Updates to cs194 week 1 page

haskell/courses/upenn_cs194/week_1.page

@@ -61,23 +61,116 @@ x = 3
   * `div` for integer division
   * `mod` for integer remainder
   * Backticks turn named functions to infix operators
+  * Operands must have the same type - no implicit coercion
+  * `fromIntegral` converts from any integral type to any numeric type
+  * `round`, `floor`, `ceiling` convert from floating point numbers to
+    Int or Integer
 
 ## Boolean Logic
 
-  *
+  * Type is `Boolean`
+  * Infix operators: `&&`, `||`
+  * `not` for negation
+  * Equality comparison: `==`, `/=`
+  * Order comparison: `<`, `>`, `<=`, `>=`
+  * Conditional: `if` *boolean* `then` *t_exp* `else` f_exp*
+  * Both *t_exp* and *f_exp* must have the same type
 
 ## Defining Basic Functions
 
+  * Definition by cases
+  * `sumtorial :: Integer -> Integer` means "function from Integer to
+    Integer"
+  * Clauses are checked from top to bottom, first match chosen
+  * Values must be the same to match, variables match anything
+  * Choice by Boolean expression can be made by *guards*
+  * `otherwise` is a synonym for `True`
+  * Don't use conditional or guards to pick `True` or `False`; just
+    use the conditional directly
+
 ## Pairs
 
+  * Syntax for type and value is `(` *x* `,` *y* `)`
+  * Types of *x* and *y* don't have to be the same
+  * Extract values via pattern-matching
+  * *n*-tuples for *n* > 2 also exist, but recommend against them
+
 ## Using Functions, Multiple Arguments
 
+  * Application via juxtaposition of function with arguments.
+  * Multi-argument function types look like `Int -> Int -> Int -> Int`
+  * Reason for the arrows to be revealed later
+  * Function application is **higher precedence** than any infix
+    operators
+
 ## Lists
 
+  * List types look like `nums :: [Integer]` which is a "list of Integers"
+  * List value syntax sugar: `[1,2,3]`
+  * Ranges: `[1..100]`; `[2,4..100]` enumerates only evens
+  * Type `String` means the same as `[Char]`
+  * Value `"hello"` means the same as `['h','e','l','l','o']`
+
 ## Constructing Lists
 
+  * Empty list: `[]`
+  * *cons* operator: *x* `:` *xs* where *xs* is a list of values of
+    the same type as *x*, possibly the empty list.
+  * Value `[2,3,4]` is the same as `2 : 3 : 4 : []`
+
 ## Functions on Lists
 
+  * Define by cases; one for empty list, the other for a cons operator
+  * The pattern `_` can be used in place of a variable when the value
+    won't be used.
+
 ## Combining Functions
 
+  * Build complex functions by combining simple ones
+  * Lazy evaluation means list elements are only calculated as needed
+  * Don't be afraid to write small functions that transform entire
+    structures and combine them; it's not as inefficient as it might
+    seem
+
 ## A Word About Error Messages
+
+  * **Don't fear error messages**
+  * How to interpret type match errors
+
+# Homework Assignment
+
+The first problem involves validating credit card numbers.
+
+  1. Find the digits of a number; write the functions:
+
+    ~~~ {.haskell}
+    toDigits    :: Integer -> [Integer]
+    toDigitsRev :: Integer -> [Integer]
+    ~~~
+
+  2. Double every other digit *from the right*
+
+    ~~~ {.haskell}
+    doubleEveryOther :: [Integer] -> [Integer]
+    ~~~
+
+  3. Sum the digits
+
+    ~~~ {.haskell}
+    sumDigits :: [Integer] -> Integer
+    ~~~
+
+  4. The number is valid iff the remainder when the sum is divided by
+     10 is 0
+
+    ~~~ {.haskell}
+    validate :: Integer -> Bool
+    ~~~
+
+The second problem is to solve the Towers of Hanoi puzzle.
+
+~~~ {.haskell}
+type Peg = String
+type Move = (Peg, Peg)
+hanoi :: Integer -> Peg -> Peg -> Peg -> [Move]
+~~~