author  oheimb 
Tue, 07 Apr 1998 13:46:05 +0200  
changeset 4800  97c3a45d092b 
parent 4752  1c334bd00038 
child 4836  fc5773ae2790 
permissions  rwrr 
2019  1 
(* Title: Option.ML 
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ID: $Id$ 

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Author: Tobias Nipkow 

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Copyright 1996 TU Muenchen 

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Derived rules 

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*) 

4133  8 
open Option; 
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qed_goal "not_None_eq" thy "(x ~= None) = (? y. x = Some y)" 

4477
b3e5857d8d99
New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents:
4133
diff
changeset

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(K [option.induct_tac "x" 1, Auto_tac]); 
4133  12 

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section "case analysis in premises"; 

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val optionE = prove_goal thy 

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"[ opt = None ==> P; !!x. opt = Some x ==> P ] ==> P" (fn prems => [ 

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case_tac "opt = None" 1, 

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eresolve_tac prems 1, 

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dtac (not_None_eq RS iffD1) 1, 

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etac exE 1, 

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eresolve_tac prems 1]); 

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fun optionE_tac s i = EVERY [ 

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res_inst_tac [("opt",s)] optionE i, 

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hyp_subst_tac (i+1), 

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hyp_subst_tac i]; 

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qed_goal "option_caseE" thy "[case x of None => P  Some y => Q y; \ 

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\ [x = None; P ] ==> R; \ 

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\ !!y. [x = Some y; Q y] ==> R] ==> R" (fn prems => [ 

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cut_facts_tac prems 1, 

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res_inst_tac [("opt","x")] optionE 1, 

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forward_tac prems 1, 

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forward_tac prems 3, 

4477
b3e5857d8d99
New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents:
4133
diff
changeset

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Auto_tac]); 
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fun option_case_tac i = EVERY [ 
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etac option_caseE i, 

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hyp_subst_tac (i+1), 

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hyp_subst_tac i]; 

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section "the"; 

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qed_goalw "the_Some" thy [the_def] 

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"the (Some x) = x" (K [Simp_tac 1]); 

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Addsimps [the_Some]; 

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section "option_map"; 

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qed_goalw "option_map_None" thy [option_map_def] 

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"option_map f None = None" (K [Simp_tac 1]); 

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qed_goalw "option_map_Some" thy [option_map_def] 

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"option_map f (Some x) = Some (f x)" (K [Simp_tac 1]); 

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Addsimps [option_map_None, option_map_Some]; 

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4800
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

56 
val option_map_eq_Some = prove_goalw thy [option_map_def] 
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

57 
"(option_map f xo = Some y) = (? z. xo = Some z & f z = y)" 
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

58 
(K [asm_full_simp_tac (simpset() addsplits [split_option_case]) 1]); 
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

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AddSDs[option_map_eq_Some RS iffD1]; 
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

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Addsimps [option_map_eq_Some]; 
4752  61 

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section "o2s"; 

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val elem_o2s = prove_goal thy "!!X. x : o2s xo = (xo = Some x)" 

4800
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

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(K [optionE_tac "xo" 1, Auto_tac]); 
4752  66 
AddSDs [elem_o2s RS iffD1]; 
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Addsimps [elem_o2s]; 

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val o2s_empty_eq = prove_goal thy "(o2s xo = {}) = (xo = None)" 

4800
97c3a45d092b
replaced option_map_SomeD by option_map_eq_Some (RS iffD1)
oheimb
parents:
4752
diff
changeset

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(K [optionE_tac "xo" 1, Auto_tac]); 
4752  71 
Addsimps [o2s_empty_eq]; 