insertion sort - Agda Programming- Proving Insertionsort makes 3 or less comparisons on a list of size 3 -


good evening fellows,

i attempting prove insertionsort perform <= 3 comparisons in list of size 3 while sorting. last part of project , cannot make headway on it. after spending fair amount of time pursuing incorrect approach, instructor informed me may accomplished writing helper function assist. unfortunately have not come piece of code help. if can offer advice or assistance, , appreciated. code follows. thanks!

insert : ℕ → 𝕃 ℕ → 𝕃 ℕ × ℕ  insert x (h :: t) = if h < x (x :: h :: t , 1) else let r = insert                                         x t  in h :: (fst r) , 1 + snd r insert x [] = x :: [] , 0  insertionsort : 𝕃 ℕ → 𝕃 ℕ × ℕ  insertionsort [] = [] , 0 insertionsort (h :: t) insertionsort t insertionsort (h :: t) | t' , c1 insert h t'  insertionsort (h :: t) | t' , c1 | r , c2 = r , c1 + c2  examplethm : ∀(x y z c : ℕ)(r : 𝕃 ℕ) → insertionsort (x :: y :: z :: [])                                                     ≡ r , c → c ≤ 3 ≡ tt  examplethm x y z = ?`

all comparisons done in course of insertionsort done in course of subordinate calls insert. may establish useful fact comparison cost of insert. if can bound cost of each call insert, should able combine bounded partial costs make bounded total cost. in case instructor concerned helping much, let me summarize saying saying structure of proof has follow structure of program.


-

Comments

Post a Comment

Popular posts from this blog

apache - PHP Soap issue while content length is larger -

we have developed soap based webservice post data third party webservice. accepts 4 params. in 1 of parameters accepts xml string no size limit restriction put in place. the webservice works fine in local environment running on php 5.2 , apache2. works content length long 10 mb. in staging server running nginx , php fpm.we have updated max post size , max upload filesize in php.ini , client_max_body param in nginx.conf allow upto 50 mb. but webservice client keeps on loading in staging environment. gives 502 timeout , gives soap error. can me understand issue here?
Read more

asynchronous - Python asyncio task got bad yield -

i confused how play around asyncio module in python 3.4. have searching api search engine, , want each search request run either parallel, or asynchronously, don't have wait 1 search finish start another. here high-level searching api build objects raw search results. search engine using kind of asyncio mechanism, won't bother that. # no asyncio module used here class search(object): ... self.s = some_search_engine() ... def searching(self, *args, **kwargs): ret = {} # raw searching according args , kwargs , build wrapped results ... return ret to try async requests, wrote following test case test how can interact stuff asyncio module. # here testing script @asyncio.coroutine def handle(f, *args, **kwargs): r = yield f(*args, **kwargs) return r s = search() loop = asyncio.get_event_loop() loop.run_until_complete(handle(s.searching, arg1, arg2, ...)) loop.close() by running pytest, return runtimeerror: task got bad yield : {results s...
Read more

javascript - Complete OpenIDConnect auth when requesting via Ajax -

the normal openidconnect server works like: you go a.com/secure-resource you 302 server your browser handles , sends identity server you login there it sends a.com via post you logged in on a.com , a.com/secure-resource on browser. however have scenario i'm trying solve need help. the user logged in on idserver the user logged in on a.com the user not logged in on b.com we need send ajax call web server b.com (from domain a.com ) b.com configured use openidconnect. but because request b.com via ajax, user cannot redirected idserver. (all in response 302 ) we can go ahead , handle 302 via ajax (i'm still not sure whether work, security-wise). but is there scenario in identityserver/openidconnect designed these situations? with identityserver in scenario setup server b.com use bearer token authentication, need use access token provided a.com in headers of ajax call $.ajax({ url: 'http://b.com', headers: { ...
Read more