coq - What are inductive predicates? -


how explain inductive predicates? used for? what's theory behind them? present in dependent type systems, or in other systems well? related gadt's in way? why true default in coq?

this example coq:

inductive : nat -> prop := | even0 : 0 | evens : forall p:nat, p -> (s (s p))

how use definition? datatype or proposition?

i think call inductive predicates objects defined inductively , sorted in prop.

they used defining properties inductively (duh). theory behind can found in literature inductive constructions. search papers cic (the calculus of inductive constructions) instance.

they related gadts, though dependent types can express more things. if not mistaken, gadts each constructor lives in 1 particular family, whereas addition of dependent types allows constructors inhabit different families based on arguments.

i not know mean "true default in coq".

even define inductive datatype. not proposition yet, type nat -> prop indicates. proposition even 0 or even 1. can inhabited (provable) in even 0, or not in even 1.


Comments

Post a Comment

Popular posts from this blog

apache - Remove .php and add trailing slash in url using htaccess not loading css -

i have add following code htaccess file removing .php extension , add trailing slash urls. worked fine reduced page loading speed , css code not loading @ all. pages ugly. please help rewriteengine on rewritebase / ## hide .php extension snippet # externally redirect /dir/foo.php /dir/foo rewritecond %{the_request} ^[a-z]{3,}\s([^.]+)\.php [nc] rewriterule ^ %1/ [r,l] # add trailing slash rewritecond %{request_filename} !-f rewritecond %{request_uri} !/$ rewriterule . %{request_uri}/ [l,r=301] # internally forward /dir/foo /dir/foo.php rewritecond %{request_filename} !-d rewritecond %{request_filename}.php -f rewriterule ^(.*?)/?$ $1.php [l] we can rewrite urls using .htaccess files. before writing in .htaccess files need verify kind of server using. can check server adding a <?php phpinfo(); ?> in php page. ensure mod_rewrite module enabled in apache server. can identified checking phpinfo included page. common methods used url rewriting follows ...
Read more

javascript - jQuery show full size image on click -

pretty self explanatory not workking . i want display full image when user click on image... yes know there tons of plugins but i want keep simple. any idea ? css : .full { display: none; width: 500px; height: 500px; margin-left: 100px; margin-top: -300px; position: fixed; background-color: #f00; z-index: 6; } .thumbnail { width: 50px; height: 50px; } html: <img class="thumbnail" src="http://4.bp.blogspot.com/-uhbdp2esxng/txneptvi92i/aaaaaaaaaky/upfqis7zto0/s1600/rihanna-wallpaper.jpg"> jquery: $(document).ready(function() { $('.thumbnail').on('click', function() { var img = $('<img />',{src:this.src,'class':'full'}); $('.full').html(img).show(); console.log('done!'); }); }); try looking how jquery works. $(document).ready(function() { $('.thumbnail').on('click', function(...
Read more