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Category theory(範疇論)之什麼是Functor, Applicative, Monad, Semigroup, Monoid?

之前曾經寫過一篇 什麼是Monad? ，裡面提到了對於Monad的解釋，而今天進一步解釋這些在Functional Programming中常見到的詞：Functor, Applicative, Monad, Semigroup, Monoid。 透過放在一起比較，讓我們更清楚這些之間的差別與關係。

##Functor

在提到Functor之前，請先了解一下scala中map的作用，map可以讓你傳入一個function，而透過這個function是可以從F[A]轉換成F[B]，這裡的F不管他(就是代表外面的包裝不會變)，而裡面的A型態轉成B型態。

例如：

zuoky

/*

Overview
--------

To run a query using anorm you need to do three things:

 1. Connect to the database (with or without a transaction)
 2. Create an instance of `anorm.SqlQuery` using the `SQL` string interpolator
 3. Call one of the methods on `SqlQuery` to actually run the query

zuoky

1. Clone your fork:

git clone git@github.com:YOUR-USERNAME/YOUR-FORKED-REPO.git

2. Add remote from original repository in your forked repository:

cd into/cloned/fork-repo
git remote add upstream git://github.com/ORIGINAL-DEV-USERNAME/REPO-YOU-FORKED-FROM.git
git fetch upstream

zuoky

vi /etc/environment

add these lines...

LANG=en_US.utf-8
LC_ALL=en_US.utf-8

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import javax.crypto.Cipher;
import javax.crypto.spec.IvParameterSpec;
import javax.crypto.spec.SecretKeySpec;

import org.apache.commons.codec.binary.Base64;

public class Encryptor {
    public static String encrypt(String key, String initVector, String value) {
        try {
            IvParameterSpec iv = new IvParameterSpec(initVector.getBytes("UTF-8"));

zuoky

# ~/.bashrc: executed by bash(1) for non-login shells.
# see /usr/share/doc/bash/examples/startup-files (in the package bash-doc)
# for examples

# If not running interactively, don't do anything
[ -z "$PS1" ] && return

# don't put duplicate lines in the history. See bash(1) for more options
# ... or force ignoredups and ignorespace
HISTCONTROL=ignoredups:ignorespace