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

    52     val lhs: term -> term

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

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

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

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

    57     val rhs: term -> term

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

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

    61     val or2list: term -> term

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

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

    64     val occurs_in: term -> term -> bool

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

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

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

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

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

    70     val even: int -> bool

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

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

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

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

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

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

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

    78     val same_funid: term -> term -> bool

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

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

    81     val list2sum: term list -> term

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

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

    85   end

    87 (**)

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

    89 struct

    90 (**)

    92 (*+ for Or_to_List +*)

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

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

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

    96   | or2list ors =

    97     let

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

    99 	        (case o2 of

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

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

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

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

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

   105 > val t' = or2list t;

   106 > term2str t';

   107 "ListC.UniversalList"

   108 > val t = @{term False};

   109 > val t' = or2list t;

   110 > term2str t';

   111 "[]"

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

   113 > val t' = or2list t;

   114 > term2str t';

   115 "[x = 3]"

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

   117 > val t' = or2list t;

   118 > term2str t';

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

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

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

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

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

   127     if TermC.matches thy tst pat

   128     then

   129       let

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

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

   132     else

   133       let

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

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

   136   | eval_matches _ _ _ _ = NONE;

   137 (*

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

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

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

   141 val it =

   142   SOME

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

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

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

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

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

   149 val it =

   150   SOME

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

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

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

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

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

   157 val it =

   158   SOME

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

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

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

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

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

   165 val it =

   166   SOME

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

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

   169 ----- before ?patterns ---:

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

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

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

   173 SOME

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

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

   176   : (string * term) option

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

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

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

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

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

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

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

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

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

   188 *)

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

   191 fun matchsub thy t pat =

   192   let

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

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

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

   196 	      | matchs (Bound _) = false

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

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

   199 	      | matchs (t as f1 $ f2) =

   200 	          if TermC.matches thy t pat then true

   201 	            else if matchs f1 then true else matchs f2

   202   in matchs t end;

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

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

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

   207     if matchsub thy tst pat

   208     then

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

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

   211     else

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

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

   214   | eval_matchsub _ _ _ _ = NONE;

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

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

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

   219     let

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

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

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

   223   | eval_var _ _ _ _ = NONE;

   225 (* refer to Thm.lhs_of *)

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

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

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

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

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

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

   232   | eval_lhs _ _ _ _ = NONE;

   233 (*

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

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

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

   237 > term2str t';

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

   239 *)

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

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

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

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

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

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

   247   | eval_rhs _ _ _ _ = NONE;

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

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

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

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

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

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

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

   257      if occurs_in v t

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

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

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

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

   262   | eval_occurs_in _ _ _ _ = NONE;

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

   265 fun some_occur_in vs t =

   266     let fun occurs_in' a b = occurs_in b a

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

   269 (*("some_occur_in", ("Prog_Expr.some_occur_in",

   270 			eval_some_occur_in "#eval_some_occur_in_"))*)

   271 fun eval_some_occur_in _ "Prog_Expr.some_occur_in"

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

   273     if some_occur_in (TermC.isalist2list vs) t

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

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

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

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

   278   | eval_some_occur_in _ _ _ _ = NONE;

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

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

   282     if TermC.is_atom arg

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

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

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

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

   287   | eval_is_atom _ _ _ _ = NONE;

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

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

   291     if TermC.is_num arg

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

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

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

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

   296   | eval_is_num _ _ _ _ = NONE;

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

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

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

   301     if TermC.is_num arg

   302     then

   303       let

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

   305       in

   306 	      if even i

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

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

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

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

   311       end

   312     else NONE

   313   | eval_is_even _ _ _ _ = NONE;

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

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

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

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

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

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

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

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

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

   324 	   if TermC.is_num n

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

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

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

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

   329   | eval_const _ _ _ _ = NONE;

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

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

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

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

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

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

   338    *)

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

   340   thmid ^ "Float ((" ^

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

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

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

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

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

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

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

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

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

   352       let

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

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

   355       in

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

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

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

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

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

   361       end

   362     else NONE

   363   | eval_equ _ _ _ _ = NONE;

   366 (*evaluate identity

   367 > reflI;

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

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

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

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

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

   374 ----------- thus needs Rule.Eval !

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

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

   377 > UnparseC.term t';

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

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

   381 atomt t; UnparseC.term t;

   382 *** -------------

   383 *** Const ( Not)

   384 *** . Const ( op =)

   385 *** . . Free ( x, )

   386 *** . . Free ( 0, )

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

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

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

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

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

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

   394   if t1 = t2

   395   then SOME (TermC.mk_thmid thmid

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

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

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

   399   else SOME (TermC.mk_thmid thmid

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

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

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

   403   | eval_ident _ _ _ _ = NONE;

   404 (* TODO

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

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

   407 > UnparseC.term t';

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

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

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

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

   412 > UnparseC.term t';

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

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

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

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

   417 > UnparseC.term t';

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

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

   420 *)

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

   424   thus returns False only for atoms *)

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

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

   427   if t1 = t2

   428   then

   429     SOME (TermC.mk_thmid thmid

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

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

   432   else

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

   434       (true, true) =>

   435         if TermC.variable_constant_pair (t1, t2)

   436         then NONE

   437         else SOME (TermC.mk_thmid thmid

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

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

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

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

   443 (*. evaluate HOL.divide .*)

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

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

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

   447       let

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

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

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

   451       in

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

   453         else

   454           let

   455             val res = TermC.mk_frac T res_int;

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

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

   458       end

   459     else NONE

   460   | eval_cancel _ _ _ _ = NONE;

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

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

   464 fun eval_argument_in _ "Prog_Expr.argument_in"

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

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

   467     then

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

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

   470     else NONE

   471   | eval_argument_in _ _ _ _ = NONE;

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

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

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

   476 fun eval_sameFunId _ "Prog_Expr.sameFunId"

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

   478     if f1 = f2

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

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

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

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

   483 | eval_sameFunId _ _ _ _ = NONE;

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

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

   488    as the fst argument;

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

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

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

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

   493 (*("filter_sameFunId" ,("Prog_Expr.filter_sameFunId",

   494 		   eval_filter_sameFunId "Prog_Expr.filter_sameFunId"))*)

   495 fun eval_filter_sameFunId _ "Prog_Expr.filter_sameFunId"

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

   497 			(fid $ _) $ fs) _ =

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

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

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

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

   502 | eval_filter_sameFunId _ _ _ _ = NONE;

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

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

   506   | list2sum [s] = s

   507   | list2sum (s::ss) =

   508     let

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

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

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

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

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

   514     in sum s ss end;

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

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

   518 fun eval_boollist2sum _ "Prog_Expr.boollist2sum"

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

   520     let

   521       val isal = TermC.isalist2list l

   522 	    val lhss = map lhs isal

   523 	    val sum = list2sum lhss

   524     in

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

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

   527     end

   528   | eval_boollist2sum _ _ _ _ = NONE;

   530 (**) end (*struct*)

   531 \<close> text \<open>

   532 open Prog_Expr

   533 \<close> ML \<open>

   534 \<close> ML \<open>

   535 \<close>

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

   538 ML \<open>

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

   540 \<close> ML \<open>

   541 \<close> ML \<open>

   542 \<close>

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

   546 rule_set_knowledge prog_expr = prog_expr

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

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

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

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

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

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

   554 ML \<open>

   555 \<close> ML \<open>

   556 \<close> ML \<open>

   557 \<close>

   559 end

author	wneuper <walther.neuper@jku.at>
	Wed, 18 Aug 2021 16:03:08 +0200
changeset 60385	d3a3cc2f0382
parent 60343	f6e98785473f
child 60386	b7ea87559ad5
permissions	-rw-r--r--