author | wenzelm |
Wed, 27 Jul 1994 15:14:31 +0200 | |
changeset 487 | af83700cb771 |
parent 474 | ac1d1988d528 |
child 560 | 6702a715281d |
permissions | -rw-r--r-- |
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(* Title: Pure/axclass.ML |
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ID: $Id$ |
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Author: Markus Wenzel, TU Muenchen |
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Higher level user interfaces for axiomatic type classes. |
449 | 6 |
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TODO: |
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remove add_sigclass (?) |
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remove goal_... (?) |
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clean signature |
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*) |
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signature AX_CLASS = |
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sig |
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structure Tactical: TACTICAL |
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local open Tactical Tactical.Thm Tactical.Thm.Sign.Syntax.Mixfix in |
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val add_thms_as_axms: (string * thm) list -> theory -> theory |
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val add_classrel_thms: thm list -> theory -> theory |
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val add_arity_thms: thm list -> theory -> theory |
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val add_axclass: class * class list -> (string * string) list |
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-> theory -> theory |
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val add_axclass_i: class * class list -> (string * term) list |
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-> theory -> theory |
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val add_sigclass: class * class list -> (string * string * mixfix) list |
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-> theory -> theory |
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val add_sigclass_i: class * class list -> (string * typ * mixfix) list |
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-> theory -> theory |
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val prove_classrel: theory -> class * class -> thm list |
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-> tactic option -> thm |
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val prove_arity: theory -> string * sort list * class -> thm list |
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-> tactic option -> thm |
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val add_inst_subclass: class * class -> string list -> thm list |
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-> tactic option -> theory -> theory |
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val add_inst_arity: string * sort list * class list -> string list |
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-> thm list -> tactic option -> theory -> theory |
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val add_defns: (string * string) list -> theory -> theory |
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val add_defns_i: (string * term) list -> theory -> theory |
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val mk_classrel: class * class -> term |
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val dest_classrel: term -> class * class |
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val mk_arity: string * sort list * class -> term |
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val dest_arity: term -> string * sort list * class |
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val class_axms: theory -> thm list |
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val axclass_tac: theory -> thm list -> tactic |
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val goal_subclass: theory -> class * class -> thm list |
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val goal_arity: theory -> string * sort list * class -> thm list |
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end |
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end; |
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functor AxClassFun(structure Logic: LOGIC and Goals: GOALS and Tactic: TACTIC |
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sharing Goals.Tactical = Tactic.Tactical): AX_CLASS = |
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struct |
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structure Tactical = Goals.Tactical; |
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structure Thm = Tactical.Thm; |
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structure Sign = Thm.Sign; |
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structure Type = Sign.Type; |
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structure Pretty = Sign.Syntax.Pretty; |
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open Logic Thm Tactical Tactic Goals; |
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(** add constant definitions **) (* FIXME -> drule.ML (?) *) |
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(* all_axioms_of *) |
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(*results may contain duplicates!*) |
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fun ancestry_of thy = |
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thy :: flat (map ancestry_of (parents_of thy)); |
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val all_axioms_of = flat o map axioms_of o ancestry_of; |
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(* clash_types, clash_consts *) |
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(*check if types have common instance (ignoring sorts)*) |
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fun clash_types ty1 ty2 = |
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let |
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val ty1' = Type.varifyT ty1; |
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val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2); |
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in |
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Type.raw_unify (ty1', ty2') |
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end; |
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fun clash_consts (c1, ty1) (c2, ty2) = |
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c1 = c2 andalso clash_types ty1 ty2; |
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(* clash_defns *) |
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fun clash_defn c_ty (name, tm) = |
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let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in |
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if clash_consts c_ty (c, ty') then Some (name, ty') else None |
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end handle TERM _ => None; |
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fun clash_defns c_ty axms = |
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distinct (mapfilter (clash_defn c_ty) axms); |
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(* dest_defn *) |
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fun dest_defn tm = |
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let |
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fun err msg = raise_term msg [tm]; |
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val (lhs, rhs) = Logic.dest_equals tm |
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handle TERM _ => err "Not a meta-equality (==)"; |
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val (head, args) = strip_comb lhs; |
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val (c, ty) = dest_Const head |
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handle TERM _ => err "Head of lhs not a constant"; |
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fun occs_const (Const c_ty') = clash_consts (c, ty) c_ty' |
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| occs_const (Abs (_, _, t)) = occs_const t |
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| occs_const (t $ u) = occs_const t orelse occs_const u |
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| occs_const _ = false; |
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in |
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if not (forall is_Free args) then |
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err "Arguments of lhs have to be variables" |
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else if not (null (duplicates args)) then |
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err "Duplicate variables on lhs" |
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else if not (term_frees rhs subset args) then |
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err "Extra variables on rhs" |
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else if not (term_tfrees rhs subset typ_tfrees ty) then |
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err "Extra type variables on rhs" |
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else if occs_const rhs then |
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err "Constant to be defined clashes with occurrence(s) on rhs" |
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else (c, ty) |
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end; |
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(* check_defn *) |
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fun err_in_axm name msg = |
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(writeln msg; error ("The error(s) above occurred in axiom " ^ quote name)); |
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fun check_defn sign (axms, (name, tm)) = |
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let |
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fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block |
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[Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sign ty])); |
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fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn; |
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fun show_defns c = commas o map (show_defn c); |
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val (c, ty) = dest_defn tm |
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handle TERM (msg, _) => err_in_axm name msg; |
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val defns = clash_defns (c, ty) axms; |
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in |
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if not (null defns) then |
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err_in_axm name ("Definition of " ^ show_const (c, ty) ^ |
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" clashes with " ^ show_defns c defns) |
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else (name, tm) :: axms |
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end; |
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|
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155 |
|
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(* add_defns *) |
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157 |
|
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fun ext_defns prep_axm raw_axms thy = |
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let |
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val axms = map (prep_axm (sign_of thy)) raw_axms; |
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val all_axms = all_axioms_of thy; |
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in |
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foldl (check_defn (sign_of thy)) (all_axms, axms); |
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add_axioms_i axms thy |
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end; |
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|
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val add_defns_i = ext_defns cert_axm; |
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val add_defns = ext_defns read_axm; |
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|
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170 |
|
423 | 171 |
|
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172 |
(** utilities **) |
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173 |
|
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(* type vars *) |
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|
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fun map_typ_frees f (Type (t, tys)) = Type (t, map (map_typ_frees f) tys) |
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| map_typ_frees f (TFree a) = f a |
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| map_typ_frees _ a = a; |
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|
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val map_term_tfrees = map_term_types o map_typ_frees; |
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181 |
|
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fun aT S = TFree ("'a", S); |
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183 |
|
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184 |
|
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(* get axioms *) |
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|
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fun get_ax thy name = |
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Some (get_axiom thy name) handle THEORY _ => None; |
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|
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val get_axioms = mapfilter o get_ax; |
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191 |
|
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192 |
|
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(* is_defn *) |
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|
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fun is_defn thm = |
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(case #prop (rep_thm thm) of |
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Const ("==", _) $ _ $ _ => true |
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| _ => false); |
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|
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201 |
|
423 | 202 |
(** abstract syntax operations **) (* FIXME -> logic.ML (?) *) |
203 |
||
204 |
(* subclass relations as terms *) |
|
205 |
||
206 |
fun mk_classrel (c1, c2) = mk_inclass (aT [c1], c2); |
|
207 |
||
208 |
fun dest_classrel tm = |
|
209 |
let |
|
210 |
fun err () = raise_term "dest_classrel" [tm]; |
|
211 |
||
212 |
val (ty, c2) = dest_inclass (freeze_vars tm) handle TERM _ => err (); |
|
213 |
val c1 = (case ty of TFree (_, [c]) => c | _ => err ()); |
|
214 |
in |
|
215 |
(c1, c2) |
|
216 |
end; |
|
217 |
||
218 |
||
219 |
(* arities as terms *) |
|
220 |
||
221 |
fun mk_arity (t, ss, c) = |
|
222 |
let |
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449 | 223 |
val names = tl (variantlist (replicate (length ss + 1) "'", [])); |
423 | 224 |
val tfrees = map TFree (names ~~ ss); |
225 |
in |
|
226 |
mk_inclass (Type (t, tfrees), c) |
|
227 |
end; |
|
228 |
||
229 |
fun dest_arity tm = |
|
230 |
let |
|
231 |
fun err () = raise_term "dest_arity" [tm]; |
|
232 |
||
233 |
val (ty, c) = dest_inclass (freeze_vars tm) handle TERM _ => err (); |
|
234 |
val (t, tfrees) = |
|
235 |
(case ty of |
|
236 |
Type (t, tys) => (t, map (fn TFree x => x | _ => err ()) tys) |
|
237 |
| _ => err ()); |
|
238 |
val ss = |
|
239 |
if null (gen_duplicates eq_fst tfrees) |
|
240 |
then map snd tfrees else err (); |
|
241 |
in |
|
242 |
(t, ss, c) |
|
243 |
end; |
|
244 |
||
245 |
||
246 |
||
247 |
(** add theorems as axioms **) (* FIXME -> drule.ML (?) *) |
|
248 |
||
249 |
fun prep_thm_axm thy thm = |
|
250 |
let |
|
251 |
fun err msg = raise THM ("prep_thm_axm: " ^ msg, 0, [thm]); |
|
252 |
||
253 |
val {sign, hyps, prop, ...} = rep_thm thm; |
|
254 |
in |
|
255 |
if not (Sign.subsig (sign, sign_of thy)) then |
|
256 |
err "theorem not of same theory" |
|
257 |
else if not (null hyps) then |
|
258 |
err "theorem may not contain hypotheses" |
|
259 |
else prop |
|
260 |
end; |
|
261 |
||
262 |
(*general theorems*) |
|
263 |
fun add_thms_as_axms thms thy = |
|
264 |
add_axioms_i (map (apsnd (prep_thm_axm thy)) thms) thy; |
|
265 |
||
266 |
(*theorems expressing class relations*) |
|
267 |
fun add_classrel_thms thms thy = |
|
268 |
let |
|
269 |
fun prep_thm thm = |
|
270 |
let |
|
271 |
val prop = prep_thm_axm thy thm; |
|
272 |
val (c1, c2) = dest_classrel prop handle TERM _ => |
|
273 |
raise THM ("add_classrel_thms: theorem is not a class relation", 0, [thm]); |
|
274 |
in (c1, c2) end; |
|
275 |
in |
|
276 |
add_classrel (map prep_thm thms) thy |
|
277 |
end; |
|
278 |
||
279 |
(*theorems expressing arities*) |
|
280 |
fun add_arity_thms thms thy = |
|
281 |
let |
|
282 |
fun prep_thm thm = |
|
283 |
let |
|
284 |
val prop = prep_thm_axm thy thm; |
|
285 |
val (t, ss, c) = dest_arity prop handle TERM _ => |
|
286 |
raise THM ("add_arity_thms: theorem is not an arity", 0, [thm]); |
|
287 |
in (t, ss, [c]) end; |
|
288 |
in |
|
289 |
add_arities (map prep_thm thms) thy |
|
290 |
end; |
|
291 |
||
292 |
||
293 |
||
294 |
(** add axiomatic type classes **) |
|
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295 |
|
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296 |
(* errors *) |
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297 |
|
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298 |
fun err_not_logic c = |
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299 |
error ("Axiomatic class " ^ quote c ^ " not subclass of \"logic\""); |
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300 |
|
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301 |
fun err_bad_axsort ax c = |
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302 |
error ("Sort constraint in axiom " ^ quote ax ^ " not supersort of " ^ quote c); |
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303 |
|
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304 |
fun err_bad_tfrees ax = |
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305 |
error ("More than one type variable in axiom " ^ quote ax); |
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306 |
|
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307 |
|
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308 |
(* ext_axclass *) |
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309 |
|
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310 |
fun ext_axclass prep_axm (class, super_classes) raw_axioms old_thy = |
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311 |
let |
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312 |
val axioms = map (prep_axm (sign_of old_thy)) raw_axioms; |
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313 |
val thy = add_classes [([], class, super_classes)] old_thy; |
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314 |
val sign = sign_of thy; |
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315 |
|
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|
316 |
|
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317 |
(* prepare abstract axioms *) |
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318 |
|
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319 |
fun abs_axm ax = |
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320 |
if null (term_tfrees ax) then |
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321 |
mk_implies (mk_inclass (aT logicS, class), ax) |
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|
322 |
else |
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323 |
map_term_tfrees (K (aT [class])) ax; |
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|
324 |
|
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325 |
val abs_axioms = map (apsnd abs_axm) axioms; |
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|
326 |
|
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|
327 |
|
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|
328 |
(* prepare introduction orule *) |
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|
329 |
|
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|
330 |
val _ = |
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|
331 |
if Sign.subsort sign ([class], logicS) then () |
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|
332 |
else err_not_logic class; |
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|
333 |
|
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|
334 |
fun axm_sort (name, ax) = |
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|
335 |
(case term_tfrees ax of |
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|
336 |
[] => [] |
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|
337 |
| [(_, S)] => |
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|
338 |
if Sign.subsort sign ([class], S) then S |
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|
339 |
else err_bad_axsort name class |
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|
340 |
| _ => err_bad_tfrees name); |
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|
341 |
|
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|
342 |
val axS = Sign.norm_sort sign (logicC :: flat (map axm_sort axioms)); |
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|
343 |
|
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344 |
val int_axm = close_form o map_term_tfrees (K (aT axS)); |
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345 |
fun inclass c = mk_inclass (aT axS, c); |
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|
346 |
|
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|
347 |
val intro_axm = list_implies |
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|
348 |
(map inclass super_classes @ map (int_axm o snd) axioms, inclass class); |
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|
349 |
in |
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|
350 |
add_axioms_i ((class ^ "I", intro_axm) :: abs_axioms) thy |
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|
351 |
end; |
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|
352 |
|
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|
353 |
|
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|
354 |
(* external interfaces *) |
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|
355 |
|
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
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356 |
val add_axclass = ext_axclass read_axm; |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
357 |
val add_axclass_i = ext_axclass cert_axm; |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
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358 |
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dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
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359 |
|
423 | 360 |
(* add signature classes *) |
404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
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361 |
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423 | 362 |
fun ext_sigclass add_cnsts (class, super_classes) consts old_thy = |
363 |
old_thy |
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364 |
|> add_axclass (class, super_classes) [] |
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365 |
|> add_defsort [class] |
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366 |
|> add_cnsts consts |
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|> add_defsort (Type.defaultS (#tsig (Sign.rep_sg (sign_of old_thy)))); |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
368 |
|
423 | 369 |
val add_sigclass = ext_sigclass add_consts; |
370 |
val add_sigclass_i = ext_sigclass add_consts_i; |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
371 |
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dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
372 |
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dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
373 |
|
423 | 374 |
(** prove class relations and type arities **) |
375 |
||
376 |
(* class_axms *) |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
377 |
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dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
378 |
fun class_axms thy = |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
379 |
let |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
380 |
val classes = Sign.classes (sign_of thy); |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
381 |
val intros = map (fn c => c ^ "I") classes; |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
382 |
in |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
383 |
get_axioms thy intros @ |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
384 |
map (class_triv thy) classes |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
385 |
end; |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
386 |
|
423 | 387 |
|
388 |
(* axclass_tac *) |
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389 |
||
487
af83700cb771
added experimental add_defns (actually should be moved somewhere else);
wenzelm
parents:
474
diff
changeset
|
390 |
(*(1) repeatedly resolve goals of form "OFCLASS(ty, c_class)", |
423 | 391 |
try "cI" axioms first and use class_triv as last resort |
392 |
(2) rewrite goals using user supplied definitions |
|
393 |
(3) repeatedly resolve goals with user supplied non-definitions*) |
|
394 |
||
395 |
fun axclass_tac thy thms = |
|
396 |
TRY (REPEAT_FIRST (resolve_tac (class_axms thy))) THEN |
|
397 |
TRY (rewrite_goals_tac (filter is_defn thms)) THEN |
|
398 |
TRY (REPEAT_FIRST (resolve_tac (filter_out is_defn thms))); |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
399 |
|
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
400 |
|
423 | 401 |
(* provers *) |
404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
402 |
|
423 | 403 |
fun prove term_of str_of thy sig_prop thms usr_tac = |
404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
404 |
let |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
405 |
val sign = sign_of thy; |
423 | 406 |
val goal = cterm_of sign (term_of sig_prop); |
407 |
val tac = axclass_tac thy thms THEN (if_none usr_tac all_tac); |
|
408 |
in |
|
409 |
prove_goalw_cterm [] goal (K [tac]) |
|
410 |
end |
|
411 |
handle ERROR => error ("The error(s) above occurred while trying to prove " |
|
412 |
^ quote (str_of sig_prop)); |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
413 |
|
423 | 414 |
val prove_classrel = |
415 |
prove mk_classrel (fn (c1, c2) => c1 ^ " < " ^ c2); |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
416 |
|
423 | 417 |
val prove_arity = |
418 |
prove mk_arity (fn (t, ss, c) => Type.str_of_arity (t, ss, [c])); |
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404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
419 |
|
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
420 |
|
423 | 421 |
(* make goals (for interactive use) *) |
422 |
||
423 |
fun mk_goal term_of thy sig_prop = |
|
424 |
goalw_cterm [] (cterm_of (sign_of thy) (term_of sig_prop)); |
|
425 |
||
426 |
val goal_subclass = mk_goal mk_classrel; |
|
427 |
val goal_arity = mk_goal mk_arity; |
|
428 |
||
429 |
||
430 |
||
449 | 431 |
(** add proved subclass relations and arities **) |
404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
432 |
|
449 | 433 |
fun add_inst_subclass (c1, c2) axms thms usr_tac thy = |
423 | 434 |
add_classrel_thms |
435 |
[prove_classrel thy (c1, c2) (get_axioms thy axms @ thms) usr_tac] thy; |
|
436 |
||
449 | 437 |
fun add_inst_arity (t, ss, cs) axms thms usr_tac thy = |
423 | 438 |
let |
439 |
val usr_thms = get_axioms thy axms @ thms; |
|
440 |
fun prove c = |
|
441 |
prove_arity thy (t, ss, c) usr_thms usr_tac; |
|
442 |
in |
|
443 |
add_arity_thms (map prove cs) thy |
|
444 |
end; |
|
404
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
445 |
|
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
446 |
|
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
447 |
end; |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
|
448 |