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(* title: ProgLang/Prog_Expr.thy
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functions for expressions (which do NOT contain Prog_Tac and Tactical, by definition))
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author: Walther Neuper, Aug.2019
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(c) copyright due to lincense terms.
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*)
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theory Prog_Expr
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imports Calculate ListC Program
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begin
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text \<open>Abstract:
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Specific constants are defined for pre-conditions of programs and for program-expressions.
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The constants are connected with ML functions for evaluation of respective expressions
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(all named eval_*), such that Isac's rewrite engine can handle it.
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\<close>
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subsection \<open>Power re-defined for a specific type\<close>
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consts
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pow :: "[real, real] => real" (infixr "^^^" 80)
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subsection \<open>consts of functions in pre-conditions and program-expressions\<close>
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consts
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lhs :: "bool => real" (*of an equality*)
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rhs :: "bool => real" (*of an equality*)
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Vars :: "'a => real list" (*get the variables of a term *)
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matches :: "['a, 'a] => bool"
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matchsub :: "['a, 'a] => bool"
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some'_occur'_in :: "[real list, 'a] => bool" ("some'_of _ occur'_in _")
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occurs'_in :: "[real , 'a] => bool" ("_ occurs'_in _")
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abs :: "real => real" ("(|| _ ||)")
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(* ~~~ FIXXXME Isabelle2002 has abs already !!!*)
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absset :: "real set => real" ("(||| _ |||)")
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(*is numeral constant ?*)
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is'_const :: "real => bool" ("_ is'_const" 10)
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(*is_const rename to is_num FIXXXME.WN.16.5.03 *)
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is'_atom :: "real => bool" ("_ is'_atom" 10)
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is'_even :: "real => bool" ("_ is'_even" 10)
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(* identity on term level*)
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ident :: "['a, 'a] => bool" ("(_ =!=/ _)" [51, 51] 50)
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argument'_in :: "real => real" ("argument'_in _" 10)
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sameFunId :: "[real, bool] => bool" (* "same'_funid _ _" 10
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WN0609 changed the id, because ".. _ _" inhibits currying *)
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filter'_sameFunId:: "[real, bool list] => bool list"
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("filter'_sameFunId _ _" 10)
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boollist2sum :: "bool list => real"
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lastI :: "'a list \<Rightarrow> 'a"
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subsection \<open>ML code for functions in pre-conditions and program-expressions\<close>
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ML \<open>
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signature PROG_EXPR =
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sig
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(*//------------------------- from Tools .thy-------------------------------------------------\\*)
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val lhs: term -> term
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val eval_lhs: 'a -> string -> term -> 'b -> (string * term) option
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val eval_matches: string -> string -> term -> theory -> (string * term) option
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val matchsub: theory -> term -> term -> bool
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val eval_matchsub: string -> string -> term -> theory -> (string * term) option
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val rhs: term -> term
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val eval_rhs: 'a -> string -> term -> 'b -> (string * term) option
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val eval_var: string -> string -> term -> theory -> (string * term) option
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val or2list: term -> term
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(*\\------------------------- from Tools .thy-------------------------------------------------//*)
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(*//------------------------- from Atools .thy------------------------------------------------\\*)
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val occurs_in: term -> term -> bool
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val eval_occurs_in: 'a -> string -> term -> 'b -> (string * term) option
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val some_occur_in: term list -> term -> bool
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val eval_some_occur_in: 'a -> string -> term -> 'b -> (string * term) option
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val eval_is_atom: string -> string -> term -> 'a -> (string * term) option
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val even: int -> bool
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val eval_is_even: string -> string -> term -> 'a -> (string * term) option
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val eval_const: string -> string -> term -> 'a -> (string * term) option
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val eval_equ: string -> string -> term -> 'a -> (string * term) option
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val eval_ident: string -> string -> term -> theory -> (string * term) option
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val eval_equal: string -> string -> term -> theory -> (string * term) option
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val eval_cancel: string -> string -> term -> 'a -> (string * term) option
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val eval_argument_in: string -> string -> term -> 'a -> (string * term) option
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val same_funid: term -> term -> bool
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val eval_sameFunId: string -> string -> term -> 'a -> (string * term) option
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val eval_filter_sameFunId: string -> string -> term -> 'a -> (string * term) option
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val list2sum: term list -> term
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val eval_boollist2sum: string -> string -> term -> 'a -> (string * term) option
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val mk_thmid_f: string -> (int * int) * (int * int) -> (int * int) * (int * int) -> string
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(*\\------------------------- from Atools.thy------------------------------------------------//*)
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end
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(**)
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structure Prog_Expr(**): PROG_EXPR =(**)
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struct
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(**)
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(*+ for Or_to_List +*)
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fun or2list (Const ("HOL.True",_)) = (tracing"### or2list True"; UniversalList)
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| or2list (Const ("HOL.False",_)) = (tracing"### or2list False"; EmptyList)
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| or2list (t as Const ("HOL.eq",_) $ _ $ _) = TermC.list2isalist HOLogic.boolT [t]
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| or2list ors =
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let
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fun get ls (Const ("HOL.disj",_) $ o1 $ o2) =
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(case o2 of
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Const ("HOL.disj",_) $ _ $ _ => get (ls @ [o1]) o2
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| _ => ls @ [o1, o2])
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| get _ t = raise TERM ("or2list: missing pattern in fun.def", [t])
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in (((TermC.list2isalist HOLogic.boolT) o (get [])) ors) end
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(*>val t = @{term True};
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> val t' = or2list t;
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> term2str t';
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"ListC.UniversalList"
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> val t = @{term False};
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> val t' = or2list t;
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> term2str t';
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"[]"
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> val t=(Thm.term_of o the o (parse thy)) "x=3";
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> val t' = or2list t;
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> term2str t';
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"[x = 3]"
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> val t=(Thm.term_of o the o (parse thy))"(x=3) | (x=-3) | (x=0)";
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> val t' = or2list t;
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> term2str t';
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"[x = #3, x = #-3, x = #0]" : string *)
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(** evaluation on the meta-level **)
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(*. evaluate the predicate matches (match on whole term only) .*)
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(*("matches",("Prog_Expr.matches", eval_matches "#matches_")):calc*)
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fun eval_matches (_:string) "Prog_Expr.matches"
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(t as Const ("Prog_Expr.matches",_) $ pat $ tst) thy =
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if TermC.matches thy tst pat
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then
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let
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val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True}))
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in SOME (Rule.term_to_string''' thy prop, prop) end
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else
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let
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val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))
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in SOME (Rule.term_to_string''' thy prop, prop) end
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| eval_matches _ _ _ _ = NONE;
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(*
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> val t = (Thm.term_of o the o (parse thy))
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"matches (?x = 0) (1 * x ^^^ 2 = 0)";
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> eval_matches "/thmid/" "/op_/" t thy;
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val it =
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SOME
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("matches (x = 0) (1 * x ^^^ 2 = 0) = False",
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Const (#,#) $ (# $ # $ Const #)) : (string * term) option
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> val t = (Thm.term_of o the o (parse thy))
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"matches (?a = #0) (#1 * x ^^^ #2 = #0)";
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> eval_matches "/thmid/" "/op_/" t thy;
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val it =
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SOME
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("matches (?a = #0) (#1 * x ^^^ #2 = #0) = True",
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Const (#,#) $ (# $ # $ Const #)) : (string * term) option
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> val t = (Thm.term_of o the o (parse thy))
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"matches (?a * x = #0) (#1 * x ^^^ #2 = #0)";
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> eval_matches "/thmid/" "/op_/" t thy;
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val it =
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SOME
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("matches (?a * x = #0) (#1 * x ^^^ #2 = #0) = False",
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Const (#,#) $ (# $ # $ Const #)) : (string * term) option
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> val t = (Thm.term_of o the o (parse thy))
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"matches (?a * x ^^^ #2 = #0) (#1 * x ^^^ #2 = #0)";
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> eval_matches "/thmid/" "/op_/" t thy;
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val it =
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SOME
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("matches (?a * x ^^^ #2 = #0) (#1 * x ^^^ #2 = #0) = True",
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Const (#,#) $ (# $ # $ Const #)) : (string * term) option
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----- before ?patterns ---:
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> val t = (Thm.term_of o the o (parse thy))
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"matches (a * b^^^#2 = c) (#3 * x^^^#2 = #1)";
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> eval_matches "/thmid/" "/op_/" t thy;
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SOME
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("matches (a * b ^^^ #2 = c) (#3 * x ^^^ #2 = #1) = True",
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Const ("HOL.Trueprop","bool => prop") $ (Const # $ (# $ #) $ Const (#,#)))
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: (string * term) option
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> val t = (Thm.term_of o the o (parse thy))
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"matches (a * b^^^#2 = c) (#3 * x^^^#2222 = #1)";
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> eval_matches "/thmid/" "/op_/" t thy;
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SOME ("matches (a * b ^^^ #2 = c) (#3 * x ^^^ #2222 = #1) = False",
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Const ("HOL.Trueprop","bool => prop") $ (Const # $ (# $ #) $ Const (#,#)))
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> val t = (Thm.term_of o the o (parse thy))
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"matches (a = b) (x + #1 + #-1 * #2 = #0)";
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> eval_matches "/thmid/" "/op_/" t thy;
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SOME ("matches (a = b) (x + #1 + #-1 * #2 = #0) = True",Const # $ (# $ #))
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*)
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(*.does a pattern match some subterm ?.*)
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fun matchsub thy t pat =
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let
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fun matchs (t as Const _) = TermC.matches thy t pat
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| matchs (t as Free _) = TermC.matches thy t pat
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| matchs (t as Var _) = TermC.matches thy t pat
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| matchs (Bound _) = false
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| matchs (t as Abs (_, _, body)) =
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if TermC.matches thy t pat then true else TermC.matches thy body pat
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| matchs (t as f1 $ f2) =
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if TermC.matches thy t pat then true
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else if matchs f1 then true else matchs f2
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in matchs t end;
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(*("matchsub",("Prog_Expr.matchsub", eval_matchsub "#matchsub_")):calc*)
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fun eval_matchsub (_:string) "Prog_Expr.matchsub"
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(t as Const ("Prog_Expr.matchsub",_) $ pat $ tst) thy =
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if matchsub thy tst pat
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then
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let val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True}))
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in SOME (Rule.term_to_string''' thy prop, prop) end
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else
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let val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))
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in SOME (Rule.term_to_string''' thy prop, prop) end
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| eval_matchsub _ _ _ _ = NONE;
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(*get the variables in an isabelle-term*)
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(*("Vars" ,("Prog_Expr.Vars" , eval_var "#Vars_")):calc*)
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fun eval_var (thmid:string) "Prog_Expr.Vars" (t as (Const _ $ arg)) thy =
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let
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val t' = ((TermC.list2isalist HOLogic.realT) o TermC.vars) t;
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val thmId = thmid ^ Rule.term_to_string''' thy arg;
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in SOME (thmId, HOLogic.Trueprop $ (TermC.mk_equality (t, t'))) end
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| eval_var _ _ _ _ = NONE;
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fun lhs (Const ("HOL.eq",_) $ l $ _) = l
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| lhs t = error("lhs called with (" ^ Rule.term2str t ^ ")");
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(*("lhs" ,("Prog_Expr.lhs" , eval_lhs "")):calc*)
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fun eval_lhs _ "Prog_Expr.lhs"
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(t as (Const ("Prog_Expr.lhs",_) $ (Const ("HOL.eq",_) $ l $ _))) _ =
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SOME ((Rule.term2str t) ^ " = " ^ (Rule.term2str l),
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HOLogic.Trueprop $ (TermC.mk_equality (t, l)))
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| eval_lhs _ _ _ _ = NONE;
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(*
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> val t = (Thm.term_of o the o (parse thy)) "lhs (1 * x ^^^ 2 = 0)";
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> val SOME (id,t') = eval_lhs 0 0 t 0;
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val id = "Prog_Expr.lhs (1 * x ^^^ 2 = 0) = 1 * x ^^^ 2" : string
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> term2str t';
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val it = "Prog_Expr.lhs (1 * x ^^^ 2 = 0) = 1 * x ^^^ 2" : string
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*)
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fun rhs (Const ("HOL.eq",_) $ _ $ r) = r
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| rhs t = error("rhs called with (" ^ Rule.term2str t ^ ")");
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(*("rhs" ,("Prog_Expr.rhs" , eval_rhs "")):calc*)
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fun eval_rhs _ "Prog_Expr.rhs"
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(t as (Const ("Prog_Expr.rhs",_) $ (Const ("HOL.eq",_) $ _ $ r))) _ =
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SOME (Rule.term2str t ^ " = " ^ Rule.term2str r,
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HOLogic.Trueprop $ (TermC.mk_equality (t, r)))
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|
252 |
| eval_rhs _ _ _ _ = NONE;
|
walther@59603
|
253 |
(*\\------------------------- from Prog_Expr.thy-------------------------------------------------//*)
|
walther@59603
|
254 |
|
walther@59603
|
255 |
(*//------------------------- from Atools.thy------------------------------------------------\\*)
|
walther@59603
|
256 |
fun occurs_in v t = member op = (((map strip_thy) o TermC.ids2str) t) (Term.term_name v);
|
walther@59603
|
257 |
|
walther@59603
|
258 |
(*("occurs_in", ("Prog_Expr.occurs'_in", Prog_Expr.eval_occurs_in ""))*)
|
walther@59603
|
259 |
fun eval_occurs_in _ "Prog_Expr.occurs'_in"
|
walther@59603
|
260 |
(p as (Const ("Prog_Expr.occurs'_in",_) $ v $ t)) _ =
|
walther@59637
|
261 |
((*tracing("#>@ eval_occurs_in: v= "^(Rule.term2str v));
|
walther@59637
|
262 |
tracing("#>@ eval_occurs_in: t= "^(Rule.term2str t));*)
|
walther@59603
|
263 |
if occurs_in v t
|
walther@59603
|
264 |
then SOME ((Rule.term2str p) ^ " = True",
|
walther@59603
|
265 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
|
walther@59603
|
266 |
else SOME ((Rule.term2str p) ^ " = False",
|
walther@59603
|
267 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False}))))
|
walther@59603
|
268 |
| eval_occurs_in _ _ _ _ = NONE;
|
walther@59603
|
269 |
|
walther@59603
|
270 |
(*some of the (bound) variables (eg. in an eqsys) "vs" occur in term "t"*)
|
walther@59603
|
271 |
fun some_occur_in vs t =
|
walther@59603
|
272 |
let fun occurs_in' a b = occurs_in b a
|
walther@59603
|
273 |
in foldl or_ (false, map (occurs_in' t) vs) end;
|
walther@59603
|
274 |
|
walther@59603
|
275 |
(*("some_occur_in", ("Prog_Expr.some'_occur'_in",
|
walther@59603
|
276 |
eval_some_occur_in "#eval_some_occur_in_"))*)
|
walther@59603
|
277 |
fun eval_some_occur_in _ "Prog_Expr.some'_occur'_in"
|
walther@59603
|
278 |
(p as (Const ("Prog_Expr.some'_occur'_in",_)
|
walther@59603
|
279 |
$ vs $ t)) _ =
|
walther@59603
|
280 |
if some_occur_in (TermC.isalist2list vs) t
|
walther@59603
|
281 |
then SOME ((Rule.term2str p) ^ " = True",
|
walther@59603
|
282 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
|
walther@59603
|
283 |
else SOME ((Rule.term2str p) ^ " = False",
|
walther@59603
|
284 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
|
walther@59603
|
285 |
| eval_some_occur_in _ _ _ _ = NONE;
|
walther@59603
|
286 |
|
walther@59603
|
287 |
(*("is_atom",("Prog_Expr.is'_atom", Prog_Expr.eval_is_atom "#is_atom_"))*)
|
walther@59603
|
288 |
fun eval_is_atom (thmid:string) "Prog_Expr.is'_atom"
|
walther@59603
|
289 |
(t as (Const _ $ arg)) _ =
|
walther@59603
|
290 |
(case arg of
|
walther@59603
|
291 |
Free (n,_) => SOME (TermC.mk_thmid thmid n "",
|
walther@59603
|
292 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59603
|
293 |
| _ => SOME (TermC.mk_thmid thmid "" "",
|
walther@59603
|
294 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))))
|
walther@59603
|
295 |
| eval_is_atom _ _ _ _ = NONE;
|
walther@59603
|
296 |
|
walther@59603
|
297 |
fun even i = (i div 2) * 2 = i;
|
walther@59603
|
298 |
(*("is_even",("Prog_Expr.is'_even", eval_is_even "#is_even_"))*)
|
walther@59603
|
299 |
fun eval_is_even (thmid:string) "Prog_Expr.is'_even"
|
walther@59603
|
300 |
(t as (Const _ $ arg)) _ =
|
walther@59603
|
301 |
(case arg of
|
walther@59603
|
302 |
Free (n,_) =>
|
walther@59603
|
303 |
(case TermC.int_of_str_opt n of
|
walther@59603
|
304 |
SOME i =>
|
walther@59603
|
305 |
if even i then SOME (TermC.mk_thmid thmid n "",
|
walther@59603
|
306 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59603
|
307 |
else SOME (TermC.mk_thmid thmid "" "",
|
walther@59603
|
308 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
walther@59603
|
309 |
| _ => NONE)
|
walther@59603
|
310 |
| _ => NONE)
|
walther@59603
|
311 |
| eval_is_even _ _ _ _ = NONE;
|
walther@59603
|
312 |
|
walther@59603
|
313 |
(*evaluate 'is_const'*)
|
walther@59603
|
314 |
(*("is_const",("Prog_Expr.is'_const", Prog_Expr.eval_const "#is_const_"))*)
|
walther@59618
|
315 |
fun eval_const (thmid:string) _ (t as (Const _ $ arg)) _ =
|
walther@59603
|
316 |
(case arg of
|
walther@59618
|
317 |
Const (n1, _) =>
|
walther@59618
|
318 |
SOME (TermC.mk_thmid thmid n1 "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
walther@59618
|
319 |
| Free (n1, _) =>
|
walther@59618
|
320 |
if TermC.is_num' n1
|
walther@59618
|
321 |
then SOME (TermC.mk_thmid thmid n1 "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59618
|
322 |
else SOME (TermC.mk_thmid thmid n1 "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
walther@59603
|
323 |
| _ => (*NONE*)
|
walther@59618
|
324 |
SOME (TermC.mk_thmid thmid (Rule.term2str arg) "", HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False}))))
|
walther@59603
|
325 |
| eval_const _ _ _ _ = NONE;
|
walther@59603
|
326 |
|
walther@59603
|
327 |
(*. evaluate binary, associative, commutative operators: *,+,^ .*)
|
walther@59603
|
328 |
(*("PLUS" ,("Groups.plus_class.plus" , (**)eval_binop "#add_")),
|
walther@59603
|
329 |
("TIMES" ,("Groups.times_class.times" , (**)eval_binop "#mult_")),
|
walther@59603
|
330 |
("POWER" ,("Prog_Expr.pow" , (**)eval_binop "#power_"))*)
|
walther@59603
|
331 |
|
walther@59603
|
332 |
(* val (thmid,op_,t as(Const (op0,t0) $ Free (n1,t1) $ Free(n2,t2)),thy) =
|
walther@59603
|
333 |
("xxxxxx",op_,t,thy);
|
walther@59603
|
334 |
*)
|
walther@59603
|
335 |
fun mk_thmid_f thmid ((v11, v12), (p11, p12)) ((v21, v22), (p21, p22)) = (* dropped *)
|
walther@59603
|
336 |
thmid ^ "Float ((" ^
|
walther@59603
|
337 |
(string_of_int v11)^","^(string_of_int v12)^"), ("^
|
walther@59603
|
338 |
(string_of_int p11)^","^(string_of_int p12)^")) __ (("^
|
walther@59603
|
339 |
(string_of_int v21)^","^(string_of_int v22)^"), ("^
|
walther@59603
|
340 |
(string_of_int p21)^","^(string_of_int p22)^"))";
|
walther@59603
|
341 |
|
walther@59603
|
342 |
(*.evaluate < and <= for numerals.*)
|
walther@59603
|
343 |
(*("le" ,("Orderings.ord_class.less" , Prog_Expr.eval_equ "#less_")),
|
walther@59603
|
344 |
("leq" ,("Orderings.ord_class.less_eq" , Prog_Expr.eval_equ "#less_equal_"))*)
|
walther@59603
|
345 |
fun eval_equ (thmid:string) (_(*op_*)) (t as
|
walther@59603
|
346 |
(Const (op0, _) $ Free (n1, _) $ Free(n2, _))) _ =
|
walther@59603
|
347 |
(case (TermC.int_of_str_opt n1, TermC.int_of_str_opt n2) of
|
walther@59603
|
348 |
(SOME n1', SOME n2') =>
|
walther@59603
|
349 |
if Calc.calc_equ (strip_thy op0) (n1', n2')
|
walther@59603
|
350 |
then SOME (TermC.mk_thmid thmid n1 n2,
|
walther@59603
|
351 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59603
|
352 |
else SOME (TermC.mk_thmid thmid n1 n2,
|
walther@59603
|
353 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
walther@59603
|
354 |
| _ => NONE)
|
walther@59603
|
355 |
|
walther@59603
|
356 |
| eval_equ _ _ _ _ = NONE;
|
walther@59603
|
357 |
|
walther@59603
|
358 |
|
walther@59603
|
359 |
(*evaluate identity
|
walther@59603
|
360 |
> reflI;
|
walther@59603
|
361 |
val it = "(?t = ?t) = True"
|
walther@59603
|
362 |
> val t = str2term "x = 0";
|
walther@59603
|
363 |
> val NONE = rewrite_ thy Rule.dummy_ord Rule.e_rls false reflI t;
|
walther@59603
|
364 |
|
walther@59603
|
365 |
> val t = str2term "1 = 0";
|
walther@59603
|
366 |
> val NONE = rewrite_ thy Rule.dummy_ord Rule.e_rls false reflI t;
|
walther@59603
|
367 |
----------- thus needs Rule.Calc !
|
walther@59603
|
368 |
> val t = str2term "0 = 0";
|
walther@59603
|
369 |
> val SOME (t',_) = rewrite_ thy Rule.dummy_ord Rule.e_rls false reflI t;
|
walther@59603
|
370 |
> Rule.term2str t';
|
walther@59603
|
371 |
val it = "HOL.True"
|
walther@59603
|
372 |
|
walther@59603
|
373 |
val t = str2term "Not (x = 0)";
|
walther@59603
|
374 |
atomt t; Rule.term2str t;
|
walther@59603
|
375 |
*** -------------
|
walther@59603
|
376 |
*** Const ( Not)
|
walther@59603
|
377 |
*** . Const ( op =)
|
walther@59603
|
378 |
*** . . Free ( x, )
|
walther@59603
|
379 |
*** . . Free ( 0, )
|
walther@59603
|
380 |
val it = "x ~= 0" : string*)
|
walther@59603
|
381 |
|
walther@59603
|
382 |
(*.evaluate identity on the term-level, =!= ,i.e. without evaluation of
|
walther@59603
|
383 |
the arguments: thus special handling by 'fun eval_binop'*)
|
walther@59603
|
384 |
(*("ident" ,("Prog_Expr.ident", Prog_Expr.eval_ident "#ident_")):calc*)
|
walther@59603
|
385 |
fun eval_ident (thmid:string) "Prog_Expr.ident" (t as
|
walther@59603
|
386 |
(Const _(*op0, t0*) $ t1 $ t2 )) thy =
|
walther@59603
|
387 |
if t1 = t2
|
walther@59603
|
388 |
then SOME (TermC.mk_thmid thmid
|
walther@59603
|
389 |
("(" ^ (Rule.term_to_string''' thy t1) ^ ")")
|
walther@59603
|
390 |
("(" ^ (Rule.term_to_string''' thy t2) ^ ")"),
|
walther@59603
|
391 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59603
|
392 |
else SOME (TermC.mk_thmid thmid
|
walther@59603
|
393 |
("(" ^ (Rule.term_to_string''' thy t1) ^ ")")
|
walther@59603
|
394 |
("(" ^ (Rule.term_to_string''' thy t2) ^ ")"),
|
walther@59603
|
395 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
walther@59603
|
396 |
| eval_ident _ _ _ _ = NONE;
|
walther@59603
|
397 |
(* TODO
|
walther@59603
|
398 |
> val t = str2term "x =!= 0";
|
walther@59603
|
399 |
> val SOME (str, t') = eval_ident "ident_" "b" t thy;
|
walther@59603
|
400 |
> Rule.term2str t';
|
walther@59603
|
401 |
val str = "ident_(x)_(0)" : string
|
walther@59603
|
402 |
val it = "(x =!= 0) = False" : string
|
walther@59603
|
403 |
> val t = str2term "1 =!= 0";
|
walther@59603
|
404 |
> val SOME (str, t') = eval_ident "ident_" "b" t thy;
|
walther@59603
|
405 |
> Rule.term2str t';
|
walther@59603
|
406 |
val str = "ident_(1)_(0)" : string
|
walther@59603
|
407 |
val it = "(1 =!= 0) = False" : string
|
walther@59603
|
408 |
> val t = str2term "0 =!= 0";
|
walther@59603
|
409 |
> val SOME (str, t') = eval_ident "ident_" "b" t thy;
|
walther@59603
|
410 |
> Rule.term2str t';
|
walther@59603
|
411 |
val str = "ident_(0)_(0)" : string
|
walther@59603
|
412 |
val it = "(0 =!= 0) = True" : string
|
walther@59603
|
413 |
*)
|
walther@59603
|
414 |
|
walther@59603
|
415 |
(*.evaluate identity of terms, which stay ready for evaluation in turn;
|
walther@59603
|
416 |
thus returns False only for atoms.*)
|
walther@59603
|
417 |
(*("equal" ,("HOL.eq", Prog_Expr.eval_equal "#equal_")):calc*)
|
walther@59603
|
418 |
fun eval_equal (thmid : string) "HOL.eq" (t as (Const _(*op0,t0*) $ t1 $ t2 )) thy =
|
walther@59603
|
419 |
if t1 = t2
|
walther@59603
|
420 |
then SOME (TermC.mk_thmid thmid
|
walther@59603
|
421 |
("(" ^ Rule.term_to_string''' thy t1 ^ ")")
|
walther@59603
|
422 |
("(" ^ Rule.term_to_string''' thy t2 ^ ")"),
|
walther@59603
|
423 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term True})))
|
walther@59603
|
424 |
else (case (TermC.is_atom t1, TermC.is_atom t2) of
|
walther@59603
|
425 |
(true, true) =>
|
walther@59603
|
426 |
SOME (TermC.mk_thmid thmid
|
walther@59603
|
427 |
("(" ^ Rule.term_to_string''' thy t1 ^ ")")
|
walther@59603
|
428 |
("(" ^ Rule.term_to_string''' thy t2 ^ ")"),
|
walther@59603
|
429 |
HOLogic.Trueprop $ (TermC.mk_equality (t, @{term False})))
|
walther@59603
|
430 |
| _ => NONE) (* NOT is_atom t1,t2 --> rew_sub *)
|
walther@59603
|
431 |
| eval_equal _ _ _ _ = NONE; (* error-exit *)
|
walther@59603
|
432 |
(*
|
walther@59603
|
433 |
val t = str2term "x ~= 0";
|
walther@59603
|
434 |
val NONE = eval_equal "equal_" "b" t thy;
|
walther@59603
|
435 |
|
walther@59603
|
436 |
|
walther@59603
|
437 |
> val t = str2term "(x + 1) = (x + 1)";
|
walther@59603
|
438 |
> val SOME (str, t') = eval_equal "equal_" "b" t thy;
|
walther@59603
|
439 |
> Rule.term2str t';
|
walther@59603
|
440 |
val str = "equal_(x + 1)_(x + 1)" : string
|
walther@59603
|
441 |
val it = "(x + 1 = x + 1) = True" : string
|
walther@59603
|
442 |
> val t = str2term "x = 0";
|
walther@59603
|
443 |
> val NONE = eval_equal "equal_" "b" t thy;
|
walther@59603
|
444 |
|
walther@59603
|
445 |
> val t = str2term "1 = 0";
|
walther@59603
|
446 |
> val SOME (str, t') = eval_equal "equal_" "b" t thy;
|
walther@59603
|
447 |
> Rule.term2str t';
|
walther@59603
|
448 |
val str = "equal_(1)_(0)" : string
|
walther@59603
|
449 |
val it = "(1 = 0) = False" : string
|
walther@59603
|
450 |
> val t = str2term "0 = 0";
|
walther@59603
|
451 |
> val SOME (str, t') = eval_equal "equal_" "b" t thy;
|
walther@59603
|
452 |
> Rule.term2str t';
|
walther@59603
|
453 |
val str = "equal_(0)_(0)" : string
|
walther@59603
|
454 |
val it = "(0 = 0) = True" : string
|
walther@59603
|
455 |
*)
|
walther@59603
|
456 |
|
walther@59603
|
457 |
(*. evaluate HOL.divide .*)
|
walther@59603
|
458 |
(*("DIVIDE" ,("Rings.divide_class.divide" , eval_cancel "#divide_e"))*)
|
walther@59603
|
459 |
fun eval_cancel (thmid: string) "Rings.divide_class.divide" (t as
|
walther@59603
|
460 |
(Const (op0,t0) $ Free (n1, _) $ Free(n2, _))) _ =
|
walther@59603
|
461 |
(case (TermC.int_of_str_opt n1, TermC.int_of_str_opt n2) of
|
walther@59603
|
462 |
(SOME n1', SOME n2') =>
|
walther@59603
|
463 |
let
|
walther@59603
|
464 |
val sg = Calc.sign_mult n1' n2';
|
walther@59603
|
465 |
val (T1,T2,Trange) = TermC.dest_binop_typ t0;
|
walther@59603
|
466 |
val gcd' = Calc.gcd (abs n1') (abs n2');
|
walther@59603
|
467 |
in if gcd' = abs n2'
|
walther@59603
|
468 |
then let val rhs = TermC.term_of_num Trange (sg * (abs n1') div gcd')
|
walther@59603
|
469 |
val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, rhs))
|
walther@59603
|
470 |
in SOME (TermC.mk_thmid thmid n1 n2, prop) end
|
walther@59603
|
471 |
else if 0 < n2' andalso gcd' = 1 then NONE
|
walther@59603
|
472 |
else let val rhs = TermC.mk_num_op_num T1 T2 (op0,t0) (sg * (abs n1') div gcd')
|
walther@59603
|
473 |
((abs n2') div gcd')
|
walther@59603
|
474 |
val prop = HOLogic.Trueprop $ (TermC.mk_equality (t, rhs))
|
walther@59603
|
475 |
in SOME (TermC.mk_thmid thmid n1 n2, prop) end
|
walther@59603
|
476 |
end
|
walther@59637
|
477 |
| _ => ((*tracing"#>@ eval_cancel NONE";*)NONE))
|
walther@59603
|
478 |
| eval_cancel _ _ _ _ = NONE;
|
walther@59603
|
479 |
|
walther@59603
|
480 |
(* get the argument from a function-definition *)
|
walther@59603
|
481 |
(*("argument_in" ,("Prog_Expr.argument'_in", Prog_Expr.eval_argument_in "Prog_Expr.argument'_in"))*)
|
walther@59603
|
482 |
fun eval_argument_in _ "Prog_Expr.argument'_in"
|
walther@59603
|
483 |
(t as (Const ("Prog_Expr.argument'_in", _) $ (_(*f*) $ arg))) _ =
|
walther@59603
|
484 |
if is_Free arg (*could be something to be simplified before*)
|
walther@59603
|
485 |
then
|
walther@59603
|
486 |
SOME (Rule.term2str t ^ " = " ^ Rule.term2str arg,
|
walther@59603
|
487 |
HOLogic.Trueprop $ (TermC.mk_equality (t, arg)))
|
walther@59603
|
488 |
else NONE
|
walther@59603
|
489 |
| eval_argument_in _ _ _ _ = NONE;
|
walther@59603
|
490 |
|
walther@59603
|
491 |
(* check if the function-identifier of the first argument matches
|
walther@59603
|
492 |
the function-identifier of the lhs of the second argument *)
|
walther@59603
|
493 |
(*("sameFunId" ,("Prog_Expr.sameFunId", eval_same_funid "Prog_Expr.sameFunId"))*)
|
walther@59603
|
494 |
fun eval_sameFunId _ "Prog_Expr.sameFunId"
|
walther@59603
|
495 |
(p as Const ("Prog_Expr.sameFunId",_) $ (f1 $ _) $ (Const ("HOL.eq", _) $ (f2 $ _) $ _)) _ =
|
walther@59603
|
496 |
if f1 = f2
|
walther@59603
|
497 |
then SOME ((Rule.term2str p) ^ " = True",
|
walther@59603
|
498 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term True})))
|
walther@59603
|
499 |
else SOME ((Rule.term2str p) ^ " = False",
|
walther@59603
|
500 |
HOLogic.Trueprop $ (TermC.mk_equality (p, @{term False})))
|
walther@59603
|
501 |
| eval_sameFunId _ _ _ _ = NONE;
|
walther@59603
|
502 |
|
walther@59603
|
503 |
|
walther@59603
|
504 |
(*.from a list of fun-definitions "f x = ..." as 2nd argument
|
walther@59603
|
505 |
filter the elements with the same fun-identfier in "f y"
|
walther@59603
|
506 |
as the fst argument;
|
walther@59603
|
507 |
this is, because Isabelles filter takes more than 1 sec.*)
|
walther@59603
|
508 |
fun same_funid f1 (Const ("HOL.eq", _) $ (f2 $ _) $ _) = f1 = f2
|
walther@59603
|
509 |
| same_funid f1 t = error ("same_funid called with t = ("
|
walther@59603
|
510 |
^Rule.term2str f1^") ("^Rule.term2str t^")");
|
walther@59603
|
511 |
(*("filter_sameFunId" ,("Prog_Expr.filter'_sameFunId",
|
walther@59603
|
512 |
eval_filter_sameFunId "Prog_Expr.filter'_sameFunId"))*)
|
walther@59603
|
513 |
fun eval_filter_sameFunId _ "Prog_Expr.filter'_sameFunId"
|
walther@59603
|
514 |
(p as Const ("Prog_Expr.filter'_sameFunId",_) $
|
walther@59603
|
515 |
(fid $ _) $ fs) _ =
|
walther@59603
|
516 |
let val fs' = ((TermC.list2isalist HOLogic.boolT) o
|
walther@59603
|
517 |
(filter (same_funid fid))) (TermC.isalist2list fs)
|
walther@59603
|
518 |
in SOME (Rule.term2str (TermC.mk_equality (p, fs')),
|
walther@59603
|
519 |
HOLogic.Trueprop $ (TermC.mk_equality (p, fs'))) end
|
walther@59603
|
520 |
| eval_filter_sameFunId _ _ _ _ = NONE;
|
walther@59603
|
521 |
|
walther@59603
|
522 |
(* make a list of terms to a sum *)
|
walther@59603
|
523 |
fun list2sum [] = error ("list2sum called with []")
|
walther@59603
|
524 |
| list2sum [s] = s
|
walther@59603
|
525 |
| list2sum (s::ss) =
|
walther@59603
|
526 |
let
|
walther@59603
|
527 |
fun sum su [s'] = Const ("Groups.plus_class.plus",
|
walther@59603
|
528 |
[HOLogic.realT,HOLogic.realT] ---> HOLogic.realT) $ su $ s'
|
walther@59603
|
529 |
| sum su (s'::ss') = sum (Const ("Groups.plus_class.plus",
|
walther@59603
|
530 |
[HOLogic.realT,HOLogic.realT] ---> HOLogic.realT) $ su $ s') ss'
|
walther@59603
|
531 |
| sum _ _ = raise ERROR "list2sum: pattern in fun.def is missing"
|
walther@59603
|
532 |
in sum s ss end;
|
walther@59603
|
533 |
|
walther@59603
|
534 |
(* make a list of equalities to the sum of the lhs *)
|
walther@59603
|
535 |
(*("boollist2sum" ,("Prog_Expr.boollist2sum" , eval_boollist2sum "")):calc*)
|
walther@59603
|
536 |
fun eval_boollist2sum _ "Prog_Expr.boollist2sum"
|
walther@59603
|
537 |
(p as Const ("Prog_Expr.boollist2sum", _) $ (l as Const ("List.list.Cons", _) $ _ $ _)) _ =
|
walther@59603
|
538 |
let
|
walther@59603
|
539 |
val isal = TermC.isalist2list l
|
walther@59603
|
540 |
val lhss = map lhs isal
|
walther@59603
|
541 |
val sum = list2sum lhss
|
walther@59603
|
542 |
in
|
walther@59603
|
543 |
SOME ((Rule.term2str p) ^ " = " ^ (Rule.term2str sum),
|
walther@59603
|
544 |
HOLogic.Trueprop $ (TermC.mk_equality (p, sum)))
|
walther@59603
|
545 |
end
|
walther@59603
|
546 |
| eval_boollist2sum _ _ _ _ = NONE;
|
walther@59603
|
547 |
|
walther@59603
|
548 |
(**) end (*struct*)
|
walther@59603
|
549 |
\<close> text \<open>
|
walther@59603
|
550 |
open Prog_Expr
|
walther@59603
|
551 |
\<close> ML \<open>
|
walther@59603
|
552 |
\<close> ML \<open>
|
walther@59603
|
553 |
\<close>
|
walther@59603
|
554 |
|
walther@59603
|
555 |
subsection \<open>extend rule-set for evaluating pre-conditions and program-expressions\<close>
|
walther@59603
|
556 |
ML \<open>
|
walther@59603
|
557 |
val list_rls = Rule.append_rls "list_rls" list_rls [Rule.Calc ("Prog_Expr.rhs", Prog_Expr.eval_rhs "")];
|
walther@59603
|
558 |
\<close> ML \<open>
|
walther@59603
|
559 |
\<close> ML \<open>
|
walther@59603
|
560 |
\<close>
|
walther@59603
|
561 |
|
walther@59603
|
562 |
subsection \<open>setup for rule-sets and ML-functions\<close>
|
walther@59603
|
563 |
setup \<open>KEStore_Elems.add_rlss [("list_rls", (Context.theory_name @{theory}, list_rls))]\<close>
|
walther@59603
|
564 |
setup \<open>KEStore_Elems.add_calcs
|
walther@59603
|
565 |
[("matches", ("Prog_Expr.matches", Prog_Expr.eval_matches "#matches_")),
|
walther@59603
|
566 |
("matchsub", ("Prog_Expr.matchsub", Prog_Expr.eval_matchsub "#matchsub_")),
|
walther@59603
|
567 |
("Vars", ("Prog_Expr.Vars", Prog_Expr.eval_var "#Vars_")),
|
walther@59603
|
568 |
("lhs", ("Prog_Expr.lhs", Prog_Expr.eval_lhs "")),
|
walther@59603
|
569 |
("rhs", ("Prog_Expr.rhs", Prog_Expr.eval_rhs ""))]\<close>
|
walther@59603
|
570 |
(*\\------------------------- from Tools .thy-------------------------------------------------//*)
|
walther@59603
|
571 |
ML \<open>
|
walther@59603
|
572 |
\<close> ML \<open>
|
walther@59603
|
573 |
\<close> ML \<open>
|
walther@59603
|
574 |
\<close>
|
walther@59603
|
575 |
|
walther@59603
|
576 |
end |