2 (c) Walther Neuper 2000
7 val calculate_: theory -> string * Eval_Def.eval_fn -> term -> (term * (string * thm)) option
8 val eval__true: theory -> int -> term list -> (term * term) list -> Rule_Set.T -> term list * bool
9 val eval_prog_expr: theory -> Rule_Set.T -> term -> term
10 val eval_true_: theory -> Rule_Set.T -> term -> bool
11 val eval_true: theory -> term list -> Rule_Set.T -> bool
12 val rew_sub: theory -> int -> (term * term) list -> Rule_Def.rew_ord_
13 -> Rule_Set.T -> bool -> TermC.path -> term -> term -> term * term list * TermC.path * bool
14 val rewrite_: theory -> Rule_Def.rew_ord_ -> Rule_Set.T -> bool -> thm ->
15 term -> (term * term list) option
16 val rewrite_inst_: theory -> Rule_Def.rew_ord_ -> Rule_Set.T -> bool
17 -> (term * term) list -> thm -> term -> (term * term list) option
18 val rewrite_set_: theory -> bool -> Rule_Set.T -> term -> (term * term list) option
19 val rewrite_set_inst_: theory -> bool -> (term * term) list -> Rule_Set.T -> term -> (term * term list) option
20 val rewrite_terms_: theory -> Rule_Def.rew_ord_ -> Rule_Set.T -> term list
21 -> term -> (term * term list) option
23 val trace_on: bool Unsynchronized.ref
24 val depth: int Unsynchronized.ref
25 val lim_deriv: int Unsynchronized.ref
27 (* ---- for tests only: shifted from below to remove the Warning "unused" at fun.def. --------- *)
29 (*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\* )
30 val rewrite__: theory -> int -> (term * term) list -> Rule_Def.rew_ord_ ->
31 Rule_Set.T -> bool -> thm -> term -> (term * term list) option
32 val rewrite__set_: theory -> int -> bool -> (term * term) list -> Rule_Set.T -> term -> (term * term list) option
33 val app_rev: theory -> int -> Rule_Set.T -> term -> term * term list * bool
34 val app_sub: theory -> int -> Rule_Set.T -> term -> term * term list * bool
35 val trace1: int -> string -> unit
36 ( *\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)
40 structure Rewrite(**): REWRITE(**) =
45 exception STOP_REW_SUB; (*WN050820 quick and dirty*)
47 val trace_on = Unsynchronized.ref false;
48 (* depth of recursion in traces of the rewriter, if trace_on:=true *)
49 val depth = Unsynchronized.ref 99999;
50 (* no of rewrites exceeding this int -> NO rewrite *)
51 val lim_deriv = Unsynchronized.ref 100;
54 if ! trace_on andalso i < ! depth then tracing (idt "#" i ^ str) else ()
56 if ! trace_on andalso i < ! depth then tracing (idt "#" (i + 1) ^ str) else ()
58 fun rewrite__ thy i bdv tless rls put_asm thm ct =
60 val (t', asms, _ (*lrd*), rew) = rew_sub thy i bdv tless rls put_asm ([(*root of the term*)]: TermC.path)
61 (((TermC.inst_bdv bdv) o Eval.norm o #prop o Thm.rep_thm) thm) ct
62 in if rew then SOME (t', distinct asms) else NONE end
63 (* one rewrite (possibly conditional, ordered) EXOR exn EXOR go into subterms *)
64 and rew_sub thy i bdv tless rls put_asm lrd r t =
66 val (lhs, rhs) = (HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r
67 (*?alternative Unify.matchers:
68 http://isabelle.in.tum.de/repos/isabelle/file/Isabelle2017/src/Pure/more_unify.ML*)
69 val r' = Envir.subst_term (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) r
70 val p' = map HOLogic.dest_Trueprop ((fst o Logic.strip_prems) (Logic.count_prems r', [], r'))
71 val t' = (snd o HOLogic.dest_eq o HOLogic.dest_Trueprop o Logic.strip_imp_concl) r'
72 val _ = if ! trace_on andalso i < ! depth andalso p' <> []
73 then tracing (idt "#" (i + 1) ^ " eval asms: " ^ UnparseC.term_in_thy thy r') else ()
74 val (t'', p'') = (*conditional rewriting*)
76 val (simpl_p', nofalse) = eval__true thy (i + 1) p' bdv rls
80 (if ! trace_on andalso i < ! depth andalso p' <> []
81 then tracing (idt "#" (i + 1) ^ " asms accepted: " ^ UnparseC.terms_in_thy thy p' ^
82 " stored: " ^ UnparseC.terms_in_thy thy simpl_p')
84 (t',simpl_p')) (* uncond.rew. from above*)
86 (if ! trace_on andalso i < ! depth
87 then tracing (idt "#" (i + 1) ^ " asms false: " ^ UnparseC.terms_in_thy thy p')
89 raise STOP_REW_SUB (* don't go into subterms of cond *))
92 if TermC.perm lhs rhs andalso not (tless bdv (t', t)) (*ordered rewriting*)
93 then (if ! trace_on andalso i < ! depth
94 then tracing (idt"#"i ^ " not: \"" ^ UnparseC.term_in_thy thy t ^ "\" > \"" ^ UnparseC.term_in_thy thy t' ^ "\"")
97 else (t'', p'', [], true)
99 ) handle _ (*TODO Pattern.MATCH when tests are ready: ERROR 364ce4699452 *) =>
101 Const(s,T) => (Const(s,T),[],lrd,false)
102 | Free(s,T) => (Free(s,T),[],lrd,false)
103 | Var(n,T) => (Var(n,T),[],lrd,false)
104 | Bound i => (Bound i,[],lrd,false)
106 let val (t', asms, _ (*lrd*), rew) = rew_sub thy i bdv tless rls put_asm (lrd @ [TermC.D]) r body
107 in (Abs(s, T, t'), asms, [], rew) end
109 let val (t2', asm2, lrd, rew2) = rew_sub thy i bdv tless rls put_asm (lrd @ [TermC.R]) r t2
111 if rew2 then (t1 $ t2', asm2, lrd, true)
113 let val (t1', asm1, lrd, rew1) = rew_sub thy i bdv tless rls put_asm (lrd @ [TermC.L]) r t1
114 in if rew1 then (t1' $ t2, asm1, lrd, true) else (t1 $ t2,[], lrd, false) end
116 and eval__true thy i asms bdv rls = (* simplify asumptions until one evaluates to false *)
117 if asms = [@{term True}] orelse asms = [] then ([], true)
118 else (* this allows to check Rrls with prepat = ([@{term True}], pat) *)
119 if asms = [@{term False}] then ([], false)
122 fun chk indets [] = (indets, true) (*return asms<>True until false*)
123 | chk indets (a :: asms) =
124 (case rewrite__set_ thy (i + 1) false bdv rls a of
125 NONE => (chk (indets @ [a]) asms)
127 if t = @{term True} then (chk (indets @ a') asms)
128 else if t = @{term False} then ([], false)
129 (*asm false .. thm not applied ^^^; continue until False vvv*)
130 else chk (indets @ [t] @ a') asms);
132 and rewrite__set_ thy _ __ Rule_Set.Empty t = (* rewrite with a rule set *)
133 raise ERROR ("rewrite__set_ called with 'Erls' for '" ^ UnparseC.term_in_thy thy t ^ "'")
134 | rewrite__set_ thy i _ _ (rrls as Rule_Set.Rrls _) t = (* rewrite with a 'reverse rule set' *)
136 val _= trace i (" rls: " ^ Rule_Set.id rrls ^ " on: " ^ UnparseC.term_in_thy thy t)
137 val (t', asm, rew) = app_rev thy (i + 1) rrls t
138 in if rew then SOME (t', distinct asm) else NONE end
139 | rewrite__set_ thy i put_asm bdv rls ct = (* Rls, Seq containing Thms or Eval, Cal1 *)
141 (* attention with cp to test/..: unbound thy, i, bdv, rls; TODO1803? pull out to rewrite__*)
142 datatype switch = Appl | Noap;
143 fun rew_once _ asm ct Noap [] = (ct, asm) (* ?TODO unify with Prog_Expr.rew_once? *)
144 | rew_once ruls asm ct Appl [] =
145 (case rls of Rule_Def.Repeat _ => rew_once ruls asm ct Noap ruls
146 | Rule_Set.Sequence _ => (ct, asm)
147 | rls => raise ERROR ("rew_once not appl. to \"" ^ Rule_Set.id rls ^ "\""))
148 | rew_once ruls asm ct apno (rul :: thms) =
150 Rule.Thm (thmid, thm) =>
151 (trace1 i (" try thm: \"" ^ thmid ^ "\"");
152 case rewrite__ thy (i + 1) bdv ((snd o #rew_ord o Rule_Set.rep) rls)
153 ((#erls o Rule_Set.rep) rls) put_asm thm ct of
154 NONE => rew_once ruls asm ct apno thms
155 | SOME (ct', asm') =>
156 (trace1 i (" rewrites to: \"" ^ UnparseC.term_in_thy thy ct' ^ "\"");
157 rew_once ruls (union (op =) asm asm') ct' Appl (rul :: thms)))
158 (* once again try the same rule, e.g. associativity against "()"*)
159 | Rule.Eval (cc as (op_, _)) =>
160 let val _= trace1 i (" try calc: \"" ^ op_ ^ "\"")
161 val ct = TermC.uminus_to_string ct (*WN190312: superfluous?*)
162 in case Eval.adhoc_thm thy cc ct of
163 NONE => rew_once ruls asm ct apno thms
166 val pairopt = rewrite__ thy (i + 1) bdv ((snd o #rew_ord o Rule_Set.rep) rls)
167 ((#erls o Rule_Set.rep) rls) put_asm thm' ct;
168 val _ = if pairopt <> NONE then () else raise ERROR ("rewrite_set_, rewrite_ \"" ^
169 ThmC.string_of_thm thm' ^ "\" " ^ UnparseC.term_in_thy thy ct ^ " = NONE")
170 val _ = trace1 i (" calc. to: " ^ UnparseC.term_in_thy thy ((fst o the) pairopt))
171 in rew_once ruls asm ((fst o the) pairopt) Appl (rul :: thms) end
173 | Rule.Cal1 (cc as (op_, _)) =>
174 let val _= trace1 i (" try cal1: " ^ op_ ^ "'");
175 val ct = TermC.uminus_to_string ct
176 in case Eval.adhoc_thm1_ thy cc ct of
180 val pairopt = rewrite__ thy (i + 1) bdv ((snd o #rew_ord o Rule_Set.rep) rls)
181 ((#erls o Rule_Set.rep) rls) put_asm thm' ct;
182 val _ = if pairopt <> NONE then () else raise ERROR ("rewrite_set_, rewrite_ \"" ^
183 ThmC.string_of_thm thm' ^ "\" " ^ UnparseC.term_in_thy thy ct ^ " = NONE")
184 val _ = trace1 i (" cal1. to: " ^ UnparseC.term_in_thy thy ((fst o the) pairopt))
188 (case rewrite__set_ thy (i + 1) put_asm bdv rls' ct of
189 SOME (t', asm') => rew_once ruls (union (op =) asm asm') t' Appl thms
190 | NONE => rew_once ruls asm ct apno thms)
191 | r => raise ERROR ("rew_once not appl. to \"" ^ Rule.to_string r ^ "\"");
192 val ruls = (#rules o Rule_Set.rep) rls;
193 val _ = trace i (" rls: " ^ Rule_Set.id rls ^ " on: " ^ UnparseC.term_in_thy thy ct)
194 val (ct', asm') = rew_once ruls [] ct Noap ruls;
195 in if ct = ct' then NONE else SOME (ct', distinct asm') end
196 (*-------------------------------------------------------------*)
197 and app_rev thy i rrls t = (* apply an Rrls; if not applicable proceed with subterms *)
198 let (* check a (precond, pattern) of a rev-set; stops with 1st true *)
199 fun chk_prepat _ _ [] _ = true
200 | chk_prepat thy erls prepat t =
202 fun chk (pres, pat) =
204 val subst: Type.tyenv * Envir.tenv =
205 Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
207 snd (eval__true thy (i + 1) (map (Envir.subst_term subst) pres) [] erls)
208 end) handle _ (*TODO Pattern.MATCH*) => false
209 fun scan_ _ [] = false
210 | scan_ f (pp :: pps) =
211 if f pp then true else scan_ f pps;
212 in scan_ chk prepat end;
213 (* apply the normal_form of a rev-set *)
214 fun app_rev' thy (Rule_Set.Rrls {erls, prepat, scr = Rule.Rfuns {normal_form, ...}, ...}) t =
215 if chk_prepat thy erls prepat t then normal_form t else NONE
216 | app_rev' _ r _ = raise ERROR ("app_rev' not appl. to \"" ^ Rule_Set.id r ^ "\"");
217 val opt = app_rev' thy rrls t
220 SOME (t', asm) => (t', asm, true)
221 | NONE => app_sub thy i rrls t
223 and app_sub thy i rrls t = (* apply an Rrls to subterms *)
225 Const (s, T) => (Const(s, T), [], false)
226 | Free (s, T) => (Free(s, T), [], false)
227 | Var (n, T) => (Var(n, T), [], false)
228 | Bound i => (Bound i, [], false)
229 | Abs (s, T, body) =>
230 let val (t', asm, rew) = app_rev thy i rrls body
231 in (Abs(s, T, t'), asm, rew) end
233 let val (t2', asm2, rew2) = app_rev thy i rrls t2
235 if rew2 then (t1 $ t2', asm2, true)
237 let val (t1', asm1, rew1) = app_rev thy i rrls t1
238 in if rew1 then (t1' $ t2, asm1, true)
239 else (t1 $ t2, [], false)
243 (* rewriting without argument [] for rew_ord; WN110603: shouldnt asm<>[] lead to false? *)
244 fun eval_true thy terms rls = (snd o (eval__true thy 1 terms [])) rls;
246 (* rewriting without internal argument [] *)
247 fun rewrite_ thy rew_ord erls bool thm term = rewrite__ thy 1 [] rew_ord erls bool thm term;
248 fun rewrite_set_ thy bool rls term = rewrite__set_ thy 1 bool [] rls term;
250 (* variants of rewrite; TODO del. put_asm *)
251 fun rewrite_inst_ thy rew_ord rls put_asm subst thm ct =
252 rewrite__ thy 1 subst rew_ord rls put_asm thm ct;
253 fun rewrite_set_inst_ thy put_asm subst rls ct = rewrite__set_ thy 1 put_asm subst rls ct;
255 (* given a list of equalities (lhs = rhs) and a term,
256 replace all occurrences of lhs in the term with rhs;
257 thus the order or equalities matters: put variables in lhs first. *)
258 fun rewrite_terms_ thy ord erls equs t =
260 fun rew_ (t', asm') [] _ = (t', asm')
261 | rew_ (t', asm') (rules as r::rs) t =
263 val (t'', asm'', _(*lrd*), rew) = rew_sub thy 1 [] ord erls false [] (HOLogic.Trueprop $ r) t
266 then rew_ (t'', asm' @ asm'') rules t''
267 else rew_ (t', asm') rs t'
269 val (t'', asm'') = rew_ (TermC.empty, []) equs t
270 in if t'' = TermC.empty then NONE else SOME (t'', asm'')
273 (* search ct for adjacent numerals and calculate them by operator isa_fn *)
274 fun calculate_ thy isa_fn ct =
275 let val ct = TermC.uminus_to_string ct
276 in case Eval.adhoc_thm thy isa_fn ct of
278 | SOME (thmID, thm) =>
279 (let val rew = case rewrite_ thy Rewrite_Ord.dummy_ord Rule_Set.empty false thm ct of
281 | NONE => raise ERROR ""
282 in SOME (rew, (thmID, thm)) end)
283 handle _ (*TODO Pattern.MATCH ?del?*)=> raise ERROR ("calculate_: " ^ thmID ^ " does not rewrite")
286 fun eval_prog_expr thy srls t =
287 let val rew = rewrite_set_ thy false srls t;
288 in case rew of SOME (res,_) => res | NONE => t end;
290 fun eval_true_ _ _ (Const ("HOL.True",_)) = true
291 | eval_true_ thy rls t =
292 case rewrite_set_ thy false rls t of
293 SOME (Const ("HOL.True",_),_) => true