wneuper/isa: src/Tools/isac/ProgLang/Prog

     1 (* title:  ProgLang/Prog_Expr.thy

     2            functions for expressions (which do NOT contain Prog_Tac and Tactical, by definition))

     3    author: Walther Neuper, Aug.2019

     4    (c) copyright due to lincense terms.

     5 *)

     7 theory Prog_Expr

     8   imports Calculate

     9 begin

    11 text \<open>Abstract:

    12   Specific constants are defined for pre-conditions of programs and for program-expressions.

    13   The constants are connected with ML functions for evaluation of respective expressions

    14   (all named eval_*), such that Isac's rewrite engine can handle it.

    15 \<close>

    17 subsection \<open>Power re-defined for a specific type\<close>

    18 consts

    19   pow              :: "[real, real] => real"    (infixr "^^^" 80)

    21 subsection \<open>consts of functions in pre-conditions and program-expressions\<close>

    22 consts

    23   lhs             :: "bool => real"           (*of an equality*)

    24   rhs             :: "bool => real"           (*of an equality*)

    25   Vars            :: "'a => real list"        (*get the variables of a term *)

    26   matches         :: "['a, 'a] => bool"

    27   matchsub        :: "['a, 'a] => bool"

    28   some'_occur'_in  :: "[real list, 'a] => bool" ("some'_of _ occur'_in _")

    29   occurs'_in       :: "[real     , 'a] => bool" ("_ occurs'_in _")

    31   abs              :: "real => real"            ("(|| _ ||)")

    32   (* ~~~ FIXXXME Isabelle2002 has abs already !!!*)

    33   absset           :: "real set => real"        ("(||| _ |||)")

    34   (*is numeral constant ?*)

    35   is'_const        :: "real => bool"            ("_ is'_const" 10)

    36   (*is_const rename to is_num FIXXXME.WN.16.5.03 *)

    37   is'_atom         :: "real => bool"            ("_ is'_atom" 10)

    38   is'_even         :: "real => bool"            ("_ is'_even" 10)

    40   (* identity on term level*)

    41   ident            :: "['a, 'a] => bool"        ("(_ =!=/ _)" [51, 51] 50)

    42   argument'_in     :: "real => real"            ("argument'_in _" 10)

    43   sameFunId        :: "[real, bool] => bool"    (* "same'_funid _ _" 10

    44 	                    WN0609 changed the id, because ".. _ _" inhibits currying *)

    45   filter'_sameFunId:: "[real, bool list] => bool list"

    46 					        ("filter'_sameFunId _ _" 10)

    47   boollist2sum     :: "bool list => real"

    48   lastI            :: "'a list \<Rightarrow> 'a"

    50 subsection \<open>ML code for functions in pre-conditions and program-expressions\<close>

    51 ML \<open>

    52 signature PROG_EXPR =

    53   sig

    54 (*//------------------------- from Tools .thy-------------------------------------------------\\*)

    55     val EmptyList: term

    56     val UniversalList: term

    58     val lhs: term -> term

    59     val eval_lhs: 'a -> string -> term -> 'b -> (string * term) option

    60     val eval_matches: string -> string -> term -> theory -> (string * term) option

    61     val matchsub: theory -> term -> term -> bool

    62     val eval_matchsub: string -> string -> term -> theory -> (string * term) option

    63     val rhs: term -> term

    64     val eval_rhs: 'a -> string -> term -> 'b -> (string * term) option

    65     val eval_var: string -> string -> term -> theory -> (string * term) option

    67     val or2list: term -> term

    68 (*\\------------------------- from Tools .thy-------------------------------------------------//*)

    69 (*//------------------------- from Atools .thy------------------------------------------------\\*)

    70     val occurs_in: term -> term -> bool

    71     val eval_occurs_in: 'a -> string -> term -> 'b -> (string * term) option

    72     val some_occur_in: term list -> term -> bool

    73     val eval_some_occur_in: 'a -> string -> term -> 'b -> (string * term) option

    74     val eval_is_atom: string -> string -> term -> 'a -> (string * term) option

    75     val even: int -> bool

    76     val eval_is_even: string -> string -> term -> 'a -> (string * term) option

    77     val eval_const: string -> string -> term -> 'a -> (string * term) option

    78     val eval_equ: string -> string -> term -> 'a -> (string * term) option

    79     val eval_ident: string -> string -> term -> theory -> (string * term) option

    80     val eval_equal: string -> string -> term -> theory -> (string * term) option

    81     val eval_cancel: string -> string -> term -> 'a -> (string * term) option

    82     val eval_argument_in: string -> string -> term -> 'a -> (string * term) option

    83     val same_funid: term -> term -> bool

    84     val eval_sameFunId: string -> string -> term -> 'a -> (string * term) option

    85     val eval_filter_sameFunId: string -> string -> term -> 'a -> (string * term) option

    86     val list2sum: term list -> term

    87     val eval_boollist2sum: string -> string -> term -> 'a -> (string * term) option

    89     val mk_thmid_f: string -> (int * int) * (int * int) -> (int * int) * (int * int) -> string

    90 (*\\------------------------- from Atools.thy------------------------------------------------//*)

    91   end

    93 (**)

    94 structure Prog_Expr(**): PROG_EXPR =(**)

    95 struct

    96 (**)

    97 (*//------------------------- from Tools .thy-------------------------------------------------\\*)

    98 (* auxiliary functions for scripts  WN.9.00*)

    99 (*11.02: for equation solving only*)

   100 val UniversalList = (Thm.term_of o the o (TermC.parse @{theory})) "UniversalList";

   101 val EmptyList = (Thm.term_of o the o (TermC.parse @{theory}))  "[]::bool list";

   103 (*+ for Or_to_List +*)

   104 fun or2list (Const ("HOL.True",_)) = (tracing"### or2list True";UniversalList)

   105   | or2list (Const ("HOL.False",_)) = (tracing"### or2list False";EmptyList)

   106   | or2list (t as Const ("HOL.eq",_) $ _ $ _) = TermC.list2isalist HOLogic.boolT [t]

   107   | or2list ors =

   108     let

   109       fun get ls (Const ("HOL.disj",_) $ o1 $ o2) =

   110 	        (case o2 of

   111 	         	Const ("HOL.disj",_) $ _ $ _ => get (ls @ [o1]) o2

   112 	        | _ => ls @ [o1, o2])

   113         | get _ t = raise TERM ("or2list: missing pattern in fun.def", [t])

   114     in (((TermC.list2isalist HOLogic.boolT) o (get [])) ors) end

   115 (*>val t = @{term True};

   116 > val t' = or2list t;

   117 > term2str t';

   118 "Prog_Expr.UniversalList"

   119 > val t = @{term False};

   120 > val t' = or2list t;

   121 > term2str t';

   122 "[]"

   123 > val t=(Thm.term_of o the o (parse thy)) "x=3";

   124 > val t' = or2list t;

   125 > term2str t';

   126 "[x = 3]"

   127 > val t=(Thm.term_of o the o (parse thy))"(x=3) | (x=-3) | (x=0)";

   128 > val t' = or2list t;

   129 > term2str t';

   130 "[x = #3, x = #-3, x = #0]" : string *)

   133 (** evaluation on the meta-level **)

   135 (*. evaluate the predicate matches (match on whole term only) .*)

   136 (*("matches",("Prog_Expr.matches", eval_matches "#matches_")):calc*)

   137 fun eval_matches (_:string) "Prog_Expr.matches"

   138 		  (t as Const ("Prog_Expr.matches",_) $ pat $ tst) thy =

   139     if TermC.matches thy tst pat

   140     then

   141       let

   142         val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True}))

   143 	    in SOME (Rule.term_to_string''' thy prop, prop) end

   144     else

   145       let

   146         val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))

   147 	    in SOME (Rule.term_to_string''' thy prop, prop) end

   148   | eval_matches _ _ _ _ = NONE;

   149 (*

   150 > val t  = (Thm.term_of o the o (parse thy))

   151 	      "matches (?x = 0) (1 * x ^^^ 2 = 0)";

   152 > eval_matches "/thmid/" "/op_/" t thy;

   153 val it =

   154   SOME

   155     ("matches (x = 0) (1 * x ^^^ 2 = 0) = False",

   156      Const (#,#) $ (# $ # $ Const #)) : (string * term) option

   158 > val t  = (Thm.term_of o the o (parse thy))

   159 	      "matches (?a = #0) (#1 * x ^^^ #2 = #0)";

   160 > eval_matches "/thmid/" "/op_/" t thy;

   161 val it =

   162   SOME

   163     ("matches (?a = #0) (#1 * x ^^^ #2 = #0) = True",

   164      Const (#,#) $ (# $ # $ Const #)) : (string * term) option

   166 > val t  = (Thm.term_of o the o (parse thy))

   167 	      "matches (?a * x = #0) (#1 * x ^^^ #2 = #0)";

   168 > eval_matches "/thmid/" "/op_/" t thy;

   169 val it =

   170   SOME

   171     ("matches (?a * x = #0) (#1 * x ^^^ #2 = #0) = False",

   172      Const (#,#) $ (# $ # $ Const #)) : (string * term) option

   174 > val t  = (Thm.term_of o the o (parse thy))

   175 	      "matches (?a * x ^^^ #2 = #0) (#1 * x ^^^ #2 = #0)";

   176 > eval_matches "/thmid/" "/op_/" t thy;

   177 val it =

   178   SOME

   179     ("matches (?a * x ^^^ #2 = #0) (#1 * x ^^^ #2 = #0) = True",

   180      Const (#,#) $ (# $ # $ Const #)) : (string * term) option

   181 ----- before ?patterns ---:

   182 > val t  = (Thm.term_of o the o (parse thy))

   183 	      "matches (a * b^^^#2 = c) (#3 * x^^^#2 = #1)";

   184 > eval_matches "/thmid/" "/op_/" t thy;

   185 SOME

   186     ("matches (a * b ^^^ #2 = c) (#3 * x ^^^ #2 = #1) = True",

   187      Const ("HOL.Trueprop","bool => prop") $ (Const # $ (# $ #) $ Const (#,#)))

   188   : (string * term) option

   190 > val t = (Thm.term_of o the o (parse thy))

   191 	      "matches (a * b^^^#2 = c) (#3 * x^^^#2222 = #1)";

   192 > eval_matches "/thmid/" "/op_/" t thy;

   193 SOME ("matches (a * b ^^^ #2 = c) (#3 * x ^^^ #2222 = #1) = False",

   194      Const ("HOL.Trueprop","bool => prop") $ (Const # $ (# $ #) $ Const (#,#)))

   196 > val t = (Thm.term_of o the o (parse thy))

   197                "matches (a = b) (x + #1 + #-1 * #2 = #0)";

   198 > eval_matches "/thmid/" "/op_/" t thy;

   199 SOME ("matches (a = b) (x + #1 + #-1 * #2 = #0) = True",Const # $ (# $ #))

   200 *)

   202 (*.does a pattern match some subterm ?.*)

   203 fun matchsub thy t pat =

   204   let

   205     fun matchs (t as Const _) = TermC.matches thy t pat

   206 	      | matchs (t as Free _) = TermC.matches thy t pat

   207 	      | matchs (t as Var _) = TermC.matches thy t pat

   208 	      | matchs (Bound _) = false

   209 	      | matchs (t as Abs (_, _, body)) =

   210 	          if TermC.matches thy t pat then true else TermC.matches thy body pat

   211 	      | matchs (t as f1 $ f2) =

   212 	          if TermC.matches thy t pat then true

   213 	            else if matchs f1 then true else matchs f2

   214   in matchs t end;

   216 (*("matchsub",("Prog_Expr.matchsub", eval_matchsub "#matchsub_")):calc*)

   217 fun eval_matchsub (_:string) "Prog_Expr.matchsub"

   218 		  (t as Const ("Prog_Expr.matchsub",_) $ pat $ tst) thy =

   219     if matchsub thy tst pat

   220     then

   221       let val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True}))

   222       in SOME (Rule.term_to_string''' thy prop, prop) end

   223     else

   224       let val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))

   225       in SOME (Rule.term_to_string''' thy prop, prop) end

   226   | eval_matchsub _ _ _ _ = NONE;

   228 (*get the variables in an isabelle-term*)

   229 (*("Vars"    ,("Prog_Expr.Vars"    , eval_var "#Vars_")):calc*)

   230 fun eval_var (thmid:string) "Prog_Expr.Vars" (t as (Const _ $ arg)) thy =

   231     let

   232       val t' = ((TermC.list2isalist HOLogic.realT) o TermC.vars) t;

   233       val thmId = thmid ^ Rule.term_to_string''' thy arg;

   234     in SOME (thmId, HOLogic.Trueprop $ (TermC.mk_equality (t, t'))) end

   235   | eval_var _ _ _ _ = NONE;

   237 fun lhs (Const ("HOL.eq",_) $ l $ _) = l

   238   | lhs t = error("lhs called with (" ^ Rule.term2str t ^ ")");

   239 (*("lhs"    ,("Prog_Expr.lhs"    , eval_lhs "")):calc*)

   240 fun eval_lhs _ "Prog_Expr.lhs"

   241 	     (t as (Const ("Prog_Expr.lhs",_) $ (Const ("HOL.eq",_) $ l $ _))) _ =

   242     SOME ((Rule.term2str t) ^ " = " ^ (Rule.term2str l),

   243 	  HOLogic.Trueprop $ (TermC.mk_equality (t, l)))

   244   | eval_lhs _ _ _ _ = NONE;

   245 (*

   246 > val t = (Thm.term_of o the o (parse thy)) "lhs (1 * x ^^^ 2 = 0)";

   247 > val SOME (id,t') = eval_lhs 0 0 t 0;

   248 val id = "Prog_Expr.lhs (1 * x ^^^ 2 = 0) = 1 * x ^^^ 2" : string

   249 > term2str t';

   250 val it = "Prog_Expr.lhs (1 * x ^^^ 2 = 0) = 1 * x ^^^ 2" : string

   251 *)

   253 fun rhs (Const ("HOL.eq",_) $ _ $ r) = r

   254   | rhs t = error("rhs called with (" ^ Rule.term2str t ^ ")");

   255 (*("rhs"    ,("Prog_Expr.rhs"    , eval_rhs "")):calc*)

   256 fun eval_rhs _ "Prog_Expr.rhs"

   257 	     (t as (Const ("Prog_Expr.rhs",_) $ (Const ("HOL.eq",_) $ _ $ r))) _ =

   258     SOME (Rule.term2str t ^ " = " ^ Rule.term2str r,

   259 	  HOLogic.Trueprop $ (TermC.mk_equality (t, r)))

   260   | eval_rhs _ _ _ _ = NONE;

   261 (*\\------------------------- from Prog_Expr.thy-------------------------------------------------//*)

   263 (*//------------------------- from Atools.thy------------------------------------------------\\*)

   264 fun occurs_in v t = member op = (((map strip_thy) o TermC.ids2str) t) (Term.term_name v);

   266 (*("occurs_in", ("Prog_Expr.occurs'_in", Prog_Expr.eval_occurs_in ""))*)

   267 fun eval_occurs_in _ "Prog_Expr.occurs'_in"

   268 	     (p as (Const ("Prog_Expr.occurs'_in",_) $ v $ t)) _ =

   269     ((*tracing("@@@ eval_occurs_in: v= "^(Rule.term2str v));

   270      tracing("@@@ eval_occurs_in: t= "^(Rule.term2str t));*)

   271      if occurs_in v t

   272     then SOME ((Rule.term2str p) ^ " = True",

   273 	  HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))

   274     else SOME ((Rule.term2str p) ^ " = False",

   275 	  HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False}))))

   276   | eval_occurs_in _ _ _ _ = NONE;

   278 (*some of the (bound) variables (eg. in an eqsys) "vs" occur in term "t"*)

   279 fun some_occur_in vs t =

   280     let fun occurs_in' a b = occurs_in b a

   281     in foldl or_ (false, map (occurs_in' t) vs) end;

   283 (*("some_occur_in", ("Prog_Expr.some'_occur'_in",

   284 			eval_some_occur_in "#eval_some_occur_in_"))*)

   285 fun eval_some_occur_in _ "Prog_Expr.some'_occur'_in"

   286 			  (p as (Const ("Prog_Expr.some'_occur'_in",_)

   287 				       $ vs $ t)) _ =

   288     if some_occur_in (TermC.isalist2list vs) t

   289     then SOME ((Rule.term2str p) ^ " = True",

   290 	       HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))

   291     else SOME ((Rule.term2str p) ^ " = False",

   292 	       HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))

   293   | eval_some_occur_in _ _ _ _ = NONE;

   295 (*("is_atom",("Prog_Expr.is'_atom", Prog_Expr.eval_is_atom "#is_atom_"))*)

   296 fun eval_is_atom (thmid:string) "Prog_Expr.is'_atom"

   297 		 (t as (Const _ $ arg)) _ =

   298     (case arg of

   299 	 Free (n,_) => SOME (TermC.mk_thmid thmid n "",

   300 			      HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))

   301        | _ => SOME (TermC.mk_thmid thmid "" "",

   302 		    HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))))

   303   | eval_is_atom _ _ _ _ = NONE;

   305 fun even i = (i div 2) * 2 = i;

   306 (*("is_even",("Prog_Expr.is'_even", eval_is_even "#is_even_"))*)

   307 fun eval_is_even (thmid:string) "Prog_Expr.is'_even"

   308 		 (t as (Const _ $ arg)) _ =

   309     (case arg of

   310 	Free (n,_) =>

   311 	 (case TermC.int_of_str_opt n of

   312 	      SOME i =>

   313 	      if even i then SOME (TermC.mk_thmid thmid n "",

   314 				   HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))

   315 	      else SOME (TermC.mk_thmid thmid "" "",

   316 			 HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))

   317 	    | _ => NONE)

   318        | _ => NONE)

   319   | eval_is_even _ _ _ _ = NONE;

   321 (*evaluate 'is_const'*)

   322 (*("is_const",("Prog_Expr.is'_const", Prog_Expr.eval_const "#is_const_"))*)

   323 fun eval_const (thmid:string) _ (t as (Const _ $ arg)) _ =

   324     (case arg of

   325        Const (n1, _) =>

   326 	     SOME (TermC.mk_thmid thmid n1 "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))

   327      | Free (n1, _) =>

   328 	     if TermC.is_num' n1

   329 	     then SOME (TermC.mk_thmid thmid n1 "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))

   330 	     else SOME (TermC.mk_thmid thmid n1 "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))

   331      | _ => (*NONE*)

   332        SOME (TermC.mk_thmid thmid (Rule.term2str arg) "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))))

   333   | eval_const _ _ _ _ = NONE;

   335 (*. evaluate binary, associative, commutative operators: *,+,^ .*)

   336 (*("PLUS"    ,("Groups.plus_class.plus"        , (**)eval_binop "#add_")),

   337   ("TIMES"   ,("Groups.times_class.times"        , (**)eval_binop "#mult_")),

   338   ("POWER"  ,("Prog_Expr.pow"  , (**)eval_binop "#power_"))*)

   340 (* val (thmid,op_,t as(Const (op0,t0) $ Free (n1,t1) $ Free(n2,t2)),thy) =

   341        ("xxxxxx",op_,t,thy);

   342    *)

   343 fun mk_thmid_f thmid ((v11, v12), (p11, p12)) ((v21, v22), (p21, p22)) = (* dropped *)

   344   thmid ^ "Float ((" ^

   345   (string_of_int v11)^","^(string_of_int v12)^"), ("^

   346   (string_of_int p11)^","^(string_of_int p12)^")) __ (("^

   347   (string_of_int v21)^","^(string_of_int v22)^"), ("^

   348   (string_of_int p21)^","^(string_of_int p22)^"))";

   350 (*.evaluate < and <= for numerals.*)

   351 (*("le"      ,("Orderings.ord_class.less"        , Prog_Expr.eval_equ "#less_")),

   352   ("leq"     ,("Orderings.ord_class.less_eq"       , Prog_Expr.eval_equ "#less_equal_"))*)

   353 fun eval_equ (thmid:string) (_(*op_*)) (t as

   354 	       (Const (op0, _) $ Free (n1, _) $ Free(n2, _))) _ =

   355     (case (TermC.int_of_str_opt n1, TermC.int_of_str_opt n2) of

   356 	 (SOME n1', SOME n2') =>

   357   if Calc.calc_equ (strip_thy op0) (n1', n2')

   358     then SOME (TermC.mk_thmid thmid n1 n2,

   359 	  HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))

   360   else SOME (TermC.mk_thmid thmid n1 n2,

   361 	  HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))

   362        | _ => NONE)

   364   | eval_equ _ _ _ _ = NONE;

   367 (*evaluate identity

   368 > reflI;

   369 val it = "(?t = ?t) = True"

   370 > val t = str2term "x = 0";

   371 > val NONE = rewrite_ thy Rule.dummy_ord Rule.e_rls false reflI t;

   373 > val t = str2term "1 = 0";

   374 > val NONE = rewrite_ thy Rule.dummy_ord Rule.e_rls false reflI t;

   375 ----------- thus needs Rule.Calc !

   376 > val t = str2term "0 = 0";

   377 > val SOME (t',_) = rewrite_ thy Rule.dummy_ord Rule.e_rls false reflI t;

   378 > Rule.term2str t';

   379 val it = "HOL.True"

   381 val t = str2term "Not (x = 0)";

   382 atomt t; Rule.term2str t;

   383 *** -------------

   384 *** Const ( Not)

   385 *** . Const ( op =)

   386 *** . . Free ( x, )

   387 *** . . Free ( 0, )

   388 val it = "x ~= 0" : string*)

   390 (*.evaluate identity on the term-level, =!= ,i.e. without evaluation of

   391   the arguments: thus special handling by 'fun eval_binop'*)

   392 (*("ident"   ,("Prog_Expr.ident", Prog_Expr.eval_ident "#ident_")):calc*)

   393 fun eval_ident (thmid:string) "Prog_Expr.ident" (t as

   394 	       (Const _(*op0, t0*) $ t1 $ t2 )) thy =

   395   if t1 = t2

   396   then SOME (TermC.mk_thmid thmid

   397 	              ("(" ^ (Rule.term_to_string''' thy t1) ^ ")")

   398 	              ("(" ^ (Rule.term_to_string''' thy t2) ^ ")"),

   399 	     HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))

   400   else SOME (TermC.mk_thmid thmid

   401 	              ("(" ^ (Rule.term_to_string''' thy t1) ^ ")")

   402 	              ("(" ^ (Rule.term_to_string''' thy t2) ^ ")"),

   403 	     HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))

   404   | eval_ident _ _ _ _ = NONE;

   405 (* TODO

   406 > val t = str2term "x =!= 0";

   407 > val SOME (str, t') = eval_ident "ident_" "b" t thy;

   408 > Rule.term2str t';

   409 val str = "ident_(x)_(0)" : string

   410 val it = "(x =!= 0) = False" : string

   411 > val t = str2term "1 =!= 0";

   412 > val SOME (str, t') = eval_ident "ident_" "b" t thy;

   413 > Rule.term2str t';

   414 val str = "ident_(1)_(0)" : string

   415 val it = "(1 =!= 0) = False" : string

   416 > val t = str2term "0 =!= 0";

   417 > val SOME (str, t') = eval_ident "ident_" "b" t thy;

   418 > Rule.term2str t';

   419 val str = "ident_(0)_(0)" : string

   420 val it = "(0 =!= 0) = True" : string

   421 *)

   423 (*.evaluate identity of terms, which stay ready for evaluation in turn;

   424   thus returns False only for atoms.*)

   425 (*("equal"   ,("HOL.eq", Prog_Expr.eval_equal "#equal_")):calc*)

   426 fun eval_equal (thmid : string) "HOL.eq" (t as (Const _(*op0,t0*) $ t1 $ t2 )) thy =

   427   if t1 = t2

   428   then SOME (TermC.mk_thmid thmid

   429                 ("(" ^ Rule.term_to_string''' thy t1 ^ ")")

   430                 ("(" ^ Rule.term_to_string''' thy t2 ^ ")"),

   431        HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))

   432   else (case (TermC.is_atom t1, TermC.is_atom t2) of

   433       (true, true) =>

   434       SOME (TermC.mk_thmid thmid

   435          ("(" ^ Rule.term_to_string''' thy t1 ^ ")")

   436          ("(" ^ Rule.term_to_string''' thy t2 ^ ")"),

   437       HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))

   438     | _ => NONE)                             (* NOT is_atom t1,t2 --> rew_sub *)

   439   | eval_equal _ _ _ _ = NONE;                                  (* error-exit *)

   440 (*

   441 val t = str2term "x ~= 0";

   442 val NONE = eval_equal "equal_" "b" t thy;

   445 > val t = str2term "(x + 1) = (x + 1)";

   446 > val SOME (str, t') = eval_equal "equal_" "b" t thy;

   447 > Rule.term2str t';

   448 val str = "equal_(x + 1)_(x + 1)" : string

   449 val it = "(x + 1 = x + 1) = True" : string

   450 > val t = str2term "x = 0";

   451 > val NONE = eval_equal "equal_" "b" t thy;

   453 > val t = str2term "1 = 0";

   454 > val SOME (str, t') = eval_equal "equal_" "b" t thy;

   455 > Rule.term2str t';

   456 val str = "equal_(1)_(0)" : string

   457 val it = "(1 = 0) = False" : string

   458 > val t = str2term "0 = 0";

   459 > val SOME (str, t') = eval_equal "equal_" "b" t thy;

   460 > Rule.term2str t';

   461 val str = "equal_(0)_(0)" : string

   462 val it = "(0 = 0) = True" : string

   463 *)

   465 (*. evaluate HOL.divide .*)

   466 (*("DIVIDE" ,("Rings.divide_class.divide"  , eval_cancel "#divide_e"))*)

   467 fun eval_cancel (thmid: string) "Rings.divide_class.divide" (t as

   468 	       (Const (op0,t0) $ Free (n1, _) $ Free(n2, _))) _ =

   469     (case (TermC.int_of_str_opt n1, TermC.int_of_str_opt n2) of

   470     	(SOME n1', SOME n2') =>

   471         let

   472           val sg = Calc.sign_mult n1' n2';

   473           val (T1,T2,Trange) = TermC.dest_binop_typ t0;

   474           val gcd' = Calc.gcd (abs n1') (abs n2');

   475         in if gcd' = abs n2'

   476            then let val rhs = TermC.term_of_num Trange (sg * (abs n1') div gcd')

   477     	        val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, rhs))

   478     	    in SOME (TermC.mk_thmid thmid n1 n2, prop) end

   479            else if 0 < n2' andalso gcd' = 1 then NONE

   480            else let val rhs = TermC.mk_num_op_num T1 T2 (op0,t0) (sg * (abs n1') div gcd')

   481     	  			   ((abs n2') div gcd')

   482     	        val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, rhs))

   483     	    in SOME (TermC.mk_thmid thmid n1 n2, prop) end

   484         end

   485       | _ => ((*tracing"@@@ eval_cancel NONE";*)NONE))

   486   | eval_cancel _ _ _ _ = NONE;

   488 (* get the argument from a function-definition *)

   489 (*("argument_in" ,("Prog_Expr.argument'_in", Prog_Expr.eval_argument_in "Prog_Expr.argument'_in"))*)

   490 fun eval_argument_in _ "Prog_Expr.argument'_in"

   491 		 (t as (Const ("Prog_Expr.argument'_in", _) $ (_(*f*) $ arg))) _ =

   492     if is_Free arg (*could be something to be simplified before*)

   493     then

   494       SOME (Rule.term2str t ^ " = " ^ Rule.term2str arg,

   495 	      HOLogic.Trueprop $ (TermC.mk_equality (t, arg)))

   496     else NONE

   497   | eval_argument_in _ _ _ _ = NONE;

   499 (* check if the function-identifier of the first argument matches

   500    the function-identifier of the lhs of the second argument *)

   501 (*("sameFunId" ,("Prog_Expr.sameFunId", eval_same_funid "Prog_Expr.sameFunId"))*)

   502 fun eval_sameFunId _ "Prog_Expr.sameFunId"

   503 		     (p as Const ("Prog_Expr.sameFunId",_) $  (f1 $ _) $ (Const ("HOL.eq", _) $ (f2 $ _) $ _)) _ =

   504     if f1 = f2

   505     then SOME ((Rule.term2str p) ^ " = True",

   506 	       HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))

   507     else SOME ((Rule.term2str p) ^ " = False",

   508 	       HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))

   509 | eval_sameFunId _ _ _ _ = NONE;

   512 (*.from a list of fun-definitions "f x = ..." as 2nd argument

   513    filter the elements with the same fun-identfier in "f y"

   514    as the fst argument;

   515    this is, because Isabelles filter takes more than 1 sec.*)

   516 fun same_funid f1 (Const ("HOL.eq", _) $ (f2 $ _) $ _) = f1 = f2

   517   | same_funid f1 t = error ("same_funid called with t = ("

   518 				   ^Rule.term2str f1^") ("^Rule.term2str t^")");

   519 (*("filter_sameFunId" ,("Prog_Expr.filter'_sameFunId",

   520 		   eval_filter_sameFunId "Prog_Expr.filter'_sameFunId"))*)

   521 fun eval_filter_sameFunId _ "Prog_Expr.filter'_sameFunId"

   522 		     (p as Const ("Prog_Expr.filter'_sameFunId",_) $

   523 			(fid $ _) $ fs) _ =

   524     let val fs' = ((TermC.list2isalist HOLogic.boolT) o

   525 		   (filter (same_funid fid))) (TermC.isalist2list fs)

   526     in SOME (Rule.term2str (TermC.mk_equality (p, fs')),

   527 	       HOLogic.Trueprop $ (TermC.mk_equality (p, fs'))) end

   528 | eval_filter_sameFunId _ _ _ _ = NONE;

   530 (* make a list of terms to a sum *)

   531 fun list2sum [] = error ("list2sum called with []")

   532   | list2sum [s] = s

   533   | list2sum (s::ss) =

   534     let

   535       fun sum su [s'] = Const ("Groups.plus_class.plus",

   536            [HOLogic.realT,HOLogic.realT] ---> HOLogic.realT) $ su $ s'

   537     	  | sum su (s'::ss') = sum (Const ("Groups.plus_class.plus",

   538            [HOLogic.realT,HOLogic.realT] ---> HOLogic.realT) $ su $ s') ss'

   539     	  | sum _ _ = raise ERROR "list2sum: pattern in fun.def is missing"

   540     in sum s ss end;

   542 (* make a list of equalities to the sum of the lhs *)

   543 (*("boollist2sum"    ,("Prog_Expr.boollist2sum"    , eval_boollist2sum "")):calc*)

   544 fun eval_boollist2sum _ "Prog_Expr.boollist2sum"

   545 		  (p as Const ("Prog_Expr.boollist2sum", _) $ (l as Const ("List.list.Cons", _) $ _ $ _)) _ =

   546     let

   547       val isal = TermC.isalist2list l

   548 	    val lhss = map lhs isal

   549 	    val sum = list2sum lhss

   550     in

   551       SOME ((Rule.term2str p) ^ " = " ^ (Rule.term2str sum),

   552 	      HOLogic.Trueprop $ (TermC.mk_equality (p, sum)))

   553     end

   554   | eval_boollist2sum _ _ _ _ = NONE;

   556 (**) end (*struct*)

   557 \<close> text \<open>

   558 open Prog_Expr

   559 \<close> ML \<open>

   560 \<close> ML \<open>

   561 \<close>

   563 subsection \<open>extend rule-set for evaluating pre-conditions and program-expressions\<close>

   564 ML \<open>

   565 val list_rls = Rule.append_rls "list_rls" list_rls [Rule.Calc ("Prog_Expr.rhs", Prog_Expr.eval_rhs "")];

   566 \<close> ML \<open>

   567 \<close> ML \<open>

   568 \<close>

   570 subsection \<open>setup for rule-sets and ML-functions\<close>

   571 setup \<open>KEStore_Elems.add_rlss [("list_rls", (Context.theory_name @{theory}, list_rls))]\<close>

   572 setup \<open>KEStore_Elems.add_calcs

   573   [("matches", ("Prog_Expr.matches", Prog_Expr.eval_matches "#matches_")),

   574     ("matchsub", ("Prog_Expr.matchsub", Prog_Expr.eval_matchsub "#matchsub_")),

   575     ("Vars", ("Prog_Expr.Vars", Prog_Expr.eval_var "#Vars_")),

   576     ("lhs", ("Prog_Expr.lhs", Prog_Expr.eval_lhs "")),

   577     ("rhs", ("Prog_Expr.rhs", Prog_Expr.eval_rhs ""))]\<close>

   578 (*\\------------------------- from Tools .thy-------------------------------------------------//*)

   579 ML \<open>

   580 \<close> ML \<open>

   581 \<close> ML \<open>

   582 \<close>

   584 end

author	Walther Neuper <walther.neuper@jku.at>
	Sat, 14 Sep 2019 16:15:05 +0200
changeset 59619	a2f67c777ccd
parent 59618	80efccb7e5c1
child 59620	086e4d9967a3
permissions	-rw-r--r--