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_equ: string -> string -> term -> 'a -> (string * term) option

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

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

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

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

    77     val same_funid: term -> term -> bool

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

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

    80     val list2sum: term list -> term

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

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

    84   end

    86 (**)

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

    88 struct

    89 (**)

    91 (*+ for Or_to_List +*)

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

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

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

    95   | or2list ors =

    96     let

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

    98 	        (case o2 of

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

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

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

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

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

   104 > val t' = or2list t;

   105 > term2str t';

   106 "ListC.UniversalList"

   107 > val t = @{term False};

   108 > val t' = or2list t;

   109 > term2str t';

   110 "[]"

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

   112 > val t' = or2list t;

   113 > term2str t';

   114 "[x = 3]"

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

   116 > val t' = or2list t;

   117 > term2str t';

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

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

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

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

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

   126     if TermC.matches thy tst pat

   127     then

   128       let

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

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

   131     else

   132       let

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

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

   135   | eval_matches _ _ _ _ = NONE;

   136 (*

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

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

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

   140 val it =

   141   SOME

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

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

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

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

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

   148 val it =

   149   SOME

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

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

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

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

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

   156 val it =

   157   SOME

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

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

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

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

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

   164 val it =

   165   SOME

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

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

   168 ----- before ?patterns ---:

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

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

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

   172 SOME

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

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

   175   : (string * term) option

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

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

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

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

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

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

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

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

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

   187 *)

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

   190 fun matchsub thy t pat =

   191   let

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

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

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

   195 	      | matchs (Bound _) = false

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

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

   198 	      | matchs (t as f1 $ f2) =

   199 	          if TermC.matches thy t pat then true

   200 	            else if matchs f1 then true else matchs f2

   201   in matchs t end;

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

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

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

   206     if matchsub thy tst pat

   207     then

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

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

   210     else

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

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

   213   | eval_matchsub _ _ _ _ = NONE;

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

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

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

   218     let

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

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

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

   222   | eval_var _ _ _ _ = NONE;

   224 (* refer to Thm.lhs_of *)

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

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

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

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

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

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

   231   | eval_lhs _ _ _ _ = NONE;

   232 (*

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

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

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

   236 > term2str t';

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

   238 *)

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

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

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

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

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

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

   246   | eval_rhs _ _ _ _ = NONE;

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

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

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

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

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

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

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

   256      if occurs_in v t

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

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

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

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

   261   | eval_occurs_in _ _ _ _ = NONE;

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

   264 fun some_occur_in vs t =

   265     let fun occurs_in' a b = occurs_in b a

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

   268 (*("some_occur_in", ("Prog_Expr.some_occur_in",

   269 			eval_some_occur_in "#eval_some_occur_in_"))*)

   270 fun eval_some_occur_in _ "Prog_Expr.some_occur_in"

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

   272     if some_occur_in (TermC.isalist2list vs) t

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

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

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

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

   277   | eval_some_occur_in _ _ _ _ = NONE;

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

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

   281     if TermC.is_atom arg

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

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

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

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

   286   | eval_is_atom _ _ _ _ = NONE;

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

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

   290     if TermC.is_num arg

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

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

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

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

   295   | eval_is_num _ _ _ _ = NONE;

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

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

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

   300     if TermC.is_num arg

   301     then

   302       let

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

   304       in

   305 	      if even i

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

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

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

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

   310       end

   311     else NONE

   312   | eval_is_even _ _ _ _ = NONE;

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

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

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

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

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

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

   321    *)

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

   323   thmid ^ "Float ((" ^

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

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

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

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

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

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

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

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

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

   335       let

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

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

   338       in

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

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

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

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

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

   344       end

   345     else NONE

   346   | eval_equ _ _ _ _ = NONE;

   349 (*evaluate identity

   350 > reflI;

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

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

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

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

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

   357 ----------- thus needs Rule.Eval !

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

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

   360 > UnparseC.term t';

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

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

   364 atomt t; UnparseC.term t;

   365 *** -------------

   366 *** Const ( Not)

   367 *** . Const ( op =)

   368 *** . . Free ( x, )

   369 *** . . Free ( 0, )

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

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

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

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

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

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

   377   if t1 = t2

   378   then SOME (TermC.mk_thmid thmid

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

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

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

   382   else SOME (TermC.mk_thmid thmid

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

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

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

   386   | eval_ident _ _ _ _ = NONE;

   387 (* TODO

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

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

   390 > UnparseC.term t';

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

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

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

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

   395 > UnparseC.term t';

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

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

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

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

   400 > UnparseC.term t';

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

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

   403 *)

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

   407   thus returns False only for atoms *)

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

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

   410   if t1 = t2

   411   then

   412     SOME (TermC.mk_thmid thmid

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

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

   415   else

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

   417       (true, true) =>

   418         if TermC.variable_constant_pair (t1, t2)

   419         then NONE

   420         else SOME (TermC.mk_thmid thmid

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

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

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

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

   426 (*. evaluate HOL.divide .*)

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

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

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

   430       let

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

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

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

   434       in

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

   436         else

   437           let

   438             val res = TermC.mk_frac T res_int;

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

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

   441       end

   442     else NONE

   443   | eval_cancel _ _ _ _ = NONE;

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

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

   447 fun eval_argument_in _ "Prog_Expr.argument_in"

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

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

   450     then

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

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

   453     else NONE

   454   | eval_argument_in _ _ _ _ = NONE;

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

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

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

   459 fun eval_sameFunId _ "Prog_Expr.sameFunId"

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

   461     if f1 = f2

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

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

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

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

   466 | eval_sameFunId _ _ _ _ = NONE;

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

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

   471    as the fst argument;

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

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

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

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

   476 (*("filter_sameFunId" ,("Prog_Expr.filter_sameFunId",

   477 		   eval_filter_sameFunId "Prog_Expr.filter_sameFunId"))*)

   478 fun eval_filter_sameFunId _ "Prog_Expr.filter_sameFunId"

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

   480 			(fid $ _) $ fs) _ =

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

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

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

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

   485 | eval_filter_sameFunId _ _ _ _ = NONE;

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

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

   489   | list2sum [s] = s

   490   | list2sum (s::ss) =

   491     let

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

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

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

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

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

   497     in sum s ss end;

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

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

   501 fun eval_boollist2sum _ "Prog_Expr.boollist2sum"

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

   503     let

   504       val isal = TermC.isalist2list l

   505 	    val lhss = map lhs isal

   506 	    val sum = list2sum lhss

   507     in

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

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

   510     end

   511   | eval_boollist2sum _ _ _ _ = NONE;

   513 (**) end (*struct*)

   514 \<close> text \<open>

   515 open Prog_Expr

   516 \<close> ML \<open>

   517 \<close> ML \<open>

   518 \<close>

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

   521 ML \<open>

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

   523 \<close> ML \<open>

   524 \<close> ML \<open>

   525 \<close>

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

   529 rule_set_knowledge prog_expr = prog_expr

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

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

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

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

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

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

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

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

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

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

   542 ML \<open>

   543 \<close> ML \<open>

   544 \<close> ML \<open>

   545 \<close>

   547 end

author	wneuper <walther.neuper@jku.at>
	Wed, 18 Aug 2021 20:34:41 +0200
changeset 60387	8e46f61fdb15
parent 60386	b7ea87559ad5
child 60391	a95071158185
permissions	-rw-r--r--