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

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

    41   (* identity on term level*)

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

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

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

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

    46   filter_sameFunId:: "[real, bool list] => bool list" ("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 lhs: term -> term

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

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

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

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

    60     val rhs: term -> term

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

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

    64     val or2list: term -> term

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

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

    67     val occurs_in: term -> term -> bool

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

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

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

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

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

    73     val even: int -> bool

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

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

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

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

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

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

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

    81     val same_funid: term -> term -> bool

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

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

    84     val list2sum: term list -> term

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

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

    88   end

    90 (**)

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

    92 struct

    93 (**)

    95 (*+ for Or_to_List +*)

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

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

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

    99   | or2list ors =

   100     let

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

   102 	        (case o2 of

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

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

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

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

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

   108 > val t' = or2list t;

   109 > term2str t';

   110 "ListC.UniversalList"

   111 > val t = @{term False};

   112 > val t' = or2list t;

   113 > term2str t';

   114 "[]"

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

   116 > val t' = or2list t;

   117 > term2str t';

   118 "[x = 3]"

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

   120 > val t' = or2list t;

   121 > term2str t';

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

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

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

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

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

   130     if TermC.matches thy tst pat

   131     then

   132       let

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

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

   135     else

   136       let

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

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

   139   | eval_matches _ _ _ _ = NONE;

   140 (*

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

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

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

   144 val it =

   145   SOME

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

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

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

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

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

   152 val it =

   153   SOME

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

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

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

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

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

   160 val it =

   161   SOME

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

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

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

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

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

   168 val it =

   169   SOME

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

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

   172 ----- before ?patterns ---:

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

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

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

   176 SOME

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

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

   179   : (string * term) option

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

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

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

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

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

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

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

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

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

   191 *)

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

   194 fun matchsub thy t pat =

   195   let

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

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

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

   199 	      | matchs (Bound _) = false

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

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

   202 	      | matchs (t as f1 $ f2) =

   203 	          if TermC.matches thy t pat then true

   204 	            else if matchs f1 then true else matchs f2

   205   in matchs t end;

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

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

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

   210     if matchsub thy tst pat

   211     then

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

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

   214     else

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

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

   217   | eval_matchsub _ _ _ _ = NONE;

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

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

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

   222     let

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

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

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

   226   | eval_var _ _ _ _ = NONE;

   228 (* refer to Thm.lhs_of *)

   229 fun lhs (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ l $ _) = l

   230   | lhs t = raise ERROR("lhs called with (" ^ UnparseC.term t ^ ")");

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

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

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

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

   235   | eval_lhs _ _ _ _ = NONE;

   236 (*

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

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

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

   240 > term2str t';

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

   242 *)

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

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

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

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

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

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

   250   | eval_rhs _ _ _ _ = NONE;

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

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

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

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

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

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

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

   260      if occurs_in v t

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

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

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

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

   265   | eval_occurs_in _ _ _ _ = NONE;

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

   268 fun some_occur_in vs t =

   269     let fun occurs_in' a b = occurs_in b a

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

   272 (*("some_occur_in", ("Prog_Expr.some_occur_in",

   273 			eval_some_occur_in "#eval_some_occur_in_"))*)

   274 fun eval_some_occur_in _ "Prog_Expr.some_occur_in"

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

   276     if some_occur_in (TermC.isalist2list vs) t

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

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

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

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

   281   | eval_some_occur_in _ _ _ _ = NONE;

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

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

   285     if TermC.is_atom arg

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

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

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

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

   290   | eval_is_atom _ _ _ _ = NONE;

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

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

   294     if TermC.is_num arg

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

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

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

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

   299   | eval_is_num _ _ _ _ = NONE;

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

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

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

   304     if TermC.is_num arg

   305     then

   306       let

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

   308       in

   309 	      if even i

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

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

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

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

   314       end

   315     else NONE

   316   | eval_is_even _ _ _ _ = NONE;

   318 (*("is_const",("Prog_Expr.is_const", Prog_Expr.eval_const "#is_const_"))*)

   319 fun eval_const thmid _ (t as (Const (\<^const_name>\<open>is_const\<close>, _) $ Const ("Partial_Fractions.AA", _))) _ =

   320     (*TODO get rid of this special case*)

   321     SOME (TermC.mk_thmid thmid (UnparseC.term t) "",

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

   323   | eval_const thmid _ (t as (Const (\<^const_name>\<open>is_const\<close>, _) $ Const _)) _ =

   324     SOME (TermC.mk_thmid thmid (UnparseC.term t) "",

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

   326   | eval_const thmid _ (t as (Const (\<^const_name>\<open>is_const\<close>, _) $ n)) _ =

   327 	   if TermC.is_num n

   328 	   then SOME (TermC.mk_thmid thmid (TermC.string_of_num n) "",

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

   330 	   else SOME (TermC.mk_thmid thmid (UnparseC.term n) "",

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

   332   | eval_const _ _ _ _ = NONE;

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

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

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

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

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

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

   341    *)

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

   343   thmid ^ "Float ((" ^

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

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

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

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

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

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

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

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

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

   355       let

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

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

   358       in

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

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

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

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

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

   364       end

   365     else NONE

   366   | eval_equ _ _ _ _ = NONE;

   369 (*evaluate identity

   370 > reflI;

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

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

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

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

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

   377 ----------- thus needs Rule.Eval !

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

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

   380 > UnparseC.term t';

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

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

   384 atomt t; UnparseC.term t;

   385 *** -------------

   386 *** Const ( Not)

   387 *** . Const ( op =)

   388 *** . . Free ( x, )

   389 *** . . Free ( 0, )

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

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

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

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

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

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

   397   if t1 = t2

   398   then SOME (TermC.mk_thmid thmid

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

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

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

   402   else SOME (TermC.mk_thmid thmid

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

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

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

   406   | eval_ident _ _ _ _ = NONE;

   407 (* TODO

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

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

   410 > UnparseC.term t';

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

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

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

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

   415 > UnparseC.term t';

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

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

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

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

   420 > UnparseC.term t';

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

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

   423 *)

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

   427   thus returns False only for atoms *)

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

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

   430   if t1 = t2

   431   then

   432     SOME (TermC.mk_thmid thmid

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

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

   435   else

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

   437       (true, true) =>

   438         if TermC.variable_constant_pair (t1, t2)

   439         then NONE

   440         else SOME (TermC.mk_thmid thmid

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

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

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

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

   446 (*. evaluate HOL.divide .*)

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

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

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

   450       let

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

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

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

   454       in

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

   456         else

   457           let

   458             val res = TermC.mk_frac T res_int;

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

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

   461       end

   462     else NONE

   463   | eval_cancel _ _ _ _ = NONE;

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

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

   467 fun eval_argument_in _ "Prog_Expr.argument_in"

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

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

   470     then

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

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

   473     else NONE

   474   | eval_argument_in _ _ _ _ = NONE;

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

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

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

   479 fun eval_sameFunId _ "Prog_Expr.sameFunId"

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

   481     if f1 = f2

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

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

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

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

   486 | eval_sameFunId _ _ _ _ = NONE;

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

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

   491    as the fst argument;

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

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

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

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

   496 (*("filter_sameFunId" ,("Prog_Expr.filter_sameFunId",

   497 		   eval_filter_sameFunId "Prog_Expr.filter_sameFunId"))*)

   498 fun eval_filter_sameFunId _ "Prog_Expr.filter_sameFunId"

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

   500 			(fid $ _) $ fs) _ =

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

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

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

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

   505 | eval_filter_sameFunId _ _ _ _ = NONE;

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

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

   509   | list2sum [s] = s

   510   | list2sum (s::ss) =

   511     let

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

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

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

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

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

   517     in sum s ss end;

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

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

   521 fun eval_boollist2sum _ "Prog_Expr.boollist2sum"

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

   523     let

   524       val isal = TermC.isalist2list l

   525 	    val lhss = map lhs isal

   526 	    val sum = list2sum lhss

   527     in

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

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

   530     end

   531   | eval_boollist2sum _ _ _ _ = NONE;

   533 (**) end (*struct*)

   534 \<close> text \<open>

   535 open Prog_Expr

   536 \<close> ML \<open>

   537 \<close> ML \<open>

   538 \<close>

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

   541 ML \<open>

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

   543 \<close> ML \<open>

   544 \<close> ML \<open>

   545 \<close>

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

   549 rule_set_knowledge prog_expr = prog_expr

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

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

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

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

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

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

   557 ML \<open>

   558 \<close> ML \<open>

   559 \<close> ML \<open>

   560 \<close>

   562 end

author	wneuper <walther.neuper@jku.at>
	Mon, 02 Aug 2021 11:38:40 +0200
changeset 60343	f6e98785473f
parent 60335	7701598a2182
child 60385	d3a3cc2f0382
permissions	-rw-r--r--