Prestashop last 1.6 version with nginx - php-fpm - mariadb.

BUILD

docker-compose run --rm -e PS_DOMAIN="prestashop.local"
-e DB_SERVER="database"
-e DB_PORT=3306
-e DB_NAME=prestashop
-e DB_USER=prestashop
-e DB_PASSWD=prestasop
-e DB_PREFIX=ps_
-e ADMIN_MAIL=demo@prestashop.com
-e ADMIN_PASSWD=prestashop_demo
-e PS_LANGUAGE=es
-e PS_COUNTRY=ES
-e PS_INSTALL_AUTO=1
-e PS_ERASE_DB=0
-e PS_DEV_MODE=0
-e PS_HOST_MODE=0
-e PS_FOLDER_ADMIN=admin
-e PS_FOLDER_INSTALL=install prestashop docker-php-prestashop

If differents user/group ids are needed: docker-compose run --rm --no-deps prestashop chown -R xxxx:xxxx /var/www/html

RUN docker-compose up

Set prestashop.local in hosts file and test it.