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.

FDS week 1 homework

Week 1 homework for FDS

Resources

Download Files

Definitions File

theory Defs
  imports Main
begin

end

Template File

theory Submission
  imports Defs
begin

fun find_pfx :: "nat list => nat => nat list" where
 "find_pfx _ _ = undefined"

lemma find_pfx_append:
  "(find_pfx (xs1 @ [x] @ xs2) x) = (find_pfx (xs1 @ [x]) x)"
  sorry

lemma last_find_pfx_val:
  "last (find_pfx (xs @ [x]) x) = x"
  sorry

lemma find_pfx_append_2:
  "\<exists>xs2. xs = find_pfx xs x @ xs2"
  sorry

end

Check File

theory Check
  imports Submission
begin

text ‹Test cases›
lemma  "find_pfx [1::nat,2,3] 2 = [1,2]"
       "find_pfx [] (1::nat) = []"
  by simp+

lemma find_pfx_append:
  "(find_pfx (xs1 @ [x] @ xs2) x) = (find_pfx (xs1 @ [x]) x)"
  by (rule Submission.find_pfx_append)

lemma last_find_pfx_val:
  "last (find_pfx (xs @ [x]) x) = x"
  by (rule Submission.last_find_pfx_val)

lemma find_pfx_append_2:
  "\<exists>xs2. xs = find_pfx xs x @ xs2"
  by (rule Submission.find_pfx_append_2)


end

Terms and Conditions