(* Jenny Zhong, Lab 2, 09/22/2017 *)
(* Problem 1 *)
(* Example 1 *)
(* r = 3*(3*3)*2 = 54 *)
val m : int = 2
val r : int =
let
val m : int = 3
val n : int = m * m
in
m * n
end * m
(* Example 2 *)
(* test = (3.0+2.0)*(1.0+3.0)*(-1.0+2.0) = 20.0 *)
val x : real = 1.0
val y : real = 2.0
fun f(x : real) : real = x + y
fun g(y : real) : real = x + y
fun h(x : real, y : real, f : real -> real, g : real -> real) : real =
let
val x : real = 3.0
in
f(x)
end * g(y) * f(x)
val test:real = h(~1.0,3.0,f,g)
(* Example 3 *)
(* x=2; y=2.0; z="2"; r=2.0 *)
val triple : int*real*string = (2, 2.0, "2")
val pair_of_pairs : (int*int) * (real*real) = ((2, 3), (2.0, 3.0))
val (x : int, y : real, z : string) = triple
val ((_,_), (r : real,_)) = pair_of_pairs
(* Problem 2 *)
(* Error 1: andalso is an operator for combining two boolean variables;
and is a logical operator for evaluating two expressions. *)
(* Error 2: val needs to be declared *)
(* Error 3: ~ is used for negative *)
(* Error 4: 3 is not of type real, 3.0 is *)
(* Error 5: a pair of pairs is not the same as a quadruple *)
local
type vec = real*real and mat = (real*real) * (real*real)
in
val x : vec = (1.0, 2.0) and y : vec = (~2.0, 3.0) and a : mat = ((1.0, 2.0), (2.0, 1.0))
end
(* Problem 3 *)
local
type vec = real*real and mat = (real*real) * (real*real)
fun help1 (x:vec, c:real) : vec =
let
val (a : real, b : real) = x
in
(c*a, c*b)
end
fun help2 (x:vec, y:vec) : vec =
let
val (m : real, n : real) = x
val (p : real, q : real) = y
in
(m+p, n+q)
end
in
fun mat_vec_mul (a:mat, x:vec) : vec =
let
val ((a11:real, a21:real), (a12:real, a22:real)) = a
val (x1 : real, x2 : real) = x
val col1 : vec = (a11, a21)
val col2 : vec = (a12, a22)
in
help2 (help1(col1,x1), help1(col2,x2))
end
val test : vec = mat_vec_mul (((1.0,3.0), (2.0,4.0)), (5.0,6.0))
fun rot (x:vec, t:real) : vec =
let
val rotation_matrix : mat = ((Math.cos(t), Math.sin(t)), (~(Math.sin(t)), Math.cos(t)))
in
mat_vec_mul(rotation_matrix, x)
end
end
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