wneuper/isa: src/Tools/isac/ProgLang/calculate.sml@22235e4dbe5f

     1 (* calculate values for function constants

     2    (c) Walther Neuper 000106

     4 use"ProgLang/calculate.sml";

     5 *)

     8 (* dirty type-conversion 30.1.00 for "fixed_values [R=R]" *)

    10 val aT = Type ("'a", []);

    11 (* isas types for Free, parseold: (1) "R=R" or (2) "R=(R::real)":

    12 (1)

    13 > val (TFree(ss2,TT2)) = T2;

    14 val ss2 = "'a" : string

    15 val TT2 = ["term"] : sort

    16 (2)

    17 > val (Type(ss2',TT2')) = T2';

    18 val ss2' = "RealDef.real" : string

    19 val TT2' = [] : typ list

    20 (3)

    21 val realType = TFree ("RealDef.real", HOLogic.termS);

    22 is different internally, too;

    24 (1) .. (3) are displayed equally !!!

    25 *)

    29 (* 30.1.00: generating special terms for ME:

    30    (1) binary numerals reconverted to Free ("#num",...)

    31        by libarary_G.num_str: called from parse (below) and

    32        interface_ME_ISA for all thms used

    33        (compare HOLogic.dest_binum)

    34    (2) 'a types converted to RealDef.real by typ_a2real

    35        in parse below

    36    (3) binary operators fixed to type real in RatArith.thy

    37        (trick by Markus Wenzel)

    38 *)

    43 (** calculate numerals **)

    45 (*27.3.00: problems with patterns below:

    46 "Vars (a // #2 = r * xxxxx b)" doesn't work, but

    47 "Vars (a // #2 = r * sqrt b)" works

    48 *)

    50 fun popt2str (SOME (str, term)) = "SOME "^term2str term

    51   | popt2str NONE = "NONE";

    53 (* scan a term for applying eval_fn ef

    54 args

    55   thy:

    56   op_: operator (as string) selecting the root of the pair

    57   ef : fn : (string -> term -> theory -> (string * term) option)

    58              ^^^^^^... for creating the string for the resulting theorem

    59   t  : term to be scanned

    60 result:

    61   (string * term) option: found by the eval_* -function of type

    62        fn : string -> string -> term -> theory -> (string * term) option

    63             ^^^^^^... the selecting operator op_ (variable for eval_binop)

    64 *)

    65 fun get_pair thy op_ (ef:string -> term -> theory -> (string * term) option)

    66     (t as (Const(op0,t0) $ arg)) =                      (* unary fns *)

    67 (* val (thy, op_, (ef),    (t as (Const(op0,t0) $ arg))) =

    68        (thy, op_, eval_fn, ct);

    69    *)

    70     if op_ = op0 then

    71 	let val popt = ef op_ t thy

    72 	in case popt of

    73 	       SOME _ => popt

    74 	     | NONE => get_pair thy op_ ef arg end

    75     else get_pair thy op_ ef arg

    77   | get_pair thy "Atools.ident" ef (t as (Const("Atools.ident",t0) $ _ $ _ )) =

    78 (* val (thy, "Atools.ident", ef,      t as (Const(op0,_) $ t1 $ t2)) =

    79        (thy, op_,            eval_fn, ct);

    80    *)

    81     ef "Atools.ident" t thy                                 (* not nested *)

    83   | get_pair thy op_ ef (t as (Const(op0,_) $ t1 $ t2)) =  (* binary funs*)

    84 (* val (thy, op_, ef,      (t as (Const(op0,_) $ t1 $ t2))) =

    85        (thy, op_, eval_fn, ct);

    86    *)

    87     ((*writeln("1.. get_pair: binop = "^op_);*)

    88      if op_ = op0 then

    89 	 let val popt = ef op_ t thy

    90 	 (*val _ = writeln("2.. get_pair: "^term2str t^" -> "^popt2str popt)*)

    91 	 in case popt of

    92 		SOME (id,_) => popt

    93 	      | NONE =>

    94 		let val popt = get_pair thy op_ ef t1

    95 		    (*val _ = writeln("3.. get_pair: "^term2str t1^

    96 				    " -> "^popt2str popt)*)

    97 		in case popt of

    98 		       SOME (id,_) => popt

    99 		     | NONE => get_pair thy op_ ef t2

   100 		end

   101 	 end

   102      else (*search subterms*)

   103 	 let val popt = get_pair thy op_ ef t1

   104 	 (*val _ = writeln("4.. get_pair: "^term2str t^" -> "^popt2str popt)*)

   105 	 in case popt of

   106 		SOME (id,_) => popt

   107 	      | NONE => get_pair thy op_ ef t2

   108 	 end)

   109   | get_pair thy op_ ef (t as (Const(op0,_) $ t1 $ t2 $ t3)) =(* trinary funs*)

   110     ((*writeln("### get_pair 4a: t= "^term2str t);

   111      writeln("### get_pair 4a: op_= "^op_);

   112      writeln("### get_pair 4a: op0= "^op0);*)

   113      if op_ = op0 then

   114 	case ef op_ t thy of

   115 	    SOME tt => SOME tt

   116 	  | NONE => (case get_pair thy op_ ef t2 of

   117 			 SOME tt => SOME tt

   118 		       | NONE => get_pair thy op_ ef t3)

   119     else (case get_pair thy op_ ef t1 of

   120 	     SOME tt => SOME tt

   121 	   | NONE => (case get_pair thy op_ ef t2 of

   122 			  SOME tt => SOME tt

   123 			| NONE => get_pair thy op_ ef t3)))

   124   | get_pair thy op_ ef (Const _) = NONE

   125   | get_pair thy op_ ef (Free _) = NONE

   126   | get_pair thy op_ ef (Var _) = NONE

   127   | get_pair thy op_ ef (Bound _) = NONE

   128   | get_pair thy op_ ef (Abs(a,T,body)) = get_pair thy op_ ef body

   129   | get_pair thy op_ ef (t1$t2) =

   130     let(*val _= writeln("5.. get_pair t1 $ t2: "^term2str t1^"

   131 						   $ "^term2str t2)*)

   132 	val popt = get_pair thy op_ ef t1

   133     in case popt of

   134 	   SOME _ => popt

   135 	 | NONE => ((*writeln"### get_pair: t1 $ t2 -> NONE";*)

   136 		    get_pair thy op_ ef t2)

   137     end;

   138  (*

   139 >  val t = (term_of o the o (parse thy)) "#3 + #4";

   140 >  val eval_fn = the (assoc (!eval_list, "op +"));

   141 >  val (SOME (id,t')) = get_pair thy "op +" eval_fn t;

   142 >  Syntax.string_of_term (thy2ctxt thy) t';

   143 >  atomty t';

   144 >

   145 >  val t = (term_of o the o (parse thy)) "(a + #3) + #4";

   146 >  val (SOME (id,t')) = get_pair thy "op +" eval_fn t;

   147 >  Syntax.string_of_term (thy2ctxt thy) t';

   148 >

   149 >  val t = (term_of o the o (parse thy)) "#3 + (#4 + (a::real))";

   150 >  val (SOME (id,t')) = get_pair thy "op +" eval_fn t;

   151 >  Syntax.string_of_term (thy2ctxt thy) t';

   152 >

   153 >  val t = (term_of o the o (parse thy)) "x = #5 * (#3 + (#4 + a))";

   154 >  atomty t;

   155 >  val (SOME (id,t')) = get_pair thy "op +" eval_fn t;

   156 >  Syntax.string_of_term (thy2ctxt thy) t';

   157 >  val it = "#3 + (#4 + a) = #7 + a" : string

   158 >

   159 >

   160 >  val t = (term_of o the o (parse thy)) "#-4//#-2";

   161 >  val eval_fn = the (assoc (!eval_list, "cancel"));

   162 >  val (SOME (id,t')) = get_pair thy "cancel" eval_fn t;

   163 >  Syntax.string_of_term (thy2ctxt thy) t';

   164 >

   165 >  val t = (term_of o the o (parse thy)) "#2^^^#3";

   166 >  eval_binop "xxx" "pow" t thy;

   167 >  val eval_fn = (eval_binop "xxx")

   168 >		 : string -> term -> theory -> (string * term) option;

   169 >  val SOME (id,t') = get_pair thy "pow" eval_fn t;

   170 >  Syntax.string_of_term (thy2ctxt thy) t';

   171 >  val eval_fn = the (assoc (!eval_list, "pow"));

   172 >  val (SOME (id,t')) = get_pair thy "pow" eval_fn t;

   173 >  Syntax.string_of_term (thy2ctxt thy) t';

   174 >

   175 >  val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4";

   176 >  val eval_fn = the (assoc (!eval_list, "op *"));

   177 >  val (SOME (id,t')) = get_pair thy "op *" eval_fn t;

   178 >  Syntax.string_of_term (thy2ctxt thy) t';

   179 >

   180 >  val t = (term_of o the o (parse thy)) "#0 < #4";

   181 >  val eval_fn = the (assoc (!eval_list, "op <"));

   182 >  val (SOME (id,t')) = get_pair thy "op <" eval_fn t;

   183 >  Syntax.string_of_term (thy2ctxt thy) t';

   184 >  val t = (term_of o the o (parse thy)) "#0 < #-4";

   185 >  val (SOME (id,t')) = get_pair thy "op <" eval_fn t;

   186 >  Syntax.string_of_term (thy2ctxt thy) t';

   187 >

   188 >  val t = (term_of o the o (parse thy)) "#3 is_const";

   189 >  val eval_fn = the (assoc (!eval_list, "is'_const"));

   190 >  val (SOME (id,t')) = get_pair thy "is'_const" eval_fn t;

   191 >  Syntax.string_of_term (thy2ctxt thy) t';

   192 >  val t = (term_of o the o (parse thy)) "a is_const";

   193 >  val (SOME (id,t')) = get_pair thy "is'_const" eval_fn t;

   194 >  Syntax.string_of_term (thy2ctxt thy) t';

   195 >

   196 >  val t = (term_of o the o (parse thy)) "#6//(#8::real)";

   197 >  val eval_fn = the (assoc (!eval_list, "cancel"));

   198 >  val (SOME (id,t')) = get_pair thy "cancel" eval_fn t;

   199 >  Syntax.string_of_term (thy2ctxt thy) t';

   200 >

   201 >  val t = (term_of o the o (parse thy)) "sqrt #12";

   202 >  val eval_fn = the (assoc (!eval_list, "SqRoot.sqrt"));

   203 >  val (SOME (id,t')) = get_pair thy "SqRoot.sqrt" eval_fn t;

   204 >  Syntax.string_of_term (thy2ctxt thy) t';

   205 >  val it = "sqrt #12 = #2 * sqrt #3 " : string

   206 >

   207 >  val t = (term_of o the o (parse thy)) "sqrt #9";

   208 >  val (SOME (id,t')) = get_pair thy "SqRoot.sqrt" eval_fn t;

   209 >  Syntax.string_of_term (thy2ctxt thy) t';

   210 >

   211 >  val t = (term_of o the o (parse thy)) "Nth #2 [#11,#22,#33]";

   212 >  val eval_fn = the (assoc (!eval_list, "Tools.Nth"));

   213 >  val (SOME (id,t')) = get_pair thy "Tools.Nth" eval_fn t;

   214 >  Syntax.string_of_term (thy2ctxt thy) t';

   215 *)

   217 (* val ((op_, eval_fn),ct)=(cc,pre);

   218    (get_calculation_ Isac.thy (op_, eval_fn) ct) handle e => print_exn e;

   219    parse thy ""

   220    *)

   221 (*.get a thm from an op_ somewhere in the term;

   222    apply ONLY to (uminus_to_string term), uminus_to_string (- 4711) --> (-4711).*)

   223 fun get_calculation_ thy (op_, eval_fn) ct =

   224 (* val (thy, (op_, eval_fn),                           ct) =

   225        (thy, (the (assoc(!calclist',"order_system"))), t);

   226    *)

   227   case get_pair thy op_ eval_fn ct of

   228 	 NONE => ((*writeln("@@@ get_calculation: NONE, op_="^op_);

   229 		  writeln("@@@ get_calculation: ct= ");atomty ct;*)

   230 		  NONE)

   231        | SOME (thmid,t) =>

   232 	   ((*writeln("@@@ get_calculation: NONE, op_="^op_);

   233 	    writeln("@@@ get_calculation: ct= ");atomty ct;*)

   234 	    SOME (thmid, (make_thm o (cterm_of thy)) t));

   235 (*

   236 > val ct = (the o (parse thy)) "#9 is_const";

   237 > get_calculation_ thy ("is'_const",the (assoc(!eval_list,"is'_const"))) ct;

   238 val it = SOME ("is_const9_","(is_const 9 ) = True  [(is_const 9 ) = True]")

   240 > val ct = (the o (parse thy)) "sqrt #9";

   241 > get_calculation_ thy ("sqrt",the (assoc(!eval_list,"sqrt"))) ct;

   242 val it = SOME ("sqrt_9_","sqrt 9  = 3  [sqrt 9  = 3]") : (string * thm) option

   244 > val ct = (the o (parse thy)) "#4<#4";

   245 > get_calculation_ thy ("op <",the (assoc(!eval_list,"op <"))) ct;fun is_no str = (hd o explode) str = "#";

   247 val it = SOME ("less_5_4","(5 < 4) = False  [(5 < 4) = False]")

   249 > val ct = (the o (parse thy)) "a<#4";

   250 > get_calculation_ thy ("op <",the (assoc(!eval_list,"op <"))) ct;

   251 val it = NONE : (string * thm) option

   253 > val ct = (the o (parse thy)) "#5<=#4";

   254 > get_calculation_ thy ("op <=",the (assoc(!eval_list,"op <="))) ct;

   255 val it = SOME ("less_equal_5_4","(5 <= 4) = False  [(5 <= 4) = False]")

   257 -------------------------------------------------------------------6.8.02:

   258  val thy = SqRoot.thy;

   259  val t = (term_of o the o (parse thy)) "1+2";

   260  get_calculation_ thy (the(assoc(!calc_list,"PLUS"))) t;

   261  val it = SOME ("add_3_4","3 + 4 = 7  [3 + 4 = 7]") : (string * thm) option

   262 -------------------------------------------------------------------6.8.02:

   263  val t = (term_of o the o (parse thy)) "-1";

   264  atomty t;

   265  val t = (term_of o the o (parse thy)) "0";

   266  atomty t;

   267  val t = (term_of o the o (parse thy)) "1";

   268  atomty t;

   269  val t = (term_of o the o (parse thy)) "2";

   270  atomty t;

   271  val t = (term_of o the o (parse thy)) "999999999";

   272  atomty t;

   273 -------------------------------------------------------------------6.8.02:

   275 > val ct = (the o (parse thy)) "a+#3+#4";

   276 > get_calculation_ thy ("op +",the (assoc(!eval_list,"op +"))) ct;

   277 val it = SOME ("add_3_4","a + 3 + 4 = a + 7  [a + 3 + 4 = a + 7]")

   279 > val ct = (the o (parse thy)) "#3+(#4+a)";

   280 > get_calculation_ thy ("op +",the (assoc(!eval_list,"op +"))) ct;

   281 val it = SOME ("add_3_4","3 + (4 + a) = 7 + a  [3 + (4 + a) = 7 + a]")

   283 > val ct = (the o (parse thy)) "a+(#3+#4)+#5";

   284 > get_calculation_ thy ("op +",the (assoc(!eval_list,"op +"))) ct;

   285 val it = SOME ("add_3_4","3 + 4 = 7  [3 + 4 = 7]") : (string * thm) option

   287 > val ct = (the o (parse thy)) "#3*(#4*a)";

   288 > get_calculation_ thy ("op *",the (assoc(!eval_list,"op *"))) ct;

   289 val it = SOME ("mult_3_4","3 * (4 * a) = 12 * a  [3 * (4 * a) = 12 * a]")

   291 > val ct = (the o (parse thy)) "#3 + #4^^^#2 + #5";

   292 > get_calculation_ thy ("pow",the (assoc(!eval_list,"pow"))) ct;

   293 val it = SOME ("4_(+2)","4 ^ 2 = 16  [4 ^ 2 = 16]") : (string * thm) option

   295 > val ct = (the o (parse thy)) "#-4//#-2";

   296 > get_calculation_ thy ("cancel",the (assoc(!eval_list,"cancel"))) ct;

   297 val it = SOME ("cancel_(-4)_(-2)","(-4) // (-2) = (+2)  [(-4) // (-2) = (+2)]")

   299 > val ct = (the o (parse thy)) "#6//#-8";

   300 > get_calculation_ thy ("cancel",the (assoc(!eval_list,"cancel"))) ct;

   301 val it = SOME ("cancel_6_(-8)","6 // (-8) = (-3) // 4  [6 // (-8) = (-3) // 4]")

   303 *)

   306 (*

   307 > val ct = (the o (parse thy)) "a + 3*4";

   308 > applicable "calculate" (Calc("op *", "mult_")) ct;

   309 val it = SOME "3 * 4 = 12  [3 * 4 = 12]" : thm option

   311 --------------------------

   312 > val ct = (the o (parse thy)) "3 =!= 3";

   313 > val (thmid, thm) = the (get_calculation_ thy "Atools.ident" ct);

   314 val thm = "(3 =!= 3) = True  [(3 =!= 3) = True]" : thm

   316 > val ct = (the o (parse thy)) "~ (3 =!= 3)";

   317 > val (thmid, thm) = the (get_calculation_ thy "Atools.ident" ct);

   318 val thm = "(3 =!= 3) = True  [(3 =!= 3) = True]" : thm

   320 > val ct = (the o (parse thy)) "3 =!= 4";

   321 > val (thmid, thm) = the (get_calculation_ thy "Atools.ident" ct);

   322 val thm = "(3 =!= 4) = False  [(3 =!= 4) = False]" : thm

   324 > val ct = (the o (parse thy)) "( 4 + (4 * x + x ^ 2) =!= (+0))";

   325 > val (thmid, thm) = the (get_calculation_ thy "Atools.ident" ct);

   326   "(4 + (4 * x + x ^ 2) =!= (+0)) = False"

   328 > val ct = (the o (parse thy)) "~ ( 4 + (4 * x + x ^ 2) =!= (+0))";

   329 > val (thmid, thm) = the (get_calculation_ thy "Atools.ident" ct);

   330   "(4 + (4 * x + x ^ 2) =!= (+0)) = False"

   332 > val ct = (the o (parse thy)) "~ ( 4 + (4 * x + x ^ 2) =!= (+0))";

   333 > val rls = eval_rls;

   334 > val (ct,_) = the (rewrite_set_ thy false rls ct);

   335 val ct = "True" : cterm

   336 --------------------------

   337 *)

   340 (*.get a thm applying an op_ to a term;

   341    apply ONLY to (numbers_to_string term), numbers_to_string (- 4711) --> (-4711).*)

   342 (* val (thy, (op_, eval_fn), ct) =

   343        (thy, ("Integrate.add'_new'_c", eval_add_new_c "add_new_c_"), term);

   344    *)

   345 fun get_calculation1_ thy ((op_, eval_fn):cal) ct =

   346     case eval_fn op_ ct thy of

   347 	NONE => NONE

   348       | SOME (thmid,t) =>

   349 	SOME (thmid, (make_thm o (cterm_of thy)) t);

   355 (*.substitute bdv in an rls and leave Calc as they are.(*28.10.02*)

   356 fun inst_thm' subs (Thm (id, thm)) =

   357     Thm (id, (*read_instantiate throws: *** No such variable in term: ?bdv*)

   358 	 (read_instantiate subs thm) handle _ => thm)

   359   | inst_thm' _ calc = calc;

   360 fun inst_thm' (subs as (bdv,_)::_) (Thm (id, thm)) =

   361     Thm (id, (writeln("@@@ inst_thm': thm= "^(string_of_thmI thm));

   362 	      if bdv mem (vars_str o #prop o rep_thm) thm

   363 	     then (writeln("@@@ inst_thm': read_instantiate, thm="^((string_of_thmI thm)));

   364 		   read_instantiate subs thm)

   365 	     else (writeln("@@@ inst_thm': not mem.. "^bdv);

   366 		   thm)))

   367   | inst_thm' _ calc = calc;

   369 fun instantiate_rls subs

   370   (Rls{preconds=preconds,rew_ord=rew_ord,erls=ev,srls=sr,calc=ca,

   371        asm_thm=at,rules=rules,scr=scr}:rls) =

   372   (Rls{preconds=preconds,rew_ord=rew_ord,erls=ev,srls=sr,calc=ca,

   373        asm_thm=at,scr=scr,

   374    rules = map (inst_thm' subs) rules}:rls);---------------------------*)

   378 (** rewriting: ordered, conditional **)

   380 fun mk_rule (prems,l,r) =

   381     Trueprop $ (list_implies (prems, mk_equality (l,r)));

   383 (* 'norms' a rule, e.g.

   384 (*1*) a = 1 ==> a*(b+c) = b+c

   385                 =>  a = 1 ==> a*(b+c) = b+c          no change

   386 (*2*) t = t     =>  (t=t) = True                        !!

   387 (*3*) [| k < l; m + l = k + n |] ==> m < n

   388 	        =>  [| k<l; m+l=k+n |] ==> m < n = True !! *)

   389 (* val it = fn : term -> term *)

   390 fun norm rule =

   391   let

   392     val (prems,concl)=(map strip_trueprop(Logic.strip_imp_prems rule),

   393 		       (strip_trueprop o  Logic.strip_imp_concl)rule)

   394   in if is_equality concl then

   395       let val (l,r) = dest_equals' concl

   396       in if l = r then

   397 	 (*2*) mk_rule(prems,concl,true_as_term)

   398 	 else (*1*) rule end

   399      else (*3*) mk_rule(prems,concl,true_as_term)

   400   end;

author	Walther Neuper <neuper@ist.tugraz.at>
	Wed, 25 Aug 2010 16:20:07 +0200
branch	isac-update-Isa09-2
changeset 37947	22235e4dbe5f
parent 37933	src/Tools/isac/Scripts/calculate.sml@b65c6037eb6d
child 38014	3e11e3c2dc42
permissions	-rw-r--r--