Title: TFL/post
ID: $Id$
Author: Konrad Slind, Cambridge University Computer Laboratory
Copyright 1997 University of Cambridge
Postprocessing of TFL definitions
*)
(*-------------------------------------------------------------------------
Three postprocessors are applied to the definition:
- a wellfoundedness prover (WF_TAC)
- a simplifier (tries to eliminate the language of termination expressions)
- a termination prover
*-------------------------------------------------------------------------*)
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 -> string -> term -> term list
-> theory * (thm * Prim.pattern list)
val define : theory -> string -> 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 = 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 HOLogic.dest_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) (HOLogic.mk_Trueprop(list_mk_conj L))
in goalw_cterm defs g
end;
fun tgoal thy = tgoalw thy [];
(*---------------------------------------------------------------------------
* 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_trancl];
val terminator = simp_tac(!simpset addsimps [less_Suc_eq]) 1
THEN TRY(best_tac
(!claset addSDs [not0_implies_Suc]
addss (!simpset)) 1);
val simpls = [less_eq RS eq_reflection,
lex_prod_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 = Rules.simpl_conv simpls};
val simplifier = rewrite_rule (simpls @ #simps(rep_ss (!simpset)) @
[pred_list_def]);
fun tflcongs thy = Prim.Context.read() @ (#case_congs(Thry.extract_info thy));
val concl = #2 o Rules.dest_thm;
(*---------------------------------------------------------------------------
* Defining a function with an associated termination relation.
*---------------------------------------------------------------------------*)
fun define_i thy fid 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 fid 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 fid R eqs =
let fun read thy = readtm (sign_of thy) (TVar(("DUMMY",0),[]))
val (thy',(_,pats)) =
define_i thy fid (read thy R) (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 = 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 lhs aconv 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 (filter(not o id_thm) L))
fun reducer thl = rewrite (map standard thl @ #simps(rep_ss (!simpset)))
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 = gen_union (op 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 (!simpset))));
*---------------------------------------------------------------------------*)
fun proof_stage theory reducer {f, R, rules, full_pats_TCs, TCs} =
let val dummy = prs "Proving induction theorem.. "
val ind = Prim.mk_induction theory f R full_pats_TCs
val dummy = writeln "Proved induction theorem."
val pp = std_postprocessor theory
val dummy = prs "Postprocessing.. "
val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs}
in
case nested_tcs
of [] => (writeln "Postprocessing done.";
{induction=induction, rules=rules,tcs=[]})
| L => let val dummy = prs "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 = writeln "Postprocessing done."
in
{induction = induction',
rules = rules',
tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
(simplified@stubborn)}
end
end;
(*lcp: curry the predicate of the induction rule*)
fun curry_rule rl = Prod_Syntax.split_rule_var
(head_of (HOLogic.dest_Trueprop (concl_of rl)),
rl);
(*lcp: put a theorem into Isabelle form, using meta-level connectives*)
val meta_outer =
curry_rule o standard o
rule_by_tactic (REPEAT_FIRST (resolve_tac [allI, impI, conjI]
ORELSE' etac conjE));
(*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,func,module} =>
error (mesg ^
"\n (In TFL function " ^ module ^ "." ^ func ^ ")")
| e => print_exn e;
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 = 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 => 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 => 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;