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'_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 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 even: int -> bool

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

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

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

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

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

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

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

    80     val same_funid: term -> term -> bool

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

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

    83     val list2sum: term list -> term

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

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

    87   end

    89 (**)

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

    91 struct

    92 (**)

    94 (*+ for Or_to_List +*)

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

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

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

    98   | or2list ors =

    99     let

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

   101 	        (case o2 of

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

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

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

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

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

   107 > val t' = or2list t;

   108 > term2str t';

   109 "ListC.UniversalList"

   110 > val t = @{term False};

   111 > val t' = or2list t;

   112 > term2str t';

   113 "[]"

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

   115 > val t' = or2list t;

   116 > term2str t';

   117 "[x = 3]"

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

   119 > val t' = or2list t;

   120 > term2str t';

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

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

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

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

   128 fun eval_matches (_:string) "Prog_Expr.matches" (t as Const ("Prog_Expr.matches",_) $ pat $ tst) thy =

   129     if TermC.matches thy tst pat

   130     then

   131       let

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

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

   134     else

   135       let

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

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

   138   | eval_matches _ _ _ _ = NONE;

   139 (*

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

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

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

   143 val it =

   144   SOME

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

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

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

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

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

   151 val it =

   152   SOME

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

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

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

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

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

   159 val it =

   160   SOME

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

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

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

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

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

   167 val it =

   168   SOME

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

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

   171 ----- before ?patterns ---:

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

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

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

   175 SOME

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

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

   178   : (string * term) option

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

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

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

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

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

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

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

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

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

   190 *)

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

   193 fun matchsub thy t pat =

   194   let

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

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

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

   198 	      | matchs (Bound _) = false

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

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

   201 	      | matchs (t as f1 $ f2) =

   202 	          if TermC.matches thy t pat then true

   203 	            else if matchs f1 then true else matchs f2

   204   in matchs t end;

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

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

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

   209     if matchsub thy tst pat

   210     then

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

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

   213     else

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

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

   216   | eval_matchsub _ _ _ _ = NONE;

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

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

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

   221     let

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

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

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

   225   | eval_var _ _ _ _ = NONE;

   227 (* refer to Thm.lhs_of *)

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

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

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

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

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

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

   234   | eval_lhs _ _ _ _ = NONE;

   235 (*

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

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

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

   239 > term2str t';

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

   241 *)

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

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

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

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

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

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

   249   | eval_rhs _ _ _ _ = NONE;

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

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

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

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

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

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

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

   259      if occurs_in v t

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

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

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

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

   264   | eval_occurs_in _ _ _ _ = NONE;

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

   267 fun some_occur_in vs t =

   268     let fun occurs_in' a b = occurs_in b a

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

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

   272 			eval_some_occur_in "#eval_some_occur_in_"))*)

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

   274 			  (p as (Const ("Prog_Expr.some'_occur'_in",_) $ vs $ t)) _ =

   275     if some_occur_in (TermC.isalist2list vs) t

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

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

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

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

   280   | eval_some_occur_in _ _ _ _ = NONE;

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

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

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

   285     (case arg of

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

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

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

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

   290   | eval_is_atom _ _ _ _ = NONE;

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

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

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

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

   296     (case arg of

   297 	Free (n,_) =>

   298 	 (case ThmC_Def.int_opt_of_string n of

   299 	      SOME i =>

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

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

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

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

   304 	    | _ => NONE)

   305        | _ => NONE)

   306   | eval_is_even _ _ _ _ = NONE;

   308 (*evaluate 'is_const'*)

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

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

   311     (case arg of

   312        Const (n1, _) =>

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

   314      | Free (n1, _) =>

   315 	     if TermC.is_num' n1

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

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

   318      | _ => (*NONE*)

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

   320   | eval_const _ _ _ _ = NONE;

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

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

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

   325   ("POWER"  ,("Transcendental.powr"  , (**)eval_binop "#power_"))*)

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

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

   329    *)

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

   331   thmid ^ "Float ((" ^

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

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

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

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

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

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

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

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

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

   342     (case (ThmC_Def.int_opt_of_string n1, ThmC_Def.int_opt_of_string n2) of

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

   344   if Eval.calc_equ (strip_thy op0) (n1', n2')

   345     then SOME (TermC.mk_thmid thmid n1 n2,

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

   347   else SOME (TermC.mk_thmid thmid n1 n2,

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

   349        | _ => NONE)

   351   | eval_equ _ _ _ _ = NONE;

   354 (*evaluate identity

   355 > reflI;

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

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

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

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

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

   362 ----------- thus needs Rule.Eval !

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

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

   365 > UnparseC.term t';

   366 val it = "HOL.True"

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

   369 atomt t; UnparseC.term t;

   370 *** -------------

   371 *** Const ( Not)

   372 *** . Const ( op =)

   373 *** . . Free ( x, )

   374 *** . . Free ( 0, )

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

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

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

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

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

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

   382   if t1 = t2

   383   then SOME (TermC.mk_thmid thmid

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

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

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

   387   else SOME (TermC.mk_thmid thmid

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

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

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

   391   | eval_ident _ _ _ _ = NONE;

   392 (* TODO

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

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

   395 > UnparseC.term t';

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

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

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

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

   400 > UnparseC.term t';

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

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

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

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

   405 > UnparseC.term t';

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

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

   408 *)

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

   412   thus returns False only for atoms *)

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

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

   415   if t1 = t2

   416   then

   417     SOME (TermC.mk_thmid thmid

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

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

   420   else

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

   422       (true, true) =>

   423         if TermC.variable_constant_pair (t1, t2)

   424         then NONE

   425         else SOME (TermC.mk_thmid thmid

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

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

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

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

   431 (*. evaluate HOL.divide .*)

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

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

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

   435     (case (ThmC_Def.int_opt_of_string n1, ThmC_Def.int_opt_of_string n2) of

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

   437         let

   438           val sg = Eval.sign_mult n1' n2';

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

   440           val gcd' = Eval.gcd (abs n1') (abs n2');

   441         in if gcd' = abs n2'

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

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

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

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

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

   447     	  			   ((abs n2') div gcd')

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

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

   450         end

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

   452   | eval_cancel _ _ _ _ = NONE;

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

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

   456 fun eval_argument_in _ "Prog_Expr.argument'_in"

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

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

   459     then

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

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

   462     else NONE

   463   | eval_argument_in _ _ _ _ = NONE;

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

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

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

   468 fun eval_sameFunId _ "Prog_Expr.sameFunId"

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

   470     if f1 = f2

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

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

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

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

   475 | eval_sameFunId _ _ _ _ = NONE;

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

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

   480    as the fst argument;

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

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

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

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

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

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

   487 fun eval_filter_sameFunId _ "Prog_Expr.filter'_sameFunId"

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

   489 			(fid $ _) $ fs) _ =

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

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

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

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

   494 | eval_filter_sameFunId _ _ _ _ = NONE;

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

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

   498   | list2sum [s] = s

   499   | list2sum (s::ss) =

   500     let

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

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

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

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

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

   506     in sum s ss end;

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

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

   510 fun eval_boollist2sum _ "Prog_Expr.boollist2sum"

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

   512     let

   513       val isal = TermC.isalist2list l

   514 	    val lhss = map lhs isal

   515 	    val sum = list2sum lhss

   516     in

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

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

   519     end

   520   | eval_boollist2sum _ _ _ _ = NONE;

   522 (**) end (*struct*)

   523 \<close> text \<open>

   524 open Prog_Expr

   525 \<close> ML \<open>

   526 \<close> ML \<open>

   527 \<close>

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

   530 ML \<open>

   531 val prog_expr = Rule_Set.append_rules "prog_expr" prog_expr [Rule.Eval ("Prog_Expr.rhs", Prog_Expr.eval_rhs "")];

   532 \<close> ML \<open>

   533 \<close> ML \<open>

   534 \<close>

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

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

   538 setup \<open>KEStore_Elems.add_calcs

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

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

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

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

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

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

   545 ML \<open>

   546 \<close> ML \<open>

   547 \<close> ML \<open>

   548 \<close>

   550 end

author	wneuper <walther.neuper@jku.at>
	Mon, 03 May 2021 08:49:50 +0200
changeset 60275	98ee674d18d3
parent 60260	6a3b143d4cf4
child 60278	343efa173023
permissions	-rw-r--r--