- (* 3.3.2 *)
- fun flip(nil) = nil
= |   flip(x::nil) = [x]
= |   flip(x::y::zs) = y::x::flip(zs);
val flip = fn : 'a list -> 'a list
- flip([1,2,3,4,5,6]);
val it = [2,1,4,3,6,5] : int list
- (* 3.3.3 *)
- (* L = [a1, a2, a3, ..., an] -> [a1, a2, .... , ai-1, ai+1, ...] *)
- val rec remove = fn (nil, _) => nil |
=                     (L, 0) => L |
=                     (x::xs, 1) => xs |
=                     (x::xs, i) => x::remove(xs, i-1);
val remove = fn : 'a list * int -> 'a list
- remove(L, 3);
val it = [1,2,4,5,6,7] : int list
- (* 3.3.4 *val it = 6 : int
- (* sumLists(L) -> 1 + sumLists([[2], nil, [3])
=                -> 1 + 2 + sumLists([nil, nil, [3]])
=                -> 1 + 2 + sumLists([nil, [3]])
=                -> 1 + 2 + sumLitsts([[3]])
=                -> 1 + 2 + 3 + sumLitsts(nil)
=                -> 6
= *)
- (* 3.3.5 *)
- (* (x::y::zs, w) *)
- (["a", "b", "c"], ["d", "e"]);
val it = (["a","b","c"],["d","e"]) : string list * string list
- (* x="a", y="b", zs=["c"], w=["d", "e"] *)
- (["a", "b"], 4.5);
val it = (["a","b"],4.5) : string list * real
- (* x="a", y="b", zs=nil, w=4.5 *)
- ([5], [6,7]);
val it = ([5],[6,7]) : int list * int list
- (* x=5, y=.... -> fail *)
- (* 3.3.6 *)
- (* 3.3.7 *)
- fun square(0) = 0
= |   square(n) = square(n-1) + 2*n - 1;
val square = fn : int -> int
- square(3);
val it = 9 : int
- square(11);
val it = 121 : int
- (* 3.3.8 *)
- fun sortPair(nil) = nil
= |   sortPair((m,n)::xs) =
=       if m<n then (m,n)::sortPair(xs) else (n,m)::sortPair(xs);
val sortPair = fn : (int * int) list -> (int * int) list
- sortPair([(2,1),(10,5),(4,3),(11,9)]);
val it = [(1,2),(5,10),(3,4),(9,11)] : (int * int) list
- (* 3.3.9 *)
- fun vowel(nil) = false
= |   vowel(c::cs) =
=       if c = #"a" orelse c = #"i" orelse c = #"u" orelse c = #"e" orelse c = #"o" then true else false;
val vowel = fn : char list -> bool
- (* ... orelse c = #"A" orelse c = #"I" orelse .... *)
- fun vowel(nil) = false
= |   vowel(c::cs) = c = #"a" orelse c = #"i" orelse c = #"u" orelse c = #"e" orelse c = #"o";
val vowel = fn : char list -> bool
- vowel(explode("abc"));
val it = true : bool
- vowel(explode("bca"));
val it = false : bool
- (* 3.3.11 *)
- fun member(_, nil) = false
= |   member(x, y::ys) =
=       if x=y then true else member(x,ys);
stdIn:126.11 Warning: calling polyEqual
val member = fn : ''a * ''a list -> bool
- member(2, [1,2,3]);
val it = true : bool
- member(1, [0,2,3,4]);
val it = false : bool
- val rec member = fn
=          (_, nil) => false |
=          (x, y::ys) => if x=y then true else member(x,ys);
stdIn:131.28 Warning: calling polyEqual
val member = fn : ''a * ''a list -> bool
- member(1, [1,2,3]);
val it = true : bool
- member(10, [1,2,5]);
val it = false : bool
- fun delete(_,nil) = nil
= |   delete(x,y::ys) = if x=y then ys else y::delete(x,ys);
stdIn:135.27 Warning: calling polyEqual
val delete = fn : ''a * ''a list -> ''a list
- delete(#"d", explode("abcdefg"));
val it = [#"a",#"b",#"c",#"e",#"f",#"g"] : char list
- fun insert(x, nil) = [x]
= |   insert(x, S) = if member(x, S) then S else x::S;
val insert = fn : ''a * ''a list -> ''a list
- insert(#"a", explode("bcde"));
val it = [#"a",#"b",#"c",#"d",#"e"] : char list
- val rec delete = fn (_, nil) => nil | (x,y::ys) => if x=y then ys else y::delete(x,ys);
stdIn:141.56 Warning: calling polyEqual
val delete = fn : ''a * ''a list -> ''a list
- delete(3, [1,2,3,4,5]);
val it = [1,2,4,5] : int list
- val insert = fn (x, nil) => [x] | (x, S) => if member(x, S) then S else x::S;
val insert = fn : ''a * ''a list -> ''a list
- insert(0, [1,2,3]);
val it = [0,1,2,3] : int list
- (* 3.3.12 *)
- fun insertHead(x, nil) = nil
= |   insertHead(x, y::ys) = (x::y)::insertHead(x, ys);
val insertHead = fn : 'a * 'a list list -> 'a list list
- insertHead(1, [[2,3],nil,[2,4,6]]);
val it = [[1,2,3],[1],[1,2,4,6]] : int list list
- (* 3.3.13 *)
- (* http://koko15.hus.osaka-u.ac.jp/members/yoshida/stattext/DraftLisp.html *)
- (* 3.3.13 *)
- val rec powerSet = fn nil => [nil] | x::xs => powerSet(xs)@insertHead(x, powerSet(xs));
val powerSet = fn : 'a list -> 'a list list
- powerSet([1,3,4]);
val it = [[],[4],[3],[3,4],[1],[1,4],[1,3],[1,3,4]] : int list list
- powerSet([2,5]);
val it = [[],[5],[2],[2,5]] : int list list
- fun powerSet(nil) = [nil]
= |   powerSet(x::xs) =
=       let
=           val L = powerSet(xs)
=       in
=           L@insertHead(x, L)
=       end;
val powerSet = fn : 'a list -> 'a list list
- powerSet([2,4,5]);
val it = [[],[5],[4],[4,5],[2],[2,5],[2,4],[2,4,5]] : int list list
- (* 3.3.14 *)
- (* a, [b1, b2, ...] -> (a-b1) * (a-b2) * ... *)
- val rec pd1 = fn (_, nil) => 1.0 | (x, y::ys) => (x-y)*pd1(x, ys);
val pd1 = fn : real * real list -> real
- pd1(10.0, [1.0, 2.0, 3.0]);
val it = 504.0 : real
- (* [a1,a2,a3,...] -> (a1-a2)*(a1-a3)*...(a2-a3)*...(ai-aj)*... [i<j] *)
- val rec prodDiv = fn nil => 1.0 | x::xs => pd1(x, xs)*prodDiv(xs);
val prodDiv = fn : real list -> real
- prodDiv([1.0,2.0]);
val it = ~1.0 : real
- prodDiv([2.2, 1.4, 3.8]);
val it = 3.072 : real
- (* 3.3.15 *)
- val rec isNill = fn nil => true | x::xs => false;
val isNill = fn : 'a list -> bool
- isNill(nil);
val it = true : bool
- isNill([1,2,3]);
val it = false : bool
- null([]);
val it = true : bool
- null([1,2,3]);
val it = false : bool
- (* 3.3.16 *)
- val rec sumPairs = fn nil => 0 | (x,y)::zs => x + y + sumPairs(zs);
val sumPairs = fn : (int * int) list -> int
- sumPairs([(1,3),(2,5)]);
val it = 11 : int
- (* nil => 0 ---> 'a list => int
=    (x,y)::zs => x + y + sumPairs(zs)
=        ---> x + y + ...: int
=        ---> x:int, y:int
=   ---> fn : (int * int) -> int
= *)