author  wenzelm 
Thu, 23 Jul 2015 14:25:05 +0200  
changeset 60770  240563fbf41d 
parent 52143  36ffe23b25f8 
child 61385  538100cc4399 
permissions  rwrr 
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(* Title: Sequents/Modal0.thy 
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Author: Martin Coen 
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Copyright 1991 University of Cambridge 
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*) 
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theory Modal0 
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imports LK0 

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begin 

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ML_file "modal.ML" 
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consts 
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box :: "o=>o" ("[]_" [50] 50) 
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dia :: "o=>o" ("<>_" [50] 50) 
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strimp :: "[o,o]=>o" (infixr "<" 25) 
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streqv :: "[o,o]=>o" (infixr "><" 25) 

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Lstar :: "two_seqi" 
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Rstar :: "two_seqi" 

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syntax 

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"_Lstar" :: "two_seqe" ("(_)L>(_)" [6,6] 5) 
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"_Rstar" :: "two_seqe" ("(_)R>(_)" [6,6] 5) 

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ML \<open> 
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fun star_tr c [s1, s2] = Const(c, dummyT) $ seq_tr s1 $ seq_tr s2; 
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fun star_tr' c [s1, s2] = Const(c, dummyT) $ seq_tr' s1 $ seq_tr' s2; 

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\<close> 
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parse_translation \<open> 
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[(@{syntax_const "_Lstar"}, K (star_tr @{const_syntax Lstar})), 
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(@{syntax_const "_Rstar"}, K (star_tr @{const_syntax Rstar}))] 

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\<close> 
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print_translation \<open> 
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[(@{const_syntax Lstar}, K (star_tr' @{syntax_const "_Lstar"})), 
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(@{const_syntax Rstar}, K (star_tr' @{syntax_const "_Rstar"}))] 

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\<close> 
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defs 

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strimp_def: "P < Q == [](P > Q)" 

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streqv_def: "P >< Q == (P < Q) & (Q < P)" 

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lemmas rewrite_rls = strimp_def streqv_def 

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lemma iffR: 

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"[ $H,P  $E,Q,$F; $H,Q  $E,P,$F ] ==> $H  $E, P <> Q, $F" 

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apply (unfold iff_def) 

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apply (assumption  rule conjR impR)+ 

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done 

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lemma iffL: 

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"[ $H,$G  $E,P,Q; $H,Q,P,$G  $E ] ==> $H, P <> Q, $G  $E" 

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apply (unfold iff_def) 

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apply (assumption  rule conjL impL basic)+ 

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done 

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lemmas safe_rls = basic conjL conjR disjL disjR impL impR notL notR iffL iffR 

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and unsafe_rls = allR exL 

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and bound_rls = allL exR 

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end 