| author | Christian Urban <urbanc@in.tum.de> |
| Sat, 24 Oct 2009 22:52:23 +0200 | |
| changeset 181 | 3e53081ad53a |
| child 184 | f3c192574d2a |
| permissions | -rw-r--r-- |
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1 |
theory IntEx |
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imports QuotMain |
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begin |
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fun |
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intrel :: "(nat \<times> nat) \<Rightarrow> (nat \<times> nat) \<Rightarrow> bool" |
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7 |
where |
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"intrel (x, y) (u, v) = (x + v = u + y)" |
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quotient my_int = "nat \<times> nat" / intrel |
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apply(unfold EQUIV_def) |
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apply(auto simp add: mem_def expand_fun_eq) |
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done |
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typ my_int |
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local_setup {*
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make_const_def @{binding "ZERO"} @{term "(0::nat, 0::nat)"} NoSyn @{typ "nat \<times> nat"} @{typ "my_int"} #> snd
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*} |
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term ZERO |
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thm ZERO_def |
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local_setup {*
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make_const_def @{binding ONE} @{term "(1::nat, 0::nat)"} NoSyn @{typ "nat \<times> nat"} @{typ "my_int"} #> snd
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*} |
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term ONE |
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thm ONE_def |
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fun |
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my_plus :: "(nat \<times> nat) \<Rightarrow> (nat \<times> nat) \<Rightarrow> (nat \<times> nat)" |
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where |
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"my_plus (x, y) (u, v) = (x + u, y + v)" |
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local_setup {*
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make_const_def @{binding PLUS} @{term "my_plus"} NoSyn @{typ "nat \<times> nat"} @{typ "my_int"} #> snd
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*} |
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term PLUS |
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thm PLUS_def |
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fun |
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my_neg :: "(nat \<times> nat) \<Rightarrow> (nat \<times> nat)" |
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where |
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"my_neg (x, y) = (y, x)" |
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local_setup {*
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make_const_def @{binding NEG} @{term "my_neg"} NoSyn @{typ "nat \<times> nat"} @{typ "my_int"} #> snd
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*} |
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term NEG |
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thm NEG_def |
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definition |
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MINUS :: "my_int \<Rightarrow> my_int \<Rightarrow> my_int" |
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where |
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"MINUS z w = PLUS z (NEG w)" |
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fun |
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my_mult :: "(nat \<times> nat) \<Rightarrow> (nat \<times> nat) \<Rightarrow> (nat \<times> nat)" |
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where |
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"my_mult (x, y) (u, v) = (x*u + y*v, x*v + y*u)" |
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local_setup {*
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make_const_def @{binding MULT} @{term "my_mult"} NoSyn @{typ "nat \<times> nat"} @{typ "my_int"} #> snd
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*} |
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term MULT |
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thm MULT_def |
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(* NOT SURE WETHER THIS DEFINITION IS CORRECT *) |
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fun |
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my_le :: "(nat \<times> nat) \<Rightarrow> (nat \<times> nat) \<Rightarrow> bool" |
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where |
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"my_le (x, y) (u, v) = (x+v \<le> u+y)" |
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local_setup {*
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make_const_def @{binding LE} @{term "my_le"} NoSyn @{typ "nat \<times> nat"} @{typ "my_int"} #> snd
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*} |
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term LE |
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thm LE_def |
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definition |
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LESS :: "my_int \<Rightarrow> my_int \<Rightarrow> bool" |
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where |
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"LESS z w = (LE z w \<and> z \<noteq> w)" |
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term LESS |
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thm LESS_def |
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definition |
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ABS :: "my_int \<Rightarrow> my_int" |
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where |
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"ABS i = (if (LESS i ZERO) then (NEG i) else i)" |
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definition |
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SIGN :: "my_int \<Rightarrow> my_int" |
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where |
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"SIGN i = (if i = ZERO then ZERO else if (LESS ZERO i) then ONE else (NEG ONE))" |
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lemma |
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fixes i j k::"my_int" |
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shows "(PLUS (PLUS i j) k) = (PLUS i (PLUS j k))" |
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apply(unfold PLUS_def) |
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apply(simp add: expand_fun_eq) |
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sorry |
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3e53081ad53a
added another example file about integers (see HOL/Int.thy)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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