ocaml the pl for the discerning hacker.. hello. i’m zach, one of sorin’s students....
TRANSCRIPT
OCamlThe PL for the discerning
hacker.
ML Anatomy 101
ML Program = One Giant, Complex Expression
Controlling complexity is the essence of computer programming.
B. Kerninghan
A complex system that works is invariably found to have evolved from a simple system that worked.
J. Gall
ML Program = ? ? ?
Building ML Programs
ML provides tools to control complexity
Build complex exprs from simple exprs
Build complex types from simple types
NOW
THU
Building Expressions
1. basic (recap)
2. let
3. if
4. fun
5. demoM.C. Escher’s Waterfall
in LEGO
basic
Type Expression Value
int 5 5
int 5 * 5 * 5 125
string “hello” “hello”
string “Je” ^ “ll” ^ “o” “Jello”
tuple (5 * 5, “ab” ^ “cd”) (25, “abcd”)
int list [1; 2] @ [3; 4] [1; 2; 3; 4]
int list 1 :: 2 :: 3 :: 4 :: [] [1; 2; 3; 4]
basic
Don’t know how it works ?
Try it in the toplevel !
Building Expressions
1. basic (recap)
2. let
3. if
4. fun
5. demoM.C. Escher’s Waterfall
in LEGO
Variables are central to programming
Associate a name with a computation
let expressions are how ML does it
let
let
let
Bind name NM to expression E1 within E2:
let NM = E1 in E2
Semantics (what it means):
1. evaluate E1 to value V
2. replace NM with V in E2
let examples
let x = 5 in x
let x = 5 in x * x
let x = 5 * 5 in x * x
let x = “hello” in print_string x
let print = print_string inprint “hello”
let chaining (outside)
Let syntax : let NM = E1 in E2
E2 can be another let
let x = 2 inlet y = 3 inlet x2 = x * x inlet y2 = y * y inx2 + y2
let nesting (inside)
Let syntax : let NM = E1 in E2
E1 can be another let
let x2 =let x = 5 inx * x
inx2 + x2
let name clashes (outside)
Let syntax : let NM = E1 in E2
What if NM appears in E2 ?
let x = 1 inlet x = 2 inx
Our naïve semantics were wrong!
let name clashes
Let syntax : let NM = E1 in E2
Semantics (what it means):
1. evaluate E1 to value V
2. replace UNBOUND NM with V in E2
Essentially, use nearest binding.
let name clashes (inside)
Let syntax : let NM = E1 in E2
What if NM appears in E1 ?
let x =let x = 5 inx * x
inx * x
name clash mania
let x =let x = 5 inlet x = x * x inlet x =
let x = x + x inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x = 5 inlet x = 5 * 5 inlet x =
let x = x + x inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x = 5 * 5 inlet x =
let x = x + x inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x = 25 inlet x =
let x = x + x inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x = 25 inlet x =
let x = 25 + 25 inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x =
let x = 25 + 25 inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x =
let x = 50 inlet x = x * x inx
inx + x
inx * x
name clash mania
let x =let x =
let x = 50 inlet x = 50 * 50 inx
inx + x
inx * x
name clash mania
let x =let x =
let x = 50 * 50 inx
inx + x
inx * x
name clash mania
let x =let x =
let x = 2500 inx
inx + x
inx * x
name clash mania
let x =let x =
let x = 2500 in2500
inx + x
inx * x
name clash mania
let x =let x =
2500inx + x
inx * x
name clash mania
let x =let x = 2500 inx + x
inx * x
name clash mania
let x =let x = 2500 in2500 + 2500
inx * x
name clash mania
let x =2500 + 2500
inx * x
name clash mania
let x = 5000 inx * x
name clash mania
let x = 5000 in5000 * 5000
name clash mania
5000 * 5000
name clash mania
25,000,000
name clash, but later
let x = 5 inlet y = x * x inlet x = 10 iny
What is the value of this expr?
25 : because x was 5 when y was defined
Binding to value is fixed at definition.
let vs. assign
What’s the difference?
No Time Travellet cannot affect anything before itself
Lexical Scopingknow where in prog each name defined
let vs. assign
No Time Travel + Lexical Scoping
Why are these good?
1. Behavior fixed at definition
2. Localize debugging
3. Simplifies reasoning
Building Expressions
1. basic (recap)
2. let
3. if
4. fun
5. demoM.C. Escher’s Waterfall
in LEGO
if
Programs make decisions
Ask our patient and careful friend (computer):
“If X is true, please go do A. Otherwise, please go do B.”
if expressions are how ML does it
if
if TEST thenE1
elseE2
If TEST evals to true, eval expr E1.
Otherwise, eval expr E2.
if : just an expression
if TEST then E1 else E2
if is an expression
evaluates to a value
has a type
use anywhere expr accepted
if examples
Type Expression Value
int if true then 5 else 10 5
int if false then 5 else 10 10
string if 1 < 5 then “hello”else “goodbye” “hello”
int list 1 :: (if 10 mod 5 = 0 then [2; 3] else [4; 5]) [1; 2; 3]
if style exercise : Java to OCaml
int foo(int i, boolean b, c, d) { if (b) { i++; } if (c) { return i + 2; } if (d) { i = i + 3; } else { return i + 4; } return i;}
if style exercise : Java to OCaml
let foo i b c d = let j = if b then i + 1 else i in if c then j + 2 else if d then j + 3 else j + 4
if
So far, then and else exprs had same type
What about: if ... then 5 else “hello”
Rejected!
then and else exprs must have same type
if rules
Typing:
if has same type as then and else exprs
Eval (semantics):
e1 : bool e2: T e3: T
if e1 then e2 else e3 : T
e1 )) true e2 )) v2 .
if e1 then e2 else e3 )) v2 e1 )) false e3 )) v3
.if e1 then e2 else e3 )) v3
Building Expressions
1. basic (recap)
2. let
3. if
4. fun
5. demoM.C. Escher’s Waterfall
in LEGO
abstraction
fun
Abstraction: ultimate complexity manager
Provide simple interface to complex expr
functions are how ML does it
fun
fun NM -> E
Accept value V as input.
Replace unbound name NM in expr E with V.
fun examples
(fun x -> x) 5
(fun x -> x * x) 5
(fun x -> 5) 10
(fun x -> “hello “ ^ x) “india”
let h = “hello ” in(fun x -> h ^ x) “india”
functions are values
bind a function to a name with let:
let double = fun x -> x + x indouble 5
let quad = fun x ->(double x) + (double x)
inquad 5
functions are values
store functions in a tuple:
( fun x -> x, fun x -> 5, fun x -> “hello”)
tuple : can have different types
: ‘a -> ‘a: ‘a -> int: ‘a -> string
functions are values
store functions in a list:
[ fun x -> x * x; fun x -> 5; fun x -> x / 2]
list : must have same type
: int -> int: int -> int: int -> int
more fun parameters
Can functions have only one parameter?
Nope.
functions can return functions!
fun x ->fun y ->
x + y
takes x and returns (takes y and returns (sum of x and y))
function on function action
let add =fun x ->
fun y ->x + y
inadd 5 10
function on function action
let str_concat =fun x ->
fun y ->x ^ y
instr_concat “hello “ “india”
functions are values
functions can take functions as input!
let apply =fun f ->
fun x ->f x
inapply print_string “hello”
functions are values
functions can take functions as input!
(fun f ->fun x ->
f x)print_string “hello”
functions are values
functions can take functions as input!
(fun x ->print_string x)
“hello”
functions are values
functions can take functions as input!
print_string “hello”
function shorthand
syntactic sugar
let NM P1 ... PN = E
means
let NM =fun P1 ->
...fun PN ->
E
function shorthand
let add5 x = x + 5
let add x y = x + y
let str_concat x y = x ^ y
let apply f x = f x
let apply_twice f x = f (f x)
recursive fun
How do we write recursive functions?
We can’t yet!
Problem: NM is not bound until after let.
Need more than just sugar . . .
recursive fun
Need let rec:
let rec NM P = E
NM is bound to this definition inside E.
recursive fun
let rec is_even n =...
recursive fun
let rec is_even n =if n = 0 then
trueelse if n = 1 then
falseelse
is_even (n – 2)
recursive fun
let rec fib n =...
recursive fun
let rec fib n =if n = 0 then
1else if n = 1 then
1else
(fib (n – 1)) + (fib (n – 2))
recursive fun
let rec factorial n =...
recursive fun
let rec factorial n =if n = 0 then
1else
n * (factorial (n – 1))
recursive fun
let rec forever () =(* infinite loop *)
recursive fun
let rec forever () =forever ()
fun and let
Simple enough:
let x = 5 inlet f y = x + y inf 10
Evals to 15.
fun and let
But what about:
let x = 5 inlet f y = x + y inlet x = 10f 10
Still evals to 15.
Behavior fixed at binding !
Building Expressions
1. basic (recap)
2. let
3. if
4. fun
5. demoM.C. Escher’s Waterfall
in LEGO
demo
Conway’s Game of Life
Building Expressions
1. basic (recap)
2. let
3. if
4. fun
5. demo
Next Time : Building Types
M.C. Escher’s Waterfallin LEGO
