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 ListC Program

     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 abbreviation real_powr :: "real \<Rightarrow> real \<Rightarrow> real"  (infixr "\<up>" 80)

    19 where "x \<up> a \<equiv> x powr a"

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

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

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

    38   (* identity on term level*)

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

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

    41   sameFunId        :: "[real, bool] => bool"    (* "same_funid _ _" 10

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

    43   filter_sameFunId:: "[real, bool list] => bool list" ("filter'_sameFunId _ _" 10)

    44   boollist2sum     :: "bool list => real"

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

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

    48 ML \<open>

    49 signature PROG_EXPR =

    50   sig

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

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

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

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

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

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

    58     val or2list: term -> term

    60     val occurs_in: term -> term -> bool

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

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

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

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

    65     val eval_is_num: string -> string -> term -> 'a -> (string * term) option

    66     val even: int -> bool

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

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

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

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

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

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

    73     val same_funid: term -> term -> bool

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

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

    76     val list2sum: term list -> term

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

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

    80   end

    82 (**)

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

    84 struct

    85 (**)

    87 (*+ for Or_to_List +*)

    88 fun or2list (Const (\<^const_name>\<open>True\<close>,_)) = ((*tracing"### or2list True";*) UniversalList)

    89   | or2list (Const (\<^const_name>\<open>False\<close>,_)) = ((*tracing"### or2list False";*) EmptyList)

    90   | or2list (t as Const (\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ _) = TermC.list2isalist HOLogic.boolT [t]

    91   | or2list ors =

    92     let

    93       fun get ls (Const (\<^const_name>\<open>disj\<close>,_) $ o1 $ o2) =

    94 	        (case o2 of

    95 	         	Const (\<^const_name>\<open>disj\<close>,_) $ _ $ _ => get (ls @ [o1]) o2

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

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

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

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

   100 > val t' = or2list t;

   101 > term2str t';

   102 "ListC.UniversalList"

   103 > val t = @{term False};

   104 > val t' = or2list t;

   105 > term2str t';

   106 "[]"

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

   108 > val t' = or2list t;

   109 > term2str t';

   110 "[x = 3]"

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

   112 > val t' = or2list t;

   113 > term2str t';

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

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

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

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

   121 fun eval_matches (_:string) "Prog_Expr.matches" (t as Const (\<^const_name>\<open>Prog_Expr.matches\<close>, _) $ pat $ tst) thy =

   122     if TermC.matches thy tst pat

   123     then

   124       let

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

   126 	    in SOME (UnparseC.term_in_thy thy prop, prop) end

   127     else

   128       let

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

   130 	    in SOME (UnparseC.term_in_thy thy prop, prop) end

   131   | eval_matches _ _ _ _ = NONE;

   132 (*

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

   134 	      "matches (?x = 0) (1 * x \<up> 2 = 0)";

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

   136 val it =

   137   SOME

   138     ("matches (x = 0) (1 * x \<up> 2 = 0) = False",

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

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

   142 	      "matches (?a = #0) (#1 * x \<up> #2 = #0)";

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

   144 val it =

   145   SOME

   146     ("matches (?a = #0) (#1 * x \<up> #2 = #0) = True",

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

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

   150 	      "matches (?a * x = #0) (#1 * x \<up> #2 = #0)";

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

   152 val it =

   153   SOME

   154     ("matches (?a * x = #0) (#1 * x \<up> #2 = #0) = False",

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

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

   158 	      "matches (?a * x \<up> #2 = #0) (#1 * x \<up> #2 = #0)";

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

   160 val it =

   161   SOME

   162     ("matches (?a * x \<up> #2 = #0) (#1 * x \<up> #2 = #0) = True",

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

   164 ----- before ?patterns ---:

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

   166 	      "matches (a * b \<up> #2 = c) (#3 * x \<up> #2 = #1)";

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

   168 SOME

   169     ("matches (a * b \<up> #2 = c) (#3 * x \<up> #2 = #1) = True",

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

   171   : (string * term) option

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

   174 	      "matches (a * b \<up> #2 = c) (#3 * x \<up> #2222 = #1)";

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

   176 SOME ("matches (a * b \<up> #2 = c) (#3 * x \<up> #2222 = #1) = False",

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

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

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

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

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

   183 *)

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

   186 fun matchsub thy t pat =

   187   let

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

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

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

   191 	      | matchs (Bound _) = false

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

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

   194 	      | matchs (t as f1 $ f2) =

   195 	          if TermC.matches thy t pat then true

   196 	            else if matchs f1 then true else matchs f2

   197   in matchs t end;

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

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

   201       (t as Const (\<^const_name>\<open>Prog_Expr.matchsub\<close>, _) $ pat $ tst) thy =

   202     if matchsub thy tst pat

   203     then

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

   205       in SOME (UnparseC.term_in_thy thy prop, prop) end

   206     else

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

   208       in SOME (UnparseC.term_in_thy thy prop, prop) end

   209   | eval_matchsub _ _ _ _ = NONE;

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

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

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

   214     let

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

   216       val thmId = thmid ^ UnparseC.term_in_thy thy arg;

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

   218   | eval_var _ _ _ _ = NONE;

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

   221 fun eval_lhs _ "Prog_Expr.lhs" (t as (Const (\<^const_name>\<open>lhs\<close>,_) $ (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ l $ _))) _ =

   222     SOME ((UnparseC.term t) ^ " = " ^ (UnparseC.term l),

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

   224   | eval_lhs _ _ _ _ = NONE;

   225 (*

   226 > val t = (Thm.term_of o the o (parse thy)) "lhs (1 * x \<up> 2 = 0)";

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

   228 val id = "Prog_Expr.lhs (1 * x \<up> 2 = 0) = 1 * x \<up> 2" : string

   229 > term2str t';

   230 val it = "Prog_Expr.lhs (1 * x \<up> 2 = 0) = 1 * x \<up> 2" : string

   231 *)

   233 fun rhs (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ r) = r

   234   | rhs t = raise ERROR("rhs called with (" ^ UnparseC.term t ^ ")");

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

   236 fun eval_rhs _ "Prog_Expr.rhs" (t as (Const (\<^const_name>\<open>rhs\<close>,_) $ (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ r))) _ =

   237     SOME (UnparseC.term t ^ " = " ^ UnparseC.term r,

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

   239   | eval_rhs _ _ _ _ = NONE;

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

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

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

   245 (*("occurs_in", ("Prog_Expr.occurs_in", Prog_Expr.eval_occurs_in ""))*)

   246 fun eval_occurs_in _ "Prog_Expr.occurs_in" (p as (Const (\<^const_name>\<open>occurs_in\<close>, _) $ v $ t)) _ =

   247     ((*tracing("#>@ eval_occurs_in: v= "^(UnparseC.term v));

   248      tracing("#>@ eval_occurs_in: t= "^(UnparseC.term t));*)

   249      if occurs_in v t

   250     then SOME ((UnparseC.term p) ^ " = True",

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

   252     else SOME ((UnparseC.term p) ^ " = False",

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

   254   | eval_occurs_in _ _ _ _ = NONE;

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

   257 fun some_occur_in vs t =

   258     let fun occurs_in' a b = occurs_in b a

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

   261 (*("some_occur_in", ("Prog_Expr.some_occur_in",

   262 			eval_some_occur_in "#eval_some_occur_in_"))*)

   263 fun eval_some_occur_in _ "Prog_Expr.some_occur_in"

   264 			  (p as (Const (\<^const_name>\<open>some_occur_in\<close>,_) $ vs $ t)) _ =

   265     if some_occur_in (TermC.isalist2list vs) t

   266     then SOME ((UnparseC.term p) ^ " = True",

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

   268     else SOME ((UnparseC.term p) ^ " = False",

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

   270   | eval_some_occur_in _ _ _ _ = NONE;

   272 (*("is_atom",("Prog_Expr.is_atom", Prog_Expr.eval_is_atom "#is_atom_"))*)

   273 fun eval_is_atom (thmid:string) "Prog_Expr.is_atom" (t as (Const _ $ arg)) _ =

   274     if TermC.is_atom arg

   275     then SOME (TermC.mk_thmid thmid (TermC.string_of_atom arg) "",

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

   277     else SOME (TermC.mk_thmid thmid (TermC.string_of_atom arg) "",

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

   279   | eval_is_atom _ _ _ _ = NONE;

   281 (*("is_num",("Prog_Expr.is_num", Prog_Expr.eval_is_num "#is_num_"))*)

   282 fun eval_is_num (thmid:string) "Prog_Expr.is_num" (t as (Const _ $ arg)) _ =

   283     if TermC.is_num arg

   284     then SOME (TermC.mk_thmid thmid (TermC.string_of_atom arg) "",

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

   286     else SOME (TermC.mk_thmid thmid (TermC.string_of_atom arg) "",

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

   288   | eval_is_num _ _ _ _ = NONE;

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

   291 (*("is_even",("Prog_Expr.is_even", eval_is_even "#is_even_"))*)

   292 fun eval_is_even (thmid:string) "Prog_Expr.is_even" (t as (Const _ $ arg)) _ =

   293     if TermC.is_num arg

   294     then

   295       let

   296         val i = arg |> HOLogic.dest_number |> snd

   297       in

   298 	      if even i

   299         then SOME (TermC.mk_thmid thmid (string_of_int i) "",

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

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

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

   303       end

   304     else NONE

   305   | eval_is_even _ _ _ _ = NONE;

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

   308 (*("PLUS"    ,(\<^const_name>\<open>plus\<close>        , (**)eval_binop "#add_")),

   309   ("TIMES"   ,(\<^const_name>\<open>times\<close>        , (**)eval_binop "#mult_")),

   310   ("POWER"  ,(\<^const_name>\<open>powr\<close>  , (**)eval_binop "#power_"))*)

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

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

   314    *)

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

   316   thmid ^ "Float ((" ^

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

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

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

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

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

   323 (*("le"      ,(\<^const_name>\<open>less\<close>        , Prog_Expr.eval_equ "#less_")),

   324   ("leq"     ,(\<^const_name>\<open>less_eq\<close>       , Prog_Expr.eval_equ "#less_equal_"))*)

   326 fun eval_equ (thmid:string) (_(*op_*)) (t as (Const (op0, _)) $ t1 $ t2) _ =

   327     if TermC.is_num t1 andalso TermC.is_num t2 then

   328       let

   329         val n1 = t1 |> HOLogic.dest_number |> snd

   330         val n2 = t2 |> HOLogic.dest_number |> snd

   331       in

   332         if Eval.calc_equ (strip_thy op0) (n1, n2)

   333         then SOME (TermC.mk_thmid thmid (string_of_int n1) (string_of_int n2),

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

   335         else SOME (TermC.mk_thmid thmid (string_of_int n1) (string_of_int n2),

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

   337       end

   338     else NONE

   339   | eval_equ _ _ _ _ = NONE;

   342 (*evaluate identity

   343 > reflI;

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

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

   346 > val NONE = rewrite_ thy Rewrite_Ord.dummy_ord Rule_Set.empty false reflI t;

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

   349 > val NONE = rewrite_ thy Rewrite_Ord.dummy_ord Rule_Set.empty false reflI t;

   350 ----------- thus needs Rule.Eval !

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

   352 > val SOME (t',_) = rewrite_ thy Rewrite_Ord.dummy_ord Rule_Set.empty false reflI t;

   353 > UnparseC.term t';

   354 val it = \<^const_name>\<open>True\<close>

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

   357 atomt t; UnparseC.term t;

   358 *** -------------

   359 *** Const ( Not)

   360 *** . Const ( op =)

   361 *** . . Free ( x, )

   362 *** . . Free ( 0, )

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

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

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

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

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

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

   370   if t1 = t2

   371   then SOME (TermC.mk_thmid thmid

   372 	              ("(" ^ (UnparseC.term_in_thy thy t1) ^ ")")

   373 	              ("(" ^ (UnparseC.term_in_thy thy t2) ^ ")"),

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

   375   else SOME (TermC.mk_thmid thmid

   376 	              ("(" ^ (UnparseC.term_in_thy thy t1) ^ ")")

   377 	              ("(" ^ (UnparseC.term_in_thy thy t2) ^ ")"),

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

   379   | eval_ident _ _ _ _ = NONE;

   380 (* TODO

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

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

   383 > UnparseC.term t';

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

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

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

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

   388 > UnparseC.term t';

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

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

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

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

   393 > UnparseC.term t';

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

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

   396 *)

   399 (* evaluate identity of terms, which stay ready for further evaluation;

   400   thus returns False only for atoms *)

   401 (*("equal"   ,(\<^const_name>\<open>HOL.eq\<close>, Prog_Expr.eval_equal "#equal_")):calc*)

   402 fun eval_equal (thmid : string) \<^const_name>\<open>HOL.eq\<close> (t as (Const _(*op0,t0*) $ t1 $ t2 )) thy =

   403   if t1 = t2

   404   then

   405     SOME (TermC.mk_thmid thmid

   406       ("(" ^ UnparseC.term_in_thy thy t1 ^ ")") ("(" ^ UnparseC.term_in_thy thy t2 ^ ")"),

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

   408   else

   409     (case (TermC.is_atom t1, TermC.is_atom t2) of

   410       (true, true) =>

   411         if TermC.variable_constant_pair (t1, t2)

   412         then NONE

   413         else SOME (TermC.mk_thmid thmid

   414           ("(" ^ UnparseC.term_in_thy thy t1 ^ ")") ("(" ^ UnparseC.term_in_thy thy t2 ^ ")"),

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

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

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

   419 (*. evaluate HOL.divide .*)

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

   421 fun eval_cancel thmid "Rings.divide_class.divide" (t as (Const _ $ t1 $ t2)) _ =

   422     if TermC.is_num t1 andalso TermC.is_num t2 then

   423       let

   424         val (T, _) = HOLogic.dest_number t1;

   425         val (i1, i2) = (Eval.int_of_numeral t1, Eval.int_of_numeral t2);

   426         val res_int as (_, (i1', i2')) = Eval.cancel_int (i1, i2);

   427       in

   428         if (i1', i2') = (i1, i2) then NONE

   429         else

   430           let

   431             val res = TermC.mk_frac T res_int;

   432             val prop = HOLogic.Trueprop $ (HOLogic.mk_eq (t, res));

   433           in SOME (TermC.mk_thmid thmid (string_of_int i1) (string_of_int i2), prop) end

   434       end

   435     else NONE

   436   | eval_cancel _ _ _ _ = NONE;

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

   439 (*("argument_in" ,("Prog_Expr.argument_in", Prog_Expr.eval_argument_in "Prog_Expr.argument_in"))*)

   440 fun eval_argument_in _ "Prog_Expr.argument_in"

   441 		 (t as (Const ("Prog_Expr.argument_in", _) $ (_(*f*) $ arg))) _ =

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

   443     then

   444       SOME (UnparseC.term t ^ " = " ^ UnparseC.term arg,

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

   446     else NONE

   447   | eval_argument_in _ _ _ _ = NONE;

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

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

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

   452 fun eval_sameFunId _ "Prog_Expr.sameFunId"

   453 		     (p as Const ("Prog_Expr.sameFunId",_) $  (f1 $ _) $ (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ (f2 $ _) $ _)) _ =

   454     if f1 = f2

   455     then SOME ((UnparseC.term p) ^ " = True",

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

   457     else SOME ((UnparseC.term p) ^ " = False",

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

   459 | eval_sameFunId _ _ _ _ = NONE;

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

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

   464    as the fst argument;

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

   466 fun same_funid f1 (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ (f2 $ _) $ _) = f1 = f2

   467   | same_funid f1 t = raise ERROR ("same_funid called with t = ("

   468 		  ^ UnparseC.term f1 ^ ") (" ^ UnparseC.term t ^ ")");

   469 (*("filter_sameFunId" ,("Prog_Expr.filter_sameFunId",

   470 		   eval_filter_sameFunId "Prog_Expr.filter_sameFunId"))*)

   471 fun eval_filter_sameFunId _ "Prog_Expr.filter_sameFunId"

   472 		     (p as Const ("Prog_Expr.filter_sameFunId",_) $

   473 			(fid $ _) $ fs) _ =

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

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

   476     in SOME (UnparseC.term (TermC.mk_equality (p, fs')),

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

   478 | eval_filter_sameFunId _ _ _ _ = NONE;

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

   481 fun list2sum [] = raise ERROR ("list2sum called with []")

   482   | list2sum [s] = s

   483   | list2sum (s::ss) =

   484     let

   485       fun sum su [s'] = Const (\<^const_name>\<open>plus\<close>,

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

   487     	  | sum su (s'::ss') = sum (Const (\<^const_name>\<open>plus\<close>,

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

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

   490     in sum s ss end;

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

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

   494 fun eval_boollist2sum _ "Prog_Expr.boollist2sum"

   495 		  (p as Const ("Prog_Expr.boollist2sum", _) $ (l as Const (\<^const_name>\<open>Cons\<close>, _) $ _ $ _)) _ =

   496     let

   497       val isal = TermC.isalist2list l

   498 	    val lhss = map TermC.lhs isal

   499 	    val sum = list2sum lhss

   500     in

   501       SOME ((UnparseC.term p) ^ " = " ^ (UnparseC.term sum),

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

   503     end

   504   | eval_boollist2sum _ _ _ _ = NONE;

   506 (**) end (*struct*)

   507 \<close> text \<open>

   508 open Prog_Expr

   509 \<close> ML \<open>

   510 \<close> ML \<open>

   511 \<close>

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

   514 ML \<open>

   515 val prog_expr = Rule_Set.append_rules "prog_expr" prog_expr [\<^rule_eval>\<open>Prog_Expr.rhs\<close> (Prog_Expr.eval_rhs "")];

   516 \<close> ML \<open>

   517 \<close> ML \<open>

   518 \<close>

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

   522 rule_set_knowledge prog_expr = prog_expr

   524 calculation lhs = \<open>Prog_Expr.eval_lhs ""\<close>

   525 calculation rhs = \<open>Prog_Expr.eval_rhs ""\<close>

   526 calculation Vars = \<open>Prog_Expr.eval_var "#Vars_"\<close>

   527 calculation matches = \<open>Prog_Expr.eval_matches "#matches_"\<close>

   528 calculation matchsub = \<open>Prog_Expr.eval_matchsub "#matchsub_"\<close>

   530 calculation some_occur_in = \<open>Prog_Expr.eval_some_occur_in "#some_occur_in_"\<close>

   531 calculation occurs_in = \<open>Prog_Expr.eval_occurs_in "#occurs_in_"\<close>

   532 calculation is_atom = \<open>Prog_Expr.eval_is_atom "#is_atom_"\<close>

   533 calculation is_num = \<open>Prog_Expr.eval_is_num "#is_num_"\<close>

   534 calculation is_even = \<open>Prog_Expr.eval_is_even "#is_even_"\<close>

   535 ML \<open>

   536 \<close> ML \<open>

   537 \<close> ML \<open>

   538 \<close>

   540 end

author	wneuper <walther.neuper@jku.at>
	Sun, 22 Aug 2021 14:28:38 +0200
changeset 60391	a95071158185
parent 60387	8e46f61fdb15
child 60392	e9a69b881f22
permissions	-rw-r--r--