--- a/TFL/tfl.sml Fri May 05 22:34:40 2000 +0200
+++ b/TFL/tfl.sml Fri May 05 22:35:51 2000 +0200
@@ -30,9 +30,9 @@
fun front_last [] = raise TFL_ERR {func="front_last", mesg="empty list"}
| front_last [x] = ([],x)
| front_last (h::t) =
- let val (pref,x) = front_last t
- in
- (h::pref,x)
+ let val (pref,x) = front_last t
+ in
+ (h::pref,x)
end;
@@ -48,28 +48,28 @@
fun congs ths = default_congs @ eq_reflect_list ths;
-val default_simps =
+val default_simps =
[less_Suc_eq RS iffD2, lex_prod_def, measure_def, inv_image_def];
(*---------------------------------------------------------------------------
- * The next function is common to pattern-match translation and
+ * The next function is common to pattern-match translation and
* proof of completeness of cases for the induction theorem.
*
* The curried function "gvvariant" returns a function to generate distinct
* variables that are guaranteed not to be in names. The names of
- * the variables go u, v, ..., z, aa, ..., az, ... The returned
+ * the variables go u, v, ..., z, aa, ..., az, ... The returned
* function contains embedded refs!
*---------------------------------------------------------------------------*)
fun gvvariant names =
let val slist = ref names
val vname = ref "u"
- fun new() =
+ fun new() =
if !vname mem_string (!slist)
then (vname := bump_string (!vname); new())
else (slist := !vname :: !slist; !vname)
- in
+ in
fn ty => Free(new(), ty)
end;
@@ -95,9 +95,9 @@
else (in_group, row::not_in_group)
end) rows ([],[])
val col_types = U.take type_of (length L, #1(hd in_group))
- in
- part{constrs = crst, rows = not_in_group,
- A = {constructor = c,
+ in
+ part{constrs = crst, rows = not_in_group,
+ A = {constructor = c,
new_formals = map gv col_types,
group = in_group}::A}
end
@@ -167,10 +167,10 @@
if (null in_group) (* Constructor not given *)
then [((prfx, #2(fresh c)), (S.ARB res_ty, (~1,false)))]
else in_group
- in
- part{constrs = crst,
- rows = not_in_group,
- A = {constructor = c',
+ in
+ part{constrs = crst,
+ rows = not_in_group,
+ A = {constructor = c',
new_formals = gvars,
group = in_group'}::A}
end
@@ -194,26 +194,26 @@
fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats)
| v_to_pats _ = raise TFL_ERR{func="mk_case", mesg="v_to_pats"};
-
+
(*----------------------------------------------------------------------------
* Translation of pattern terms into nested case expressions.
*
- * This performs the translation and also builds the full set of patterns.
- * Thus it supports the construction of induction theorems even when an
+ * This performs the translation and also builds the full set of patterns.
+ * Thus it supports the construction of induction theorems even when an
* incomplete set of patterns is given.
*---------------------------------------------------------------------------*)
fun mk_case ty_info ty_match usednames range_ty =
- let
+ let
fun mk_case_fail s = raise TFL_ERR{func = "mk_case", mesg = s}
- val fresh_var = gvvariant usednames
+ val fresh_var = gvvariant usednames
val divide = partition fresh_var ty_match
fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row"
- | expand constructors ty (row as ((prfx, p::rst), rhs)) =
- if (is_Free p)
+ | expand constructors ty (row as ((prfx, p::rst), rhs)) =
+ if (is_Free p)
then let val fresh = fresh_constr ty_match ty fresh_var
- fun expnd (c,gvs) =
+ fun expnd (c,gvs) =
let val capp = list_comb(c,gvs)
in ((prfx, capp::rst), pattern_subst[(p,capp)] rhs)
end
@@ -223,14 +223,14 @@
| mk{path=[], rows = ((prfx, []), (tm,tag))::_} = (* Done *)
([(prfx,tag,[])], tm)
| mk{path=[], rows = _::_} = mk_case_fail"blunder"
- | mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} =
- mk{path = path,
+ | mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} =
+ mk{path = path,
rows = ((prfx, [fresh_var(type_of u)]), rhs)::rst}
| mk{path = u::rstp, rows as ((_, p::_), _)::_} =
let val (pat_rectangle,rights) = ListPair.unzip rows
val col0 = map(hd o #2) pat_rectangle
- in
- if (forall is_Free col0)
+ in
+ if (forall is_Free col0)
then let val rights' = map (fn(v,e) => pattern_subst[(v,u)] e)
(ListPair.zip (col0, rights))
val pat_rectangle' = map v_to_prfx pat_rectangle
@@ -246,7 +246,7 @@
of None => mk_case_fail("Not a known datatype: "^ty_name)
| Some{case_const,constructors} =>
let
- val case_const_name = #1(dest_Const case_const)
+ val case_const_name = #1(dest_Const case_const)
val nrows = List.concat (map (expand constructors pty) rows)
val subproblems = divide(constructors, pty, range_ty, nrows)
val groups = map #group subproblems
@@ -264,14 +264,14 @@
val pat_rect1 = List.concat
(ListPair.map mk_pat (constructors', pat_rect))
in (pat_rect1,tree)
- end
+ end
end end
in mk
end;
(* Repeated variable occurrences in a pattern are not allowed. *)
-fun FV_multiset tm =
+fun FV_multiset tm =
case (S.dest_term tm)
of S.VAR{Name,Ty} => [Free(Name,Ty)]
| S.CONST _ => []
@@ -282,39 +282,39 @@
let fun check [] = true
| check (v::rst) =
if mem_term (v,rst) then
- raise TFL_ERR{func = "no_repeat_vars",
- mesg = quote(#1(dest_Free v)) ^
- " occurs repeatedly in the pattern " ^
- quote (string_of_cterm (Thry.typecheck thy pat))}
+ raise TFL_ERR{func = "no_repeat_vars",
+ mesg = quote(#1(dest_Free v)) ^
+ " occurs repeatedly in the pattern " ^
+ quote (string_of_cterm (Thry.typecheck thy pat))}
else check rst
in check (FV_multiset pat)
end;
fun dest_atom (Free p) = p
| dest_atom (Const p) = p
- | dest_atom _ = raise TFL_ERR {func="dest_atom",
- mesg="function name not an identifier"};
+ | dest_atom _ = raise TFL_ERR {func="dest_atom",
+ mesg="function name not an identifier"};
fun same_name (p,q) = #1(dest_atom p) = #1(dest_atom q);
local fun mk_functional_err s = raise TFL_ERR{func = "mk_functional", mesg=s}
- fun single [_$_] =
- mk_functional_err "recdef does not allow currying"
+ fun single [_$_] =
+ mk_functional_err "recdef does not allow currying"
| single [f] = f
- | single fs =
- (*multiple function names?*)
- if length (gen_distinct same_name fs) < length fs
+ | single fs =
+ (*multiple function names?*)
+ if length (gen_distinct same_name fs) < length fs
then mk_functional_err
- "the function being declared appears with multiple types"
- else mk_functional_err
- (Int.toString (length fs) ^
- " distinct function names being declared")
+ "The function being declared appears with multiple types"
+ else mk_functional_err
+ (Int.toString (length fs) ^
+ " distinct function names being declared")
in
fun mk_functional thy clauses =
let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses)
handle _ => raise TFL_ERR
- {func = "mk_functional",
- mesg = "recursion equations must use the = relation"}
+ {func = "mk_functional",
+ mesg = "recursion equations must use the = relation"}
val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L)
val atom = single (gen_distinct (op aconv) funcs)
val (fname,ftype) = dest_atom atom
@@ -328,10 +328,10 @@
val ty_info = Thry.match_info thy
val ty_match = Thry.match_type thy
val range_ty = type_of (hd R)
- val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty
+ val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty
{path=[a], rows=rows}
- val patts1 = map (fn (_,tag,[pat]) => (pat,tag)) patts
- handle _ => mk_functional_err "error in pattern-match translation"
+ val patts1 = map (fn (_,tag,[pat]) => (pat,tag)) patts
+ handle _ => mk_functional_err "error in pattern-match translation"
val patts2 = U.sort(fn p1=>fn p2=> row_of_pat p1 < row_of_pat p2) patts1
val finals = map row_of_pat patts2
val originals = map (row_of_pat o #2) rows
@@ -339,10 +339,10 @@
of [] => ()
| L => mk_functional_err
("The following clauses are redundant (covered by preceding clauses): " ^
- commas (map Int.toString L) ^ "\n(counting from zero)")
+ commas (map (fn i => Int.toString (i + 1)) L))
in {functional = Abs(Sign.base_name fname, ftype,
- abstract_over (atom,
- absfree(aname,atype, case_tm))),
+ abstract_over (atom,
+ absfree(aname,atype, case_tm))),
pats = patts2}
end end;
@@ -357,7 +357,7 @@
(*For Isabelle, the lhs of a definition must be a constant.*)
fun mk_const_def sign (Name, Ty, rhs) =
Sign.infer_types sign (K None) (K None) [] false
- ([Const("==",dummyT) $ Const(Name,Ty) $ rhs], propT)
+ ([Const("==",dummyT) $ Const(Name,Ty) $ rhs], propT)
|> #1;
(*Make all TVars available for instantiation by adding a ? to the front*)
@@ -365,22 +365,22 @@
| poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort)
| poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort);
-local val f_eq_wfrec_R_M =
+local val f_eq_wfrec_R_M =
#ant(S.dest_imp(#2(S.strip_forall (concl Thms.WFREC_COROLLARY))))
val {lhs=f, rhs} = S.dest_eq f_eq_wfrec_R_M
val (fname,_) = dest_Free f
val (wfrec,_) = S.strip_comb rhs
in
fun wfrec_definition0 thy fid R (functional as Abs(Name, Ty, _)) =
- let val def_name = if Name<>fid then
- raise TFL_ERR{func = "wfrec_definition0",
- mesg = "Expected a definition of " ^
- quote fid ^ " but found one of " ^
- quote Name}
- else Name ^ "_def"
- val wfrec_R_M = map_term_types poly_tvars
- (wfrec $ map_term_types poly_tvars R)
- $ functional
+ let val def_name = if Name<>fid then
+ raise TFL_ERR{func = "wfrec_definition0",
+ mesg = "Expected a definition of " ^
+ quote fid ^ " but found one of " ^
+ quote Name}
+ else Name ^ "_def"
+ val wfrec_R_M = map_term_types poly_tvars
+ (wfrec $ map_term_types poly_tvars R)
+ $ functional
val def_term = mk_const_def (Theory.sign_of thy) (Name, Ty, wfrec_R_M)
in #1 (PureThy.add_defs_i [Thm.no_attributes (def_name, def_term)] thy) end
end;
@@ -391,7 +391,7 @@
* This structure keeps track of congruence rules that aren't derived
* from a datatype definition.
*---------------------------------------------------------------------------*)
-fun extraction_thms thy =
+fun extraction_thms thy =
let val {case_rewrites,case_congs} = Thry.extract_info thy
in (case_rewrites, case_congs)
end;
@@ -400,20 +400,20 @@
(*---------------------------------------------------------------------------
* Pair patterns with termination conditions. The full list of patterns for
* a definition is merged with the TCs arising from the user-given clauses.
- * There can be fewer clauses than the full list, if the user omitted some
+ * There can be fewer clauses than the full list, if the user omitted some
* cases. This routine is used to prepare input for mk_induction.
*---------------------------------------------------------------------------*)
fun merge full_pats TCs =
let fun insert (p,TCs) =
- let fun insrt ((x as (h,[]))::rst) =
+ let fun insrt ((x as (h,[]))::rst) =
if (p aconv h) then (p,TCs)::rst else x::insrt rst
| insrt (x::rst) = x::insrt rst
| insrt[] = raise TFL_ERR{func="merge.insert",
- mesg="pattern not found"}
+ mesg="pattern not found"}
in insrt end
fun pass ([],ptcl_final) = ptcl_final
| pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl)
-in
+in
pass (TCs, map (fn p => (p,[])) full_pats)
end;
@@ -422,7 +422,7 @@
(*called only by Tfl.simplify_defn*)
fun post_definition meta_tflCongs (theory, (def, pats)) =
- let val tych = Thry.typecheck theory
+ let val tych = Thry.typecheck theory
val f = #lhs(S.dest_eq(concl def))
val corollary = R.MATCH_MP Thms.WFREC_COROLLARY def
val pats' = filter given pats
@@ -431,12 +431,12 @@
val WFR = #ant(S.dest_imp(concl corollary))
val R = #Rand(S.dest_comb WFR)
val corollary' = R.UNDISCH corollary (* put WF R on assums *)
- val corollaries = map (fn pat => R.SPEC (tych pat) corollary')
- given_pats
+ val corollaries = map (fn pat => R.SPEC (tych pat) corollary')
+ given_pats
val (case_rewrites,context_congs) = extraction_thms theory
val corollaries' = map(rewrite_rule case_rewrites) corollaries
- val extract = R.CONTEXT_REWRITE_RULE
- (f, [R], cut_apply, meta_tflCongs@context_congs)
+ val extract = R.CONTEXT_REWRITE_RULE
+ (f, [R], cut_apply, meta_tflCongs@context_congs)
val (rules, TCs) = ListPair.unzip (map extract corollaries')
val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules
val mk_cond_rule = R.FILTER_DISCH_ALL(not o curry (op aconv) WFR)
@@ -445,7 +445,7 @@
{theory = theory, (* holds def, if it's needed *)
rules = rules1,
rows = rows,
- full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)),
+ full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)),
TCs = TCs}
end;
@@ -470,93 +470,93 @@
val given_pats = givens pats
(* val f = Free(Name,Ty) *)
val Type("fun", [f_dty, f_rty]) = Ty
- val dummy = if Name<>fid then
- raise TFL_ERR{func = "wfrec_eqns",
- mesg = "Expected a definition of " ^
- quote fid ^ " but found one of " ^
- quote Name}
- else ()
+ val dummy = if Name<>fid then
+ raise TFL_ERR{func = "wfrec_eqns",
+ mesg = "Expected a definition of " ^
+ quote fid ^ " but found one of " ^
+ quote Name}
+ else ()
val (case_rewrites,context_congs) = extraction_thms thy
val tych = Thry.typecheck thy
val WFREC_THM0 = R.ISPEC (tych functional) Thms.WFREC_COROLLARY
val Const("All",_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0
val R = Free (variant (foldr add_term_names (eqns,[])) Rname,
- Rtype)
+ Rtype)
val WFREC_THM = R.ISPECL [tych R, tych g] WFREC_THM0
val ([proto_def, WFR],_) = S.strip_imp(concl WFREC_THM)
- val dummy =
- if !trace then
- writeln ("ORIGINAL PROTO_DEF: " ^
- Sign.string_of_term (Theory.sign_of thy) proto_def)
+ val dummy =
+ if !trace then
+ writeln ("ORIGINAL PROTO_DEF: " ^
+ Sign.string_of_term (Theory.sign_of thy) proto_def)
else ()
val R1 = S.rand WFR
val corollary' = R.UNDISCH(R.UNDISCH WFREC_THM)
val corollaries = map (fn pat => R.SPEC (tych pat) corollary') given_pats
val corollaries' = map (rewrite_rule case_rewrites) corollaries
- fun extract X = R.CONTEXT_REWRITE_RULE
- (f, R1::SV, cut_apply, tflCongs@context_congs) X
+ fun extract X = R.CONTEXT_REWRITE_RULE
+ (f, R1::SV, cut_apply, tflCongs@context_congs) X
in {proto_def = proto_def,
SV=SV,
- WFR=WFR,
+ WFR=WFR,
pats=pats,
extracta = map extract corollaries'}
end;
(*---------------------------------------------------------------------------
- * Define the constant after extracting the termination conditions. The
+ * Define the constant after extracting the termination conditions. The
* wellfounded relation used in the definition is computed by using the
* choice operator on the extracted conditions (plus the condition that
* such a relation must be wellfounded).
*---------------------------------------------------------------------------*)
fun lazyR_def thy fid tflCongs eqns =
- let val {proto_def,WFR,pats,extracta,SV} =
- wfrec_eqns thy fid (congs tflCongs) eqns
+ let val {proto_def,WFR,pats,extracta,SV} =
+ wfrec_eqns thy fid (congs tflCongs) eqns
val R1 = S.rand WFR
val f = #lhs(S.dest_eq proto_def)
val (extractants,TCl) = ListPair.unzip extracta
- val dummy = if !trace
- then (writeln "Extractants = ";
- prths extractants;
- ())
- else ()
+ val dummy = if !trace
+ then (writeln "Extractants = ";
+ prths extractants;
+ ())
+ else ()
val TCs = foldr (gen_union (op aconv)) (TCl, [])
val full_rqt = WFR::TCs
val R' = S.mk_select{Bvar=R1, Body=S.list_mk_conj full_rqt}
val R'abs = S.rand R'
val proto_def' = subst_free[(R1,R')] proto_def
val dummy = if !trace then writeln ("proto_def' = " ^
- Sign.string_of_term
- (Theory.sign_of thy) proto_def')
- else ()
+ Sign.string_of_term
+ (Theory.sign_of thy) proto_def')
+ else ()
val {lhs,rhs} = S.dest_eq proto_def'
val (c,args) = S.strip_comb lhs
val (Name,Ty) = dest_atom c
- val defn = mk_const_def (Theory.sign_of thy)
- (Name, Ty, S.list_mk_abs (args,rhs))
+ val defn = mk_const_def (Theory.sign_of thy)
+ (Name, Ty, S.list_mk_abs (args,rhs))
val (theory, [def0]) =
thy
- |> PureThy.add_defs_i
+ |> PureThy.add_defs_i
[Thm.no_attributes (fid ^ "_def", defn)]
val def = freezeT def0;
val dummy = if !trace then writeln ("DEF = " ^ string_of_thm def)
- else ()
+ else ()
(* val fconst = #lhs(S.dest_eq(concl def)) *)
val tych = Thry.typecheck theory
val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt
- (*lcp: a lot of object-logic inference to remove*)
+ (*lcp: a lot of object-logic inference to remove*)
val baz = R.DISCH_ALL
- (U.itlist R.DISCH full_rqt_prop
- (R.LIST_CONJ extractants))
+ (U.itlist R.DISCH full_rqt_prop
+ (R.LIST_CONJ extractants))
val dum = if !trace then writeln ("baz = " ^ string_of_thm baz)
- else ()
+ else ()
val f_free = Free (fid, fastype_of f) (*'cos f is a Const*)
val SV' = map tych SV;
val SVrefls = map reflexive SV'
val def0 = (U.rev_itlist (fn x => fn th => R.rbeta(combination th x))
- SVrefls def)
- RS meta_eq_to_obj_eq
+ SVrefls def)
+ RS meta_eq_to_obj_eq
val def' = R.MP (R.SPEC (tych R') (R.GEN (tych R1) baz)) def0
val body_th = R.LIST_CONJ (map R.ASSUME full_rqt_prop)
val bar = R.MP (R.ISPECL[tych R'abs, tych R1] Thms.SELECT_AX)
@@ -581,10 +581,10 @@
* [x_1,...,x_n] ?v_1...v_n. M[v_1,...,v_n]
* -----------------------------------------------------------
* ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]),
- * ...
+ * ...
* (x_j,?v_n. M[x_1,...,x_(n-1),v_n])] )
*
- * This function is totally ad hoc. Used in the production of the induction
+ * This function is totally ad hoc. Used in the production of the induction
* theorem. The nchotomy theorem can have clauses that look like
*
* ?v1..vn. z = C vn..v1
@@ -600,7 +600,7 @@
val vlist = #2(S.strip_comb (S.rhs body))
val plist = ListPair.zip (vlist, xlist)
val args = map (fn qv => the (gen_assoc (op aconv) (plist, qv))) qvars
- handle OPTION => error
+ handle OPTION => error
"TFL fault [alpha_ex_unroll]: no correspondence"
fun build ex [] = []
| build (_$rex) (v::rst) =
@@ -608,7 +608,7 @@
in ex1 :: build ex1 rst
end
val (nex::exl) = rev (tm::build tm args)
- in
+ in
(nex, ListPair.zip (args, rev exl))
end;
@@ -621,19 +621,19 @@
*---------------------------------------------------------------------------*)
fun mk_case ty_info usednames thy =
- let
+ let
val divide = ipartition (gvvariant usednames)
val tych = Thry.typecheck thy
fun tych_binding(x,y) = (tych x, tych y)
fun fail s = raise TFL_ERR{func = "mk_case", mesg = s}
fun mk{rows=[],...} = fail"no rows"
- | mk{path=[], rows = [([], (thm, bindings))]} =
+ | mk{path=[], rows = [([], (thm, bindings))]} =
R.IT_EXISTS (map tych_binding bindings) thm
| mk{path = u::rstp, rows as (p::_, _)::_} =
let val (pat_rectangle,rights) = ListPair.unzip rows
val col0 = map hd pat_rectangle
val pat_rectangle' = map tl pat_rectangle
- in
+ in
if (forall is_Free col0) (* column 0 is all variables *)
then let val rights' = map (fn ((thm,theta),v) => (thm,theta@[(u,v)]))
(ListPair.zip (rights, col0))
@@ -655,17 +655,17 @@
val constraints = map #1 existentials
val vexl = map #2 existentials
fun expnd tm (pats,(th,b)) = (pats,(R.SUBS[R.ASSUME(tych tm)]th,b))
- val news = map (fn (nf,rows,c) => {path = nf@rstp,
+ val news = map (fn (nf,rows,c) => {path = nf@rstp,
rows = map (expnd c) rows})
(U.zip3 new_formals groups constraints)
val recursive_thms = map mk news
val build_exists = foldr
- (fn((x,t), th) =>
+ (fn((x,t), th) =>
R.CHOOSE (tych x, R.ASSUME (tych t)) th)
val thms' = ListPair.map build_exists (vexl, recursive_thms)
val same_concls = R.EVEN_ORS thms'
in R.DISJ_CASESL thm' same_concls
- end
+ end
end end
in mk
end;
@@ -687,11 +687,11 @@
val th0 = R.ASSUME (tych a_eq_v)
val rows = map (fn x => ([x], (th0,[]))) pats
in
- R.GEN (tych a)
+ R.GEN (tych a)
(R.RIGHT_ASSOC
(R.CHOOSE(tych v, ex_th0)
(mk_case ty_info (vname::aname::names)
- thy {path=[v], rows=rows})))
+ thy {path=[v], rows=rows})))
end end;
@@ -708,16 +708,16 @@
local infix 5 ==>
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2}
in
-fun build_ih f P (pat,TCs) =
+fun build_ih f P (pat,TCs) =
let val globals = S.free_vars_lr pat
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm)
- fun dest_TC tm =
+ fun dest_TC tm =
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm))
val (R,y,_) = S.dest_relation R_y_pat
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y
- in case cntxt
+ in case cntxt
of [] => (P_y, (tm,[]))
- | _ => let
+ | _ => let
val imp = S.list_mk_conj cntxt ==> P_y
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals)
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle _ => lvs
@@ -736,17 +736,17 @@
local infix 5 ==>
fun (tm1 ==> tm2) = S.mk_imp{ant = tm1, conseq = tm2}
in
-fun build_ih f (P,SV) (pat,TCs) =
+fun build_ih f (P,SV) (pat,TCs) =
let val pat_vars = S.free_vars_lr pat
val globals = pat_vars@SV
fun nested tm = is_some (S.find_term (curry (op aconv) f) tm)
- fun dest_TC tm =
+ fun dest_TC tm =
let val (cntxt,R_y_pat) = S.strip_imp(#2(S.strip_forall tm))
val (R,y,_) = S.dest_relation R_y_pat
val P_y = if (nested tm) then R_y_pat ==> P$y else P$y
- in case cntxt
+ in case cntxt
of [] => (P_y, (tm,[]))
- | _ => let
+ | _ => let
val imp = S.list_mk_conj cntxt ==> P_y
val lvs = gen_rems (op aconv) (S.free_vars_lr imp, globals)
val locals = #2(U.pluck (curry (op aconv) P) lvs) handle _ => lvs
@@ -762,9 +762,9 @@
end;
(*---------------------------------------------------------------------------
- * This function makes good on the promise made in "build_ih".
+ * This function makes good on the promise made in "build_ih".
*
- * Input is tm = "(!y. R y pat ==> P y) ==> P pat",
+ * Input is tm = "(!y. R y pat ==> P y) ==> P pat",
* TCs = TC_1[pat] ... TC_n[pat]
* thm = ih1 /\ ... /\ ih_n |- ih[pat]
*---------------------------------------------------------------------------*)
@@ -776,17 +776,17 @@
fun get_cntxt TC = tych(#ant(S.dest_imp(#2(S.strip_forall(concl TC)))))
fun mk_ih ((TC,locals),th2,nested) =
R.GENL (map tych locals)
- (if nested
+ (if nested
then R.DISCH (get_cntxt TC) th2 handle _ => th2
- else if S.is_imp(concl TC)
- then R.IMP_TRANS TC th2
+ else if S.is_imp(concl TC)
+ then R.IMP_TRANS TC th2
else R.MP th2 TC)
- in
+ in
R.DISCH antc
(if S.is_imp(concl thm') (* recursive calls in this clause *)
then let val th1 = R.ASSUME antc
val TCs = map #1 TCs_locals
- val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o
+ val ylist = map (#2 o S.dest_relation o #2 o S.strip_imp o
#2 o S.strip_forall) TCs
val TClist = map (fn(TC,lvs) => (R.SPEC_ALL(R.ASSUME(tych TC)),lvs))
TCs_locals
@@ -806,8 +806,8 @@
* ?v1 ... vn. x = (v1,...,vn) |- M[x]
*
*---------------------------------------------------------------------------*)
-fun LEFT_ABS_VSTRUCT tych thm =
- let fun CHOOSER v (tm,thm) =
+fun LEFT_ABS_VSTRUCT tych thm =
+ let fun CHOOSER v (tm,thm) =
let val ex_tm = S.mk_exists{Bvar=v,Body=tm}
in (ex_tm, R.CHOOSE(tych v, R.ASSUME (tych ex_tm)) thm)
end
@@ -821,7 +821,7 @@
* Input : f, R, and [(pat1,TCs1),..., (patn,TCsn)]
*
* Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove
- * recursion induction (Rinduct) by proving the antecedent of Sinduct from
+ * recursion induction (Rinduct) by proving the antecedent of Sinduct from
* the antecedent of Rinduct.
*---------------------------------------------------------------------------*)
fun mk_induction thy {fconst, R, SV, pat_TCs_list} =
@@ -830,8 +830,8 @@
val (pats,TCsl) = ListPair.unzip pat_TCs_list
val case_thm = complete_cases thy pats
val domain = (type_of o hd) pats
- val Pname = Term.variant (foldr (foldr add_term_names)
- (pats::TCsl, [])) "P"
+ val Pname = Term.variant (foldr (foldr add_term_names)
+ (pats::TCsl, [])) "P"
val P = Free(Pname, domain --> HOLogic.boolT)
val Sinduct = R.SPEC (tych P) Sinduction
val Sinduct_assumf = S.rand ((#ant o S.dest_imp o concl) Sinduct)
@@ -842,11 +842,11 @@
val tasks = U.zip3 cases TCl' (R.CONJUNCTS Rinduct_assum)
val proved_cases = map (prove_case fconst thy) tasks
val v = Free (variant (foldr add_term_names (map concl proved_cases, []))
- "v",
- domain)
+ "v",
+ domain)
val vtyped = tych v
val substs = map (R.SYM o R.ASSUME o tych o (curry HOLogic.mk_eq v)) pats
- val proved_cases1 = ListPair.map (fn (th,th') => R.SUBS[th]th')
+ val proved_cases1 = ListPair.map (fn (th,th') => R.SUBS[th]th')
(substs, proved_cases)
val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1
val dant = R.GEN vtyped (R.DISJ_CASESL (R.ISPEC vtyped case_thm) abs_cases)
@@ -855,7 +855,7 @@
val vars = map (gvvariant[Pname]) (S.strip_prod_type Parg_ty)
val dc' = U.itlist (R.GEN o tych) vars
(R.SPEC (tych(S.mk_vstruct Parg_ty vars)) dc)
-in
+in
R.GEN (tych P) (R.DISCH (tych(concl Rinduct_assum)) dc')
end
handle _ => raise TFL_ERR{func = "mk_induction", mesg = "failed derivation"};
@@ -864,23 +864,23 @@
(*---------------------------------------------------------------------------
- *
+ *
* POST PROCESSING
*
*---------------------------------------------------------------------------*)
-fun simplify_induction thy hth ind =
+fun simplify_induction thy hth ind =
let val tych = Thry.typecheck thy
val (asl,_) = R.dest_thm ind
val (_,tc_eq_tc') = R.dest_thm hth
val tc = S.lhs tc_eq_tc'
fun loop [] = ind
- | loop (asm::rst) =
+ | loop (asm::rst) =
if (U.can (Thry.match_term thy asm) tc)
then R.UNDISCH
(R.MATCH_MP
- (R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind))
+ (R.MATCH_MP Thms.simp_thm (R.DISCH (tych asm) ind))
hth)
else loop rst
in loop asl
@@ -888,10 +888,10 @@
(*---------------------------------------------------------------------------
- * The termination condition is an antecedent to the rule, and an
+ * The termination condition is an antecedent to the rule, and an
* assumption to the theorem.
*---------------------------------------------------------------------------*)
-fun elim_tc tcthm (rule,induction) =
+fun elim_tc tcthm (rule,induction) =
(R.MP rule tcthm, R.PROVE_HYP tcthm induction)
@@ -901,10 +901,10 @@
(*---------------------------------------------------------------------
* Attempt to eliminate WF condition. It's the only assumption of rules
*---------------------------------------------------------------------*)
- val (rules1,induction1) =
- let val thm = R.prove(tych(HOLogic.mk_Trueprop
- (hd(#1(R.dest_thm rules)))),
- WFtac)
+ val (rules1,induction1) =
+ let val thm = R.prove(tych(HOLogic.mk_Trueprop
+ (hd(#1(R.dest_thm rules)))),
+ WFtac)
in (R.PROVE_HYP thm rules, R.PROVE_HYP thm induction)
end handle _ => (rules,induction)
@@ -917,11 +917,11 @@
* 3. replace tc by tc' in both the rules and the induction theorem.
*---------------------------------------------------------------------*)
- fun print_thms s L =
+ fun print_thms s L =
if !trace then writeln (cat_lines (s :: map string_of_thm L))
else ();
- fun print_cterms s L =
+ fun print_cterms s L =
if !trace then writeln (cat_lines (s :: map string_of_cterm L))
else ();;
@@ -930,25 +930,25 @@
val _ = print_cterms "TC before simplification: " [tc1]
val tc_eq = simplifier tc1
val _ = print_thms "result: " [tc_eq]
- in
+ in
elim_tc (R.MATCH_MP Thms.eqT tc_eq) (r,ind)
- handle _ =>
+ handle _ =>
(elim_tc (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq)
- (R.prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))),
- terminator)))
+ (R.prove(tych(HOLogic.mk_Trueprop(S.rhs(concl tc_eq))),
+ terminator)))
(r,ind)
- handle _ =>
- (R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq),
+ handle _ =>
+ (R.UNDISCH(R.MATCH_MP (R.MATCH_MP Thms.simp_thm r) tc_eq),
simplify_induction theory tc_eq ind))
end
(*----------------------------------------------------------------------
* Nested termination conditions are harder to get at, since they are
- * left embedded in the body of the function (and in induction
- * theorem hypotheses). Our "solution" is to simplify them, and try to
- * prove termination, but leave the application of the resulting theorem
- * to a higher level. So things go much as in "simplify_tc": the
- * termination condition (tc) is simplified to |- tc = tc' (there might
+ * left embedded in the body of the function (and in induction
+ * theorem hypotheses). Our "solution" is to simplify them, and try to
+ * prove termination, but leave the application of the resulting theorem
+ * to a higher level. So things go much as in "simplify_tc": the
+ * termination condition (tc) is simplified to |- tc = tc' (there might
* not be a change) and then 2 attempts are made:
*
* 1. if |- tc = T, then return |- tc; otherwise,
@@ -963,12 +963,12 @@
handle _
=> (R.MATCH_MP(R.MATCH_MP Thms.rev_eq_mp tc_eq)
(R.prove(tych(HOLogic.mk_Trueprop (S.rhs(concl tc_eq))),
- terminator))
+ terminator))
handle _ => tc_eq))
end
(*-------------------------------------------------------------------
- * Attempt to simplify the termination conditions in each rule and
+ * Attempt to simplify the termination conditions in each rule and
* in the induction theorem.
*-------------------------------------------------------------------*)
fun strip_imp tm = if S.is_neg tm then ([],tm) else S.strip_imp tm