Pattern matching and constructors - functional-programming

Why do i get errors when I write this kind of pattern matching :
type t = A of int | B of float
let f = function
| (A i | B f) -> true
| _ -> false
or
let f = function
| A i | B f -> true
| _ -> false
Error: Variable f must occur on both sides of this | pattern
let f = function
| (A i | B i) -> true
| _ -> false
or
let f = function
| A i | B i -> true
| _ -> false
Error: This pattern matches values of type ints of type float
but a pattern was expected which matches value

If you provide a single right-hand side for multiple patterns (as you do), OCaml requires that the patterns consistently bind to pattern variables.
In the first situation,
match ... with
| A i | B f -> ...
...
the patterns don't agree on the variables they bind to: the first pattern binds to i, while the second binds to f.
In the second situation,
match ... with
| A i | B i -> ...
...
the patterns don't agree on the type of values to bind to their variables: the first pattern binds a value of type int to i, while the second binds a value of type float to i.
The only way in which these two pattern can consistently bind to variables is not to bind to any variables at all:
match ... with
| A _ | B _ -> ...
...
The complete example then becomes
type t = A of int | B of float
let f = function
| A _ | B _ -> true
| _ -> false
(But note that the last arm of the pattern match is superfluous as the first two pattern already exhaustively match all values of your type t. Hence, we get:
let f = function
| A _ | B _ -> true
This of course is equivalent to writing let f _ = true.)

In Or pattern (| pattern), you lose track of which constructors you are in. Therefore, you need to bind the same set of variables to work without referring to constructors.
And OCaml is strongly-typed; a value i cannot have both type int and type float.
If type t has more than two cases, you should write:
let f = function
| A _ | B _ -> true
| _ -> false
otherwise:
let f = function
| A _ | B _ -> true
is enough since pattern matching is already exhaustive.
I agree that Or pattern is quite restrictive, but sometimes it is helpful when you have symmetric cases in your function:
type num =
| Int of int
| Float of float
let add s1 s2 =
match s1, s2 with
| Int i1, Int i2 -> Int (i1 + i2)
| Int i, Float f | Float f, Int i -> Float (float i +. f)
| Float f1, Float f2 -> Float (f1 +. f2)

Related

Errors while iterating and processing the split string in recursive functions

Let's say we have a string
"+x1 +x2 -x3
+x4 +x5 -x6
..."
and a type formula:
type formula =
| Bot
| Top
| Atom of string
| Imp of (formula * formula)
| Or of (formula * formula)
| And of (formula * formula)
| Not of formula
let atom x = Atom x
(aka predicate logic)
and we want to:
Create a function which takes one line, splits it and turns it into disjunction using the formula type. (sort of like Or(Atom "x1", Atom "x2", Not Atom "x3") if we give the first line as an input)
I've written this:
let string_to_disj st =
let lst = Str.split (Str.regexp " \t") st in
let rec total lst =
match lst with
| [] -> Or (Bot, Bot) (*Is this correct btw?*)
| h :: t -> Or (string_to_lit h, total t);;
where
let string_to_lit =
match String.get s 0 with
| '+' -> atom (String.sub s 1 (String.length s-1))
| '-' -> Not(atom(String.sub s 1 (String.length s-1)))
| _ -> atom(s);;
However, string_to_disj raises a syntax error at line
| h :: t -> Or (string_to_lit h, total t)
What have I done wrong?
You have let rec total lst but you have no matching in. Every let requires a matching in. (Except at the top level of a module where it is for defining exported symbols of the module).
Also note that you are defining a function named total but you have no calls to the function except the one recursive call.

Making sure types are correct for all the contents of a record type recursively in OCaml

I'm not sure if there is a better way to do this but was wondering how can I make sure that all the types of a record are accurate. I tried the following code below (making a recursive function to search the record) and was going to put matches for every level / scenario... I'm somewhat new to OCaml (more of a C and Python guy) so I'm struggling with this syntax.
type typeA= Int | Bool | List of typeA
type highestLevelObject= typeA* typeB and typeB=
|Float of float
| BoolLit of bool
| Int of int
| Seq of highestLevelObjectlist
| Bool of bool
(* The function to ensure my Object came in good *)
let rec verifyFields (highestLevelObject: highestLevelObject): bool =
match highestLevelObject with
| int-> true
| bool -> true
| _ -> verifyFields highestLevelObject
This compiles with warnings...
Warning 10: this expression should have type unit. (regarding _ -> case)
Warning 11: this match case is unused. (regarding _ -> case and bool -> case)
oddly
There must be something special with the List and getting a base case here... is matching each type manually or if there is a better(more elegant) way to do this?
Looking at https://ocaml.org/learn/tutorials/data_types_and_matching.html also but still struggling.
In the pattern matching, you should deconstruct data using data constructors, like this
match highestLevelObject with
| Int -> true
| Bool -> true
| Seq objs -> ...
| _ -> false
Notice the capitalized Int which is the data constructor, contrary to int which is just a variable name, so when you write
match highestLevelObject with
| int -> ...
it is the same as saying
match highestLevelObject with
| anything -> ...
in fact, anything here could be any variable name, which will match any data and bind itself to it. In other words, match x with y -> f y is the same as let y = x in f y

Trying to use match statements in OCaml to write a function that checks if an element is in a list

I am new to OCaml and struggling to work with matches. I want to write a function that takes a list and a value and then returns true if the value is in that list and false if it is not. Here is my idea but I am struggling to get it to work.
let rec contains xs x =
match xs with
| [] -> false
| z :: zs ->
match x with
| z -> true
| _ -> contains zs x
When you use an identifier as a pattern, you will bind the value you match on to that identifier. I.e
match x with
| z -> true
will bind the value of x to the name z. You will also get a warning about z and the _ branch being unused.
You also don't need a second pattern match since it can be folded into the first:
let rec contains xs x =
match xs with
| [] -> false
| z :: _ when z = x -> true
| _ :: zs -> contains zs x

fsharp function doesn't return anything

I have the following smaller tokenizer for simple arithmetic expressions. I am new to fsharp and I don't know why this function doesn't return anything when being called. Can someone please help?
let tokenizer s =
let chars1 = scan s
let rec repeat list =
match list with
| []->[]
| char::chars ->
match char with
| ')' -> RP::repeat chars
| '(' -> LP::repeat chars
| '+' -> Plus::repeat chars
| '*' -> Times::repeat chars
| '^' -> Pow::repeat chars
| _ ->
let (x,y) = makeInt (toInt char) chars
Int x::repeat chars
repeat chars1
The implementation of scan, toInt, makeInt and the union type for the expression was not presented, but might be inferred as:
let scan (s:string) = s.ToCharArray() |> Array.toList
let toInt c = int c - int '0'
let makeInt n chars = (n,chars)
type expr = RP | LP | Plus | Times | Pow | Int of int
let tokenizer s =
let chars1 = scan s
let rec repeat list =
match list with
| []->[]
| char::chars ->
match char with
| ')' -> RP::repeat chars
| '(' -> LP::repeat chars
| '+' -> Plus::repeat chars
| '*' -> Times::repeat chars
| '^' -> Pow::repeat chars
| _ ->
let (x,y) = makeInt (toInt char) chars
Int x::repeat chars
repeat chars1
in which case:
tokenizer "1+1"
gives:
val it : expr list = [Int 1; Plus; Int 1]
It's possible the issue is in the implementation of your scan function.

How to write a pattern match in Ocaml so it is easy to scale?

I am learning Jason Hickey's Introduction to Objective Caml.
There is an exercise like this:
Exercise 4.3 Suppose we have a crypto-system based on the following substitution cipher, where each plain letter is encrypted according to the following table.
Plain | A B C D
--------------------
Encrypted | C A D B
For example, the string BAD would be encrypted as ACB.
Write a function check that, given a plaintext string s1 and a ciphertext string s2, returns true if, and only if, s2 is the ciphertext for s1. Your function should raise an exception if s1 is not a plaintext string. You may wish to refer to the string operations on page 8. How does your code scale as the alphabet gets larger? [emphasis added]
Basically, I wrote two functions with might-be-stupid-naive ways for this exercise.
I would like to ask for advice on my solutions first.
Then I would like to ask for hints for the scaled solution as highlighted in the exercise.
Using if else
let check_cipher_1 s1 s2 =
let len1 = String.length s1 in
let len2 = String.length s2 in
if len1 = len2 then
let rec check pos =
if pos = -1 then
true
else
let sub1 = s1.[pos] in
let sub2 = s2.[pos] in
match sub1 with
| 'A' -> (match sub2 with
|'C' -> check (pos-1)
| _ -> false)
| 'B' -> (match sub2 with
|'A' -> check (pos-1)
| _ -> false)
| 'C' -> (match sub2 with
|'D' -> check (pos-1)
| _ -> false)
| 'D' -> (match sub2 with
|'B' -> check (pos-1)
| _ -> false)
| _ -> false;
in
check (len1-1)
else
false
Using pure match everywhere
let check_cipher_2 s1 s2 =
let len1 = String.length s1 in
let len2 = String.length s2 in
match () with
| () when len1 = len2 ->
let rec check pos =
match pos with
| -1 -> true
| _ ->
let sub1 = s1.[pos] in
let sub2 = s2.[pos] in
(*http://stackoverflow.com/questions/257605/ocaml-match-expression-inside-another-one*)
match sub1 with
| 'A' -> (match sub2 with
|'C' -> check (pos-1)
| _ -> false)
| 'B' -> (match sub2 with
|'A' -> check (pos-1)
| _ -> false)
| 'C' -> (match sub2 with
|'D' -> check (pos-1)
| _ -> false)
| 'D' -> (match sub2 with
|'B' -> check (pos-1)
| _ -> false)
| _ -> false
in
check (len1-1)
| () -> false
Ok. The above two solutions are similar.
I produced these two, because in here http://www.quora.com/OCaml/What-is-the-syntax-for-nested-IF-statements-in-OCaml, some people say that if else is not prefered.
This is essentially the first time I ever wrote a not-that-simple function in my whole life. So I am really hungry for suggestions here.
For exmaple,
how can I improve these solutions?
should I prefer match over if else?
Am I designing the rec or use the rec correctly?
if that in check (len1-1) correct?
Scale it
The exercise asks How does your code scale as the alphabet gets larger?. I really don't have a clue for now. In Java, I would say I will have a map, then for each char in s1, I am looking s2 for the according char and to see whether it is the value in the map.
Any suggestions on this?
Here's a simple solution:
let tr = function
| 'A' -> 'C'
| 'B' -> 'A'
| 'C' -> 'D'
| 'D' -> 'B'
| _ -> failwith "not a plaintext"
let check ~tr s1 s2 = (String.map tr s1) = s2
check ~tr "BAD" "ACD"
you can add more letters by composing with tr. I.e.
let comp c1 c2 x = try (c1 x) with _ -> (c2 x)
let tr2 = comp tr (function | 'X' -> 'Y')
how can I improve these solutions?
You misuse indentation which makes the program much harder to read. Eliminating unnecessary tabs and move check to outer scope for readability:
let check_cipher_1 s1 s2 =
let rec check pos =
if pos = -1 then
true
else
let sub1 = s1.[pos] in
let sub2 = s2.[pos] in
match sub1 with
| 'A' -> (match sub2 with
|'C' -> check (pos-1)
| _ -> false)
| 'B' -> (match sub2 with
|'A' -> check (pos-1)
| _ -> false)
| 'C' -> (match sub2 with
|'D' -> check (pos-1)
| _ -> false)
| 'D' -> (match sub2 with
|'B' -> check (pos-1)
| _ -> false)
| _ -> false in
let len1 = String.length s1 in
let len2 = String.length s2 in
if len1 = len2 then
check (len1-1)
else false
should I prefer match over if else?
It depends on situations. If pattern matching is superficial as you demonstrate in the 2nd function (match () with | () when len1 = len2) then it brings no value compared to a simple if/else construct. If you pattern match on values, it is better than if/else and potentially shorter when you make use of advanced constructs. For example, you can shorten the function by matching on tuples:
let check_cipher_1 s1 s2 =
let rec check pos =
if pos = -1 then
true
else
match s1.[pos], s2.[pos] with
| 'A', 'C' | 'B', 'A'
| 'C', 'D' | 'D', 'B' -> check (pos-1)
| _ -> false in
let len1 = String.length s1 in
let len2 = String.length s2 in
len1 = len2 && check (len1 - 1)
Here we also use Or pattern to group patterns having the same output actions and replace an unnecessary if/else block by &&.
Am I designing the rec or use the rec correctly?
if that in check (len1-1) correct?
Your function looks nice. There's no better way than testing with a few inputs on OCaml top-level.
Scale it
The number of patterns grows linearly with the size of the alphabet. It's pretty nice IMO.
The simplest solution seems to be to just cipher the text and compare the result:
let cipher_char = function
| 'A' -> 'C'
| 'B' -> 'A'
| 'C' -> 'D'
| 'D' -> 'B'
| _ -> failwith "cipher_char"
let cipher = String.map cipher_char
let check_cipher s1 s2 = (cipher s1 = s2)
The cipher_char function scales linearly with the size of the alphabet. To make it a bit more compact and generic you could use a lookup table of some form, e.g.
(* Assume that only letters are needed *)
let cipher_mapping = "CADB"
let cipher_char c =
try cipher_mapping.[Char.code c - Char.code 'A']
with Invalid_argument _ -> failwith "cipher_char"

Resources