author | nipkow |
Sun, 05 Jan 2003 21:03:14 +0100 | |
changeset 13771 | 6cd59cc885a1 |
parent 25 | 3ac1c0c0016e |
permissions | -rw-r--r-- |
0 | 1 |
(* Title: ZF/list-fn.ML |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1992 University of Cambridge |
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For list-fn.thy. Lists in Zermelo-Fraenkel Set Theory |
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*) |
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open ListFn; |
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(** hd and tl **) |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
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goalw ListFn.thy [hd_def] "hd(Cons(a,l)) = a"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
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by (resolve_tac List.case_eqns 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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parents:
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val hd_Cons = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
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goalw ListFn.thy [tl_def] "tl(Nil) = Nil"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
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by (resolve_tac List.case_eqns 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
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val tl_Nil = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
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goalw ListFn.thy [tl_def] "tl(Cons(a,l)) = l"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
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by (resolve_tac List.case_eqns 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
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val tl_Cons = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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goal ListFn.thy "!!l. l: list(A) ==> tl(l) : list(A)"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
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by (etac List.elim 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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by (ALLGOALS (asm_simp_tac (ZF_ss addsimps (List.intrs @ [tl_Nil,tl_Cons])))); |
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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val tl_type = result(); |
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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(** drop **) |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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goalw ListFn.thy [drop_def] "drop(0, l) = l"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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by (rtac rec_0 1); |
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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val drop_0 = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
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goalw ListFn.thy [drop_def] "!!i. i:nat ==> drop(i, Nil) = Nil"; |
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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by (etac nat_induct 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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by (ALLGOALS (asm_simp_tac (nat_ss addsimps [tl_Nil]))); |
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ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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val drop_Nil = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
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goalw ListFn.thy [drop_def] |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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"!!i. i:nat ==> drop(succ(i), Cons(a,l)) = drop(i,l)"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
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changeset
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by (etac nat_induct 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
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by (ALLGOALS (asm_simp_tac (nat_ss addsimps [tl_Cons]))); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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val drop_succ_Cons = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
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1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
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goalw ListFn.thy [drop_def] |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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"!!i l. [| i:nat; l: list(A) |] ==> drop(i,l) : list(A)"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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by (etac nat_induct 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
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by (ALLGOALS (asm_simp_tac (nat_ss addsimps [tl_type]))); |
1c0926788772
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val drop_type = result(); |
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(** list_rec -- by Vset recursion **) |
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goal ListFn.thy "list_rec(Nil,c,h) = c"; |
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by (rtac (list_rec_def RS def_Vrec RS trans) 1); |
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by (simp_tac (ZF_ss addsimps List.case_eqns) 1); |
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val list_rec_Nil = result(); |
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goal ListFn.thy "list_rec(Cons(a,l), c, h) = h(a, l, list_rec(l,c,h))"; |
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by (rtac (list_rec_def RS def_Vrec RS trans) 1); |
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3ac1c0c0016e
ordinal: DEFINITION of < and le to replace : and <= on ordinals! Many
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by (simp_tac (rank_ss addsimps (rank_Cons2::List.case_eqns)) 1); |
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val list_rec_Cons = result(); |
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(*Type checking -- proved by induction, as usual*) |
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val prems = goal ListFn.thy |
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"[| l: list(A); \ |
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\ c: C(Nil); \ |
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\ !!x y r. [| x:A; y: list(A); r: C(y) |] ==> h(x,y,r): C(Cons(x,y)) \ |
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\ |] ==> list_rec(l,c,h) : C(l)"; |
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by (list_ind_tac "l" prems 1); |
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by (ALLGOALS (asm_simp_tac |
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(ZF_ss addsimps (prems@[list_rec_Nil,list_rec_Cons])))); |
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val list_rec_type = result(); |
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(** Versions for use with definitions **) |
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val [rew] = goal ListFn.thy |
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"[| !!l. j(l)==list_rec(l, c, h) |] ==> j(Nil) = c"; |
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by (rewtac rew); |
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by (rtac list_rec_Nil 1); |
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val def_list_rec_Nil = result(); |
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val [rew] = goal ListFn.thy |
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"[| !!l. j(l)==list_rec(l, c, h) |] ==> j(Cons(a,l)) = h(a,l,j(l))"; |
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by (rewtac rew); |
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by (rtac list_rec_Cons 1); |
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val def_list_rec_Cons = result(); |
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fun list_recs def = map standard |
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([def] RL [def_list_rec_Nil, def_list_rec_Cons]); |
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(** map **) |
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val [map_Nil,map_Cons] = list_recs map_def; |
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val prems = goalw ListFn.thy [map_def] |
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"[| l: list(A); !!x. x: A ==> h(x): B |] ==> map(h,l) : list(B)"; |
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by (REPEAT (ares_tac (prems@[list_rec_type, NilI, ConsI]) 1)); |
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val map_type = result(); |
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val [major] = goal ListFn.thy "l: list(A) ==> map(h,l) : list({h(u). u:A})"; |
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by (rtac (major RS map_type) 1); |
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by (etac RepFunI 1); |
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val map_type2 = result(); |
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(** length **) |
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val [length_Nil,length_Cons] = list_recs length_def; |
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goalw ListFn.thy [length_def] |
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"!!l. l: list(A) ==> length(l) : nat"; |
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by (REPEAT (ares_tac [list_rec_type, nat_0I, nat_succI] 1)); |
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val length_type = result(); |
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(** app **) |
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val [app_Nil,app_Cons] = list_recs app_def; |
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goalw ListFn.thy [app_def] |
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"!!xs ys. [| xs: list(A); ys: list(A) |] ==> xs@ys : list(A)"; |
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by (REPEAT (ares_tac [list_rec_type, ConsI] 1)); |
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val app_type = result(); |
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(** rev **) |
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val [rev_Nil,rev_Cons] = list_recs rev_def; |
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val prems = goalw ListFn.thy [rev_def] |
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"xs: list(A) ==> rev(xs) : list(A)"; |
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by (REPEAT (ares_tac (prems @ [list_rec_type, NilI, ConsI, app_type]) 1)); |
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val rev_type = result(); |
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(** flat **) |
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val [flat_Nil,flat_Cons] = list_recs flat_def; |
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val prems = goalw ListFn.thy [flat_def] |
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"ls: list(list(A)) ==> flat(ls) : list(A)"; |
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by (REPEAT (ares_tac (prems @ [list_rec_type, NilI, ConsI, app_type]) 1)); |
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val flat_type = result(); |
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(** list_add **) |
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val [list_add_Nil,list_add_Cons] = list_recs list_add_def; |
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val prems = goalw ListFn.thy [list_add_def] |
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"xs: list(nat) ==> list_add(xs) : nat"; |
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by (REPEAT (ares_tac (prems @ [list_rec_type, nat_0I, add_type]) 1)); |
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val list_add_type = result(); |
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(** ListFn simplification **) |
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val list_typechecks = |
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[NilI, ConsI, list_rec_type, |
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map_type, map_type2, app_type, length_type, rev_type, flat_type, |
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list_add_type]; |
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val list_ss = arith_ss |
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8ce8c4d13d4d
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addsimps List.case_eqns |
8ce8c4d13d4d
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addsimps [list_rec_Nil, list_rec_Cons, |
0 | 164 |
map_Nil, map_Cons, |
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app_Nil, app_Cons, |
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length_Nil, length_Cons, |
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rev_Nil, rev_Cons, |
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flat_Nil, flat_Cons, |
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list_add_Nil, list_add_Cons] |
8ce8c4d13d4d
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setsolver (type_auto_tac list_typechecks); |
8ce8c4d13d4d
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171 |
(*Could also rewrite using the list_typechecks...*) |
0 | 172 |
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(*** theorems about map ***) |
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val prems = goal ListFn.thy |
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"l: list(A) ==> map(%u.u, l) = l"; |
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by (list_ind_tac "l" prems 1); |
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8ce8c4d13d4d
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by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 179 |
val map_ident = result(); |
180 |
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val prems = goal ListFn.thy |
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"l: list(A) ==> map(h, map(j,l)) = map(%u.h(j(u)), l)"; |
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by (list_ind_tac "l" prems 1); |
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8ce8c4d13d4d
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lcp
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184 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 185 |
val map_compose = result(); |
186 |
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187 |
val prems = goal ListFn.thy |
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"xs: list(A) ==> map(h, xs@ys) = map(h,xs) @ map(h,ys)"; |
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by (list_ind_tac "xs" prems 1); |
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8ce8c4d13d4d
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changeset
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190 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 191 |
val map_app_distrib = result(); |
192 |
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193 |
val prems = goal ListFn.thy |
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"ls: list(list(A)) ==> map(h, flat(ls)) = flat(map(map(h),ls))"; |
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195 |
by (list_ind_tac "ls" prems 1); |
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6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
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changeset
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196 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [map_app_distrib]))); |
0 | 197 |
val map_flat = result(); |
198 |
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199 |
val prems = goal ListFn.thy |
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"l: list(A) ==> \ |
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\ list_rec(map(h,l), c, d) = \ |
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\ list_rec(l, c, %x xs r. d(h(x), map(h,xs), r))"; |
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by (list_ind_tac "l" prems 1); |
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6
8ce8c4d13d4d
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lcp
parents:
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changeset
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204 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 205 |
val list_rec_map = result(); |
206 |
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207 |
(** theorems about list(Collect(A,P)) -- used in ex/term.ML **) |
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208 |
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209 |
(* c : list(Collect(B,P)) ==> c : list(B) *) |
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val list_CollectD = standard (Collect_subset RS list_mono RS subsetD); |
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212 |
val prems = goal ListFn.thy |
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"l: list({x:A. h(x)=j(x)}) ==> map(h,l) = map(j,l)"; |
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by (list_ind_tac "l" prems 1); |
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6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
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changeset
|
215 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 216 |
val map_list_Collect = result(); |
217 |
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218 |
(*** theorems about length ***) |
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219 |
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220 |
val prems = goal ListFn.thy |
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221 |
"xs: list(A) ==> length(map(h,xs)) = length(xs)"; |
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222 |
by (list_ind_tac "xs" prems 1); |
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6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
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diff
changeset
|
223 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 224 |
val length_map = result(); |
225 |
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226 |
val prems = goal ListFn.thy |
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227 |
"xs: list(A) ==> length(xs@ys) = length(xs) #+ length(ys)"; |
|
228 |
by (list_ind_tac "xs" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
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|
229 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 230 |
val length_app = result(); |
231 |
||
232 |
(* [| m: nat; n: nat |] ==> m #+ succ(n) = succ(n) #+ m |
|
233 |
Used for rewriting below*) |
|
234 |
val add_commute_succ = nat_succI RSN (2,add_commute); |
|
235 |
||
236 |
val prems = goal ListFn.thy |
|
237 |
"xs: list(A) ==> length(rev(xs)) = length(xs)"; |
|
238 |
by (list_ind_tac "xs" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
239 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [length_app, add_commute_succ]))); |
0 | 240 |
val length_rev = result(); |
241 |
||
242 |
val prems = goal ListFn.thy |
|
243 |
"ls: list(list(A)) ==> length(flat(ls)) = list_add(map(length,ls))"; |
|
244 |
by (list_ind_tac "ls" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
245 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [length_app]))); |
0 | 246 |
val length_flat = result(); |
247 |
||
14
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
248 |
(** Length and drop **) |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
249 |
|
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
250 |
(*Lemma for the inductive step of drop_length*) |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
251 |
goal ListFn.thy |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
252 |
"!!xs. xs: list(A) ==> \ |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
253 |
\ ALL x. EX z zs. drop(length(xs), Cons(x,xs)) = Cons(z,zs)"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
254 |
by (etac List.induct 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
255 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [drop_0,drop_succ_Cons]))); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
256 |
by (fast_tac ZF_cs 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
257 |
val drop_length_Cons_lemma = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
258 |
val drop_length_Cons = standard (drop_length_Cons_lemma RS spec); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
259 |
|
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
260 |
goal ListFn.thy |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
261 |
"!!l. l: list(A) ==> ALL i: length(l). EX z zs. drop(i,l) = Cons(z,zs)"; |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
262 |
by (etac List.induct 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
263 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps bquant_simps))); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
264 |
by (rtac conjI 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
265 |
by (etac drop_length_Cons 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
266 |
by (rtac ballI 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
267 |
by (rtac natE 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
268 |
by (etac ([asm_rl, length_type, Ord_nat] MRS Ord_trans) 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
269 |
by (assume_tac 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
270 |
by (asm_simp_tac (list_ss addsimps [drop_0]) 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
271 |
by (fast_tac ZF_cs 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
272 |
by (asm_simp_tac (list_ss addsimps [drop_succ_Cons]) 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
273 |
by (dtac bspec 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
274 |
by (fast_tac ZF_cs 2); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
275 |
by (fast_tac (ZF_cs addEs [succ_in_naturalD,length_type]) 1); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
276 |
val drop_length_lemma = result(); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
277 |
val drop_length = standard (drop_length_lemma RS bspec); |
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
278 |
|
1c0926788772
ex/{bin.ML,comb.ML,prop.ML}: replaced NewSext by Syntax.simple_sext
lcp
parents:
6
diff
changeset
|
279 |
|
0 | 280 |
(*** theorems about app ***) |
281 |
||
282 |
val [major] = goal ListFn.thy "xs: list(A) ==> xs@Nil=xs"; |
|
283 |
by (rtac (major RS List.induct) 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
284 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 285 |
val app_right_Nil = result(); |
286 |
||
287 |
val prems = goal ListFn.thy "xs: list(A) ==> (xs@ys)@zs = xs@(ys@zs)"; |
|
288 |
by (list_ind_tac "xs" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
289 |
by (ALLGOALS (asm_simp_tac list_ss)); |
0 | 290 |
val app_assoc = result(); |
291 |
||
292 |
val prems = goal ListFn.thy |
|
293 |
"ls: list(list(A)) ==> flat(ls@ms) = flat(ls)@flat(ms)"; |
|
294 |
by (list_ind_tac "ls" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
295 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [app_assoc]))); |
0 | 296 |
val flat_app_distrib = result(); |
297 |
||
298 |
(*** theorems about rev ***) |
|
299 |
||
300 |
val prems = goal ListFn.thy "l: list(A) ==> rev(map(h,l)) = map(h,rev(l))"; |
|
301 |
by (list_ind_tac "l" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
302 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [map_app_distrib]))); |
0 | 303 |
val rev_map_distrib = result(); |
304 |
||
305 |
(*Simplifier needs the premises as assumptions because rewriting will not |
|
306 |
instantiate the variable ?A in the rules' typing conditions; note that |
|
307 |
rev_type does not instantiate ?A. Only the premises do. |
|
308 |
*) |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
309 |
goal ListFn.thy |
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
310 |
"!!xs. [| xs: list(A); ys: list(A) |] ==> rev(xs@ys) = rev(ys)@rev(xs)"; |
0 | 311 |
by (etac List.induct 1); |
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
312 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [app_right_Nil,app_assoc]))); |
0 | 313 |
val rev_app_distrib = result(); |
314 |
||
315 |
val prems = goal ListFn.thy "l: list(A) ==> rev(rev(l))=l"; |
|
316 |
by (list_ind_tac "l" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
317 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [rev_app_distrib]))); |
0 | 318 |
val rev_rev_ident = result(); |
319 |
||
320 |
val prems = goal ListFn.thy |
|
321 |
"ls: list(list(A)) ==> rev(flat(ls)) = flat(map(rev,rev(ls)))"; |
|
322 |
by (list_ind_tac "ls" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
323 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps |
0 | 324 |
[map_app_distrib, flat_app_distrib, rev_app_distrib, app_right_Nil]))); |
325 |
val rev_flat = result(); |
|
326 |
||
327 |
||
328 |
(*** theorems about list_add ***) |
|
329 |
||
330 |
val prems = goal ListFn.thy |
|
331 |
"[| xs: list(nat); ys: list(nat) |] ==> \ |
|
332 |
\ list_add(xs@ys) = list_add(ys) #+ list_add(xs)"; |
|
333 |
by (cut_facts_tac prems 1); |
|
334 |
by (list_ind_tac "xs" prems 1); |
|
335 |
by (ALLGOALS |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
336 |
(asm_simp_tac (list_ss addsimps [add_0_right, add_assoc RS sym]))); |
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
337 |
by (rtac (add_commute RS subst_context) 1); |
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
338 |
by (REPEAT (ares_tac [refl, list_add_type] 1)); |
0 | 339 |
val list_add_app = result(); |
340 |
||
341 |
val prems = goal ListFn.thy |
|
342 |
"l: list(nat) ==> list_add(rev(l)) = list_add(l)"; |
|
343 |
by (list_ind_tac "l" prems 1); |
|
344 |
by (ALLGOALS |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
345 |
(asm_simp_tac (list_ss addsimps [list_add_app, add_0_right]))); |
0 | 346 |
val list_add_rev = result(); |
347 |
||
348 |
val prems = goal ListFn.thy |
|
349 |
"ls: list(list(nat)) ==> list_add(flat(ls)) = list_add(map(list_add,ls))"; |
|
350 |
by (list_ind_tac "ls" prems 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
351 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps [list_add_app]))); |
0 | 352 |
by (REPEAT (ares_tac [refl, list_add_type, map_type, add_commute] 1)); |
353 |
val list_add_flat = result(); |
|
354 |
||
355 |
(** New induction rule **) |
|
356 |
||
357 |
val major::prems = goal ListFn.thy |
|
358 |
"[| l: list(A); \ |
|
359 |
\ P(Nil); \ |
|
360 |
\ !!x y. [| x: A; y: list(A); P(y) |] ==> P(y @ [x]) \ |
|
361 |
\ |] ==> P(l)"; |
|
362 |
by (rtac (major RS rev_rev_ident RS subst) 1); |
|
363 |
by (rtac (major RS rev_type RS List.induct) 1); |
|
6
8ce8c4d13d4d
Installation of new simplifier for ZF. Deleted all congruence rules not
lcp
parents:
0
diff
changeset
|
364 |
by (ALLGOALS (asm_simp_tac (list_ss addsimps prems))); |
0 | 365 |
val list_append_induct = result(); |
366 |