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%----------------------------------------------------------------------------%
% Datatype for a full representation of a theorem %
% The first string is for the theory name. The second is for the theorem %
% name. %
lettype foundthm = thmkind # string # string # thm;;
% Datatype for representing theorem patterns %
% The first seven constructors generate representations for theorem patterns. %
% The rest combine or modify such representations. %
rectype thmpattern_rep = Kind' of thmkind
| Thryname' of namepattern
| Thmname' of namepattern
| Conc' of termpattern
| HypP' of termpattern list
| HypF' of termpattern list
| Side' of side_condition
| Andalso' of thmpattern_rep # thmpattern_rep
| Orelse' of thmpattern_rep # thmpattern_rep
| Not' of thmpattern_rep
| Where' of thmpattern_rep # thmpattern_rep;;
% Abstract datatype for theorem patterns %
% There are two types of theorem pattern clause. %
% There are main clauses, in which tests are performed on a foundthm. All of %
% the constructors are allowed in this type of clause, though in principle, %
% side-condition tests should not be. Side-condition tests within main %
% clauses are re-interpreted as follows: %
% %
% Side <side-condition> %
% %
% is interpreted as %
% %
% (Conc (autotermpattern "conc:bool")) Where (Side <side-condition>) %
% %
% This only makes sense if <side-condition> tests "conc". %
% Only `Side', `Andalso', `Orelse', and `Not' constructors are permitted %
% within a side-condition clause. %
% `Where' is used to link these two types of clause. Its first argument is a %
% main clause. Its second argument is a side-condition clause. Note that %
% `Where' cannot occur within a side-condition clause. %
% All of these constraints are imposed by the abstract datatype, which uses %
% the type `thmpattern_rep' as its representing type. %
abstype thmpattern = thmpattern_rep
with show_thmpattern thmp = rep_thmpattern thmp
% : (thmpattern -> thmpattern_rep) %
and Kind knd = abs_thmpattern (Kind' knd)
% : (thmkind -> thmpattern) %
and Thryname nmp = abs_thmpattern (Thryname' nmp)
% : (namepattern -> thmpattern) %
and Thmname nmp = abs_thmpattern (Thmname' nmp)
% : (namepattern -> thmpattern) %
and Conc patt = abs_thmpattern (Conc' patt)
% : (termpattern -> thmpattern) %
and HypP pattl = abs_thmpattern (HypP' pattl)
% : (termpattern list -> thmpattern) %
and HypF pattl = abs_thmpattern (HypF' pattl)
% : (termpattern list -> thmpattern) %
and Side x = abs_thmpattern (Side' x)
% : (side_condition -> thmpattern) %
and Andalso (thmp1,thmp2) =
% : ((thmpattern # thmpattern) -> thmpattern) %
abs_thmpattern (Andalso' (rep_thmpattern thmp1,rep_thmpattern thmp2))
and Orelse (thmp1,thmp2) =
% : ((thmpattern # thmpattern) -> thmpattern) %
abs_thmpattern (Orelse' (rep_thmpattern thmp1,rep_thmpattern thmp2))
and Not thmp = abs_thmpattern (Not' (rep_thmpattern thmp))
% : (thmpattern -> thmpattern) %
and Where (thmp1,thmp2) =
% : ((thmpattern # thmpattern) -> thmpattern) %
% Function to check that a side-condition clause is legal %
% The function either returns `true' or fails. The failure which %
% occurs in the body of `Where' if `is_legal_sidecond' returns false %
% is therefore unnecessary. %
letrec is_legal_sidecond thmp_rep =
% : (thmpattern_rep -> bool) %
case thmp_rep
of (Kind' _) . failwith `Where -- \`Kind' used in side-condition`
| (Thryname' _) .
failwith `Where -- \`Thryname' used in side-condition`
| (Thmname' _) .
failwith `Where -- \`Thmname' used in side-condition`
| (Conc' _) . failwith `Where -- \`Conc' used in side-condition`
| (HypP' _) . failwith `Where -- \`HypP' used in side-condition`
| (HypF' _) . failwith `Where -- \`HypF' used in side-condition`
| (Side' _) . true
| (Andalso' (thmp_rep1,thmp_rep2)) .
((is_legal_sidecond thmp_rep1) & (is_legal_sidecond thmp_rep2))
| (Orelse' (thmp_rep1,thmp_rep2)) .
((is_legal_sidecond thmp_rep1) & (is_legal_sidecond thmp_rep2))
| (Not' thmp_rep1) . (is_legal_sidecond thmp_rep1)
| (Where' _) . failwith `Where -- \`Where' used in side-condition`
in if (is_legal_sidecond (rep_thmpattern thmp2))
then abs_thmpattern
(Where' (rep_thmpattern thmp1,rep_thmpattern thmp2))
else failwith `Where -- illegal side-condition`
% Function to test a theorem pattern against a foundthm %
% It calls `mainmatch' to attempt the matching. `mainmatch' returns a %
% `result_of_match', which `thmmatch' converts to a Boolean value. %
and thmmatch thmp fthm =
% : (thmpattern -> foundthm -> bool) %
rom_to_bool (mainmatch (rep_thmpattern thmp) fthm ())
% The following auxiliary matching functions are local to the abstract type %
% definition. Hence, they are hidden from the user. %
% `mainmatch' is used for processing main clauses of theorem patterns, given %
% a foundthm to match against. For the first six cases of clause type, %
% auxiliary functions are called. Note that these and `mainmatch' itself are %
% lazy. That is they require a null argument before they actually perform %
% any computation. %
% Side-condition clauses are re-interpreted when they occur within a main %
% clause, as described at the beginning of this abstract type definition. %
% `Andalso' and `Orelse' call `mainmatch' recursively on their two arguments %
% and use subsidiary functions to combine the results. `Not' calls %
% `mainmatch' on its argument and then calls a subsidiary function to %
% process the result. `Where' calls `mainmatch' on its first argument, and %
% then passes the result along with its second argument to a function which %
% deals with the side-condition clause. %
whererec mainmatch thmp_rep fthm () =
% : (thmpattern_rep -> foundthm -> void -> result_of_match) %
case thmp_rep
of (Kind' x) . (kindfn x fthm ())
| (Thryname' x) . (thrynamefn x fthm ())
| (Thmname' x) . (thmnamefn x fthm ())
| (Conc' x) . (concfn x fthm ())
| (HypP' x) . (hypPfn x fthm ())
| (HypF' x) . (hypFfn x fthm ())
| (Side' _) . (mainmatch
(Where' ((Conc' o autotermpattern) "conc:bool",thmp_rep))
fthm
()
)
| (Andalso' (x,y)) . (andalsofn
(mainmatch x fthm)
(mainmatch y fthm)
()
)
| (Orelse' (x,y)) . (approms
(mainmatch x fthm)
(mainmatch y fthm)
()
)
| (Not' x) . (notfn (mainmatch x fthm) ())
| (Where' (x,y)) . (wherefn y (mainmatch x fthm) ())
% `sidematch' is used for processing side-condition clauses, given an %
% environment which consists of a single matching. All side-condition tests %
% within the clause are applied to this matching. %
% Tests on the foundthm itself are prohibited (there is no foundthm %
% available to test). This means that the first six cases for theorem %
% patterns all cause failures. %
% If the side-condition clause is simply a side-condition, the side- %
% condition is applied to the environment. If the test succeeds, the %
% result is passed back up. If not, `Nomatch' is passed back up. %
% `Andalso', `Orelse' and `Not' cause `sidematch' to be called recursively, %
% and the results of these calls are processed further by subsidiary %
% functions. `Where' is prohibited within side-condition clauses. %
% The failures due to illegal constructor use should never occur because %
% the abstract datatype will prevent such constructions. %
and sidematch thmp_rep env () =
% : (thmpattern_rep -> matching -> void -> result_of_match) %
case thmp_rep
of (Kind' _) . (failwith `sidematch -- illegal use of Kind`)
| (Thryname' _) . (failwith `sidematch -- illegal use of Thryname`)
| (Thmname' _) . (failwith `sidematch -- illegal use of Thmname`)
| (Conc' _) . (failwith `sidematch -- illegal use of Conc`)
| (HypP' _) . (failwith `sidematch -- illegal use of HypP`)
| (HypF' _) . (failwith `sidematch -- illegal use of HypF`)
| (Side' x) . ((x env) ??[`no match`] (Nomatch))
| (Andalso' (x,y)) . (andalsofn
(sidematch x env)
(sidematch y env)
()
)
| (Orelse' (x,y)) . (approms
(sidematch x env)
(sidematch y env)
()
)
| (Not' x) . (notfn (sidematch x env) ())
| (Where' _) . (failwith `sidematch -- illegal use of Where`)
% `andalsofn' is used for ANDing two `result_of_matches' together. %
% The first argument is applied to (). If the result is `Nomatch', then the %
% result of the whole evaluation is `Nomatch'. If not, the second argument %
% is treated similarly. If both the arguments contain matchings, the %
% function attempts to join the two `heads'. If this succeeds, the result %
% becomes the `head' of the combined `result_of_match'. If not, the result %
% is discarded. %
% The rest of the `result_of_match' is (when required) obtained by calling %
% `andalsofn' recursively, firstly on the original first argument and the %
% `tail' of the second, and then on the tail of the first and the original %
% second argument. The two resulting `result_of_matches' are appended using %
% `approms'. %
% The overall effect of this is to combine a `list' of n matchings with a %
% `list' of m matchings to form a `list' of all the possible combinations %
% of matchings which can be joined successfully (maximum length n * m). %
and andalsofn rom1fn rom2fn () =
% : ((void -> result_of_match) -> (void -> result_of_match) -> %
% (void -> result_of_match)) %
case (rom1fn ())
of (Nomatch) . (Nomatch)
| (Match (m1,romfn1)) .
(case (rom2fn ())
of (Nomatch) . (Nomatch)
| (Match (m2,romfn2)) .
(let rest = (approms
(andalsofn rom1fn romfn2)
(andalsofn romfn1 rom2fn)
)
in ( (Match (join_matchings m1 m2,rest))
??[`no match`] (rest ())
)
)
)
% `notfn' simply negates a `result_of_match', discarding any matchings, %
% since they make no sense when negated. `Not' can therefore be very %
% destructive. %
and notfn rom1fn () =
% : ((void -> result_of_match) -> (void -> result_of_match)) %
case (rom1fn ())
of (Nomatch) . (Match_null)
| (Match _) . (Nomatch)
% `wherefn' is used for handling side-condition clauses. %
% It passes each matching in the `result_of_match' it is given to the %
% theorem pattern. The matchings are passed in turn as environments. %
% The evaluation proceeds only as far as is necessary, but the %
% potential to continue it is retained. %
% `sidematch' is used to test the theorem pattern under each of the %
% environments. It returns a `result_of_match'. Only those matchings %
% consistent with the environment should be retained. That is, any %
% wildcard which appears in the environment as well as in the matching %
% should match to the same object in both cases. `andalsofn' is used %
% to perform this checking. %
% The `result_of_matches' generated for each environment are appended %
% using `approms'. %
and wherefn thmp_rep rom1fn () =
% : (thmpattern_rep -> (void -> result_of_match) -> %
% (void -> result_of_match)) %
case (rom1fn ())
of (Nomatch) . (Nomatch)
| (Match (m,romfn)) . (approms
(andalsofn
(\().Match (m,(\().Nomatch)))
(sidematch thmp_rep m))
(wherefn thmp_rep romfn)
()
)
% `kindfn' tests the kind of a found theorem. %
and kindfn knd fthm () =
% : (thmkind -> foundthm -> (void -> result_of_match)) %
bool_to_rom (knd = (fst fthm))
% `thrynamefn' uses a `namepattern' to test the name of the theory to which %
% a found theorem belongs. %
and thrynamefn nmp fthm () =
% : (namepattern -> foundthm -> (void -> result_of_match)) %
bool_to_rom (namematch nmp ((fst o snd) fthm))
% `thmnamefn' uses a `namepattern' to test the name of a found theorem. %
and thmnamefn nmp fthm () =
% : (namepattern -> foundthm -> (void -> result_of_match)) %
bool_to_rom (namematch nmp ((fst o snd o snd) fthm))
% `concfn' tests the conclusion of a found theorem against a termpattern. %
% The conclusion is extracted and then matched against the termpattern. %
% If the match succeeds, the matching is made into a `result_of_match'. %
% Otherwise, `Nomatch' is returned as the `result_of_match'. %
and concfn patt fthm () =
% : (termpattern -> foundthm -> (void -> result_of_match)) %
(Match (make_matching patt ((concl o snd o snd o snd) fthm),(\().Nomatch)))
??[`no match`] Nomatch
% `hypPfn' tests the hypotheses of a found theorem against a list of %
% termpatterns. Not all of the hypotheses need to be matched for the match to %
% succeed. %
% The list of hypotheses is extracted from the found theorem. If there are %
% more termpatterns than hypotheses, `Nomatch' is returned. Otherwise, %
% `hypfn' is used to test the termpatterns against the hypotheses. %
and hypPfn pattl fthm () =
% : (termpattern list -> foundthm -> (void -> result_of_match)) %
let hypl = (hyp o snd o snd o snd) fthm
in if ((length pattl) > (length hypl))
then Nomatch
else hypfn pattl hypl ()
% `hypFfn' tests the hypotheses of a found theorem against a list of %
% termpatterns. All of the hypotheses need to be matched for the match to %
% succeed. %
% The list of hypotheses is extracted from the found theorem. If there are %
% the same number of termpatterns as there are hypotheses, `hypfn' is used to %
% test the termpatterns against the hypotheses. Otherwise, `Nomatch' is %
% returned. %
and hypFfn pattl fthm () =
% : (termpattern list -> foundthm -> (void -> result_of_match)) %
let hypl = (hyp o snd o snd o snd) fthm
in if ((length pattl) = (length hypl))
then hypfn pattl hypl ()
else Nomatch
% `hypfn' tests a list of termpatterns against a list of hypotheses %
% The result is a `result_of_match'. A subsidiary function is used to allow %
% backtracking. %
% `hypmatch' takes four arguments plus a null argument to provide `lazy' %
% evaluation. The first argument is an accumulated matching for the %
% wildcards bound so far. The second argument is a list of hypotheses left %
% unmatched. This has to be remembered while the various ways of matching %
% them are attempted. The third argument is the list of patterns not yet %
% matched. The fourth argument is the list of hypotheses which have not yet %
% been tried against the head of the pattern list. %
% When the pattern list is empty, the accumulated matching is made into a %
% `result_of_match', and returned as result. If the list of hypotheses runs %
% out before the patterns, `Nomatch' is returned. %
% If the head of the pattern list matches the head of the hypothesis list, %
% and the resulting matching is consistent with the accumulated matching, %
% the head of the hypothesis list is removed from the previous level's list %
% and `hypmatch' is called recursively to attempt a new level of match. Any %
% other ways of matching are found as described below, and are appended to %
% the result of this call. %
% Any other ways of matching are found by a recursive call to `hypmatch' %
% with all of the original arguments except that the fourth argument is the %
% tail of the original list. The result of this call becomes the result of %
% the original call if the head of the pattern list did not match the head %
% of the hypothesis list. %
and hypfn pattl hypl () =
% : (termpattern list -> term list -> (void -> result_of_match)) %
letrec hypmatch m prevtl pl terml () =
% : (matching -> term list -> termpattern list -> term list -> %
% (void -> result_of_match)) %
if (null pl)
then Match(m,(\().Nomatch))
else if (null terml)
then Nomatch
else (let rest = hypmatch m prevtl pl (tl terml)
in ((let newm = join_matchings m
(make_matching (hd pl) (hd terml))
in (let newtl = filter (\x. not (x = (hd terml))) prevtl
in approms
(hypmatch newm newtl (tl pl) newtl)
rest
()
)
)
??[`no match`] rest ()
)
)
in hypmatch null_matching hypl pattl hypl ();;
% Infix declarations to make construction of theorem patterns nicer %
ml_paired_infix `Andalso`;;
ml_paired_infix `Orelse`;;
ml_paired_infix `Where`;;
% Function to filter a list of theorems using a theorem pattern %
let thmfilter thmp fthml = filter (thmmatch thmp) fthml;;
% : (thmpattern -> foundthm list -> foundthm list) %
%----------------------------------------------------------------------------%
|