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products/sources/formale Sprachen/Isabelle/Sequents/ (Beweissystem Isabelle Version 2025-1^©) Datei vom 16.11.2025 mit Größe 4 kB

Quelle Sequents.thy Sprache: Isabelle

(*  Title:      Sequents/Sequents.thy
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1993  University of Cambridge
*)

section \<open>Parsing and pretty-printing of sequences\<close>

theory Sequents
imports Pure
keywords "print_pack" :: diag
begin

setup Pure_Thy.old_appl_syntax_setup

declare [[unify_trace_bound = 20, unify_search_bound = 40]]

typedecl o

subsection \<open>Sequences\<close>

typedecl seq'
consts
SeqO' :: "[o,seq']\<Rightarrow>seq'"
Seq1' :: "o\seq'"

subsection \<open>Concrete syntax\<close>

nonterminal seq and seqobj and seqcont

syntax
"_SeqEmp"         :: seq                                  (\<open>\<close>)
"_SeqApp"         :: "[seqobj,seqcont] \ seq" (\__\)

"_SeqContEmp"     :: seqcont                              (\<open>\<close>)
"_SeqContApp"     :: "[seqobj,seqcont] \ seqcont" (\,/ __\)

"_SeqO"           :: "o \ seqobj" (\_\)
"_SeqId"          :: "'a \ seqobj" (\$_\)

type_synonym single_seqe = "[seq,seqobj] \ prop"
type_synonym single_seqi = "[seq'\seq',seq'\seq'] \ prop"
type_synonym two_seqi = "[seq'\seq', seq'\seq'] \ prop"
type_synonym two_seqe = "[seq, seq] \ prop"
type_synonym three_seqi = "[seq'\seq', seq'\seq', seq'\seq'] \ prop"
type_synonym three_seqe = "[seq, seq, seq] \ prop"
type_synonym four_seqi = "[seq'\seq', seq'\seq', seq'\seq', seq'\seq'] \ prop"
type_synonym four_seqe = "[seq, seq, seq, seq] \ prop"
type_synonym sequence_name = "seq'\seq'"

syntax
  (*Constant to allow definitions of SEQUENCES of formulas*)
  "_Side"        :: "seq$seq'\seq')" (\<<(_)>>$

ML \<open>

(* parse translation for sequences *)

fun abs_seq' t = Abs ("s", \<^Type>\seq'\, t);

fun seqobj_tr (Const (\<^syntax_const>\<open>_SeqO\<close>, _) $ f) = Syntax.const \<^const_syntax>\<open>SeqO'\<close> $ f
  | seqobj_tr (_ $ i) = i;

fun seqcont_tr (Const (\<^syntax_const>\<open>_SeqContEmp\<close>, _)) = Bound 0
  | seqcont_tr (Const (\<^syntax_const>\<open>_SeqContApp\<close>, _) $ so $ sc) =
      seqobj_tr so $ seqcont_tr sc;

fun seq_tr (Const (\<^syntax_const>\<open>_SeqEmp\<close>, _)) = abs_seq' (Bound 0)
  | seq_tr (Const (\<^syntax_const>\<open>_SeqApp\<close>, _) $ so $ sc) =
      abs_seq'(seqobj_tr so $ seqcont_tr sc);

fun singlobj_tr (Const (\<^syntax_const>\<open>_SeqO\<close>,_) $ f) =
  abs_seq' ((Syntax.const \<^const_syntax>\SeqO'\ $ f) $ Bound 0);

(* print translation for sequences *)

fun seqcont_tr' (Bound 0) = Syntax.const \<^syntax_const>\_SeqContEmp\
  | seqcont_tr' (Const (\<^const_syntax>\SeqO'\, _) $ f $ s) =
      Syntax.const \<^syntax_const>\<open>_SeqContApp\<close> $
        (Syntax.const \<^syntax_const>\<open>_SeqO\<close> $ f) $ seqcont_tr' s
  | seqcont_tr' (i $ s) =
      Syntax.const \<^syntax_const>\<open>_SeqContApp\<close> $
        (Syntax.const \<^syntax_const>\<open>_SeqId\<close> $ i) $ seqcont_tr' s;

fun seq_tr' s =
  let
    fun seq_itr' (Bound 0) = Syntax.const \<^syntax_const>\_SeqEmp\
      | seq_itr' (Const (\<^const_syntax>\SeqO'\, _) $ f $ s) =
          Syntax.const \<^syntax_const>\<open>_SeqApp\<close> $
            (Syntax.const \<^syntax_const>\<open>_SeqO\<close> $ f) $ seqcont_tr' s
      | seq_itr' (i $ s) =
          Syntax.const \<^syntax_const>\<open>_SeqApp\<close> $
            (Syntax.const \<^syntax_const>\<open>_SeqId\<close> $ i) $ seqcont_tr' s
  in
    case s of
      Abs (_, _, t) => seq_itr' t
    | _ => s $ Bound 0
  end;

fun single_tr c [s1, s2] =
  Syntax.const c $ seq_tr s1 $ singlobj_tr s2;

fun two_seq_tr c [s1, s2] =
  Syntax.const c $ seq_tr s1 $ seq_tr s2;

fun three_seq_tr c [s1, s2, s3] =
  Syntax.const c $ seq_tr s1 $ seq_tr s2 $ seq_tr s3;

fun four_seq_tr c [s1, s2, s3, s4] =
  Syntax.const c $ seq_tr s1 $ seq_tr s2 $ seq_tr s3 $ seq_tr s4;

fun singlobj_tr' (Const (\<^const_syntax>\SeqO'\,_) $ fm) = fm
  | singlobj_tr' id = Syntax.const \<^syntax_const>\_SeqId\ $ id;

fun single_tr' c [s1, s2] =
  Syntax.const c $ seq_tr' s1 $ seq_tr' s2;

fun two_seq_tr' c [s1, s2] =
  Syntax.const c $ seq_tr' s1 $ seq_tr' s2;

fun three_seq_tr' c [s1, s2, s3] =
  Syntax.const c $ seq_tr' s1 $ seq_tr' s2 $ seq_tr' s3;

fun four_seq_tr' c [s1, s2, s3, s4] =
  Syntax.const c $ seq_tr' s1 $ seq_tr' s2 $ seq_tr' s3 $ seq_tr' s4;

(** for the <<...>> notation **)

fun side_tr [s1] = seq_tr s1;
\<close>

parse_translation \<open>[(\<^syntax_const>\<open>_Side\<close>, K side_tr)]\<close>

subsection \<open>Proof tools\<close>

ML_file \<open>prover.ML\<close>

end

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