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Isabelle Task 1 complete

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Aadi Desai 2022-12-08 14:34:49 +00:00
parent ba694b4e41
commit d226d0a21b
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1 changed files with 18 additions and 10 deletions
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20
isabelle/2022/HSV_tasks_2022.thy
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@ -1,20 +1,28 @@
theory HSV_tasks_2022 imports Complex_Main begin
section {* Task 1: Full adders *}
section "Task 1: Full adders"
fun halfadder :: "bool * bool \<Rightarrow> bool * bool"
where "halfadder (a,b) = (
let cout = (a \<and> b) in
let s = (a \<or> b) \<and> \<not>(a \<and> b) in
(cout, s))"
fun fulladder :: "bool * bool * bool \<Rightarrow> bool * bool"
where
"fulladder (a,b,cin) = (
where "fulladder (a,b,cin) = (
let (tmp1, tmp2) = halfadder(a,b) in
let (tmp3, s) = halfadder(cin,tmp2) in
let cout = tmp1 | tmp3 in
(cout, s))"
fun b2i :: "bool \<Rightarrow> int"
where "b2i (b) = (if (b) then 1 else 0)"
section {* Task 2: Fifth powers *}
theorem "\<forall>a b.(co,s) = halfadder(a,b) \<Longrightarrow> (2*b2i(co)+b2i(s)) = (b2i(a)+b2i(b))"
by auto
theorem "(n::nat) ^ 5 mod 10 = n mod 10"
oops
theorem "\<forall>a b ci.(co,s) = fulladder(a,b,ci) \<Longrightarrow> (2*b2i(co)+b2i(s)) = (b2i(a)+b2i(b)+b2i(ci))"
by auto
section {* Task 3: Logic optimisation *}