Cookies disclaimer

I agree Our site saves small pieces of text information (cookies) on your device in order to deliver better content and for statistical purposes. You can disable the usage of cookies by changing the settings of your browser. By browsing our website without changing the browser settings you grant us permission to store that information on your device.

Abstract Interpretation

This is the task corresponding to exercise 4. Abstract Interpretation.


Download Files

Definitions File

theory Defs
  imports Main

no_notation less_eq  ("(_/ \<le> _)"  [51, 51] 50)
datatype bin = Zero | One | Single | More | Any

fun \<gamma> :: "bin \<Rightarrow> nat set" where
  "\<gamma> Zero = {0}" |
  "\<gamma> One = {2^0}" |
  "\<gamma> Single = {2^n| n. True }" |
  "\<gamma> More = {n. (\<nexists>k. n = 2^k) \<and> n\<noteq>0 }" |
  "\<gamma> Any = UNIV"

consts less_bin :: "bin \<Rightarrow> bin \<Rightarrow> bool"

consts plus' :: "bin \<Rightarrow> bin \<Rightarrow> bin"


Template File

theory Submission
  imports Defs

definition less_bin :: "bin \<Rightarrow> bin \<Rightarrow> bool" ("(_/ \<le> _)"  [51, 51] 50) where
  "x \<le> y = undefined"

theorem less_bin_sub: "(x::bin) \<le> y \<Longrightarrow> \<gamma> x \<subseteq> \<gamma> y"

fun plus' :: "bin \<Rightarrow> bin \<Rightarrow> bin" where
  "plus' _ = undefined"

theorem plus'_\<gamma>: "\<lbrakk>n1 \<in> \<gamma> x; n2 \<in> \<gamma> y\<rbrakk> \<Longrightarrow> n1+n2 \<in> \<gamma> (plus' x y)"

type_synonym entry = "(bin*bin) option"
type_synonym row = "(nat*entry) list"

definition table :: "row list" where
  "table = undefined"


Check File

theory Check
  imports Submission

lemma "(x::bin) \<le> y \<Longrightarrow> \<gamma> x \<subseteq> \<gamma> y"
  by (rule Submission.less_bin_sub)

lemma "\<lbrakk>n1 \<in> \<gamma> x; n2 \<in> \<gamma> y\<rbrakk> \<Longrightarrow> n1+n2 \<in> \<gamma> (plus' x y)"
  by (rule'_\<gamma>)


Terms and Conditions