Difference between revisions of "Pattern Matching Assignment"
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for our made-up pattern language are defined by: | for our made-up pattern language are defined by: | ||
− | + | <syntaxhighlight lang="sml"> | |
+ | datatype typ = Anything (* any type of value is okay *) | ||
| UnitT (* type for Unit *) | | UnitT (* type for Unit *) | ||
| IntT (* type for integers *) | | IntT (* type for integers *) | ||
| TupleT of typ list (* tuple types *) | | TupleT of typ list (* tuple types *) | ||
| Datatype of string (* some named datatype *)</nowiki> | | Datatype of string (* some named datatype *)</nowiki> | ||
+ | </syntaxhighlight> | ||
<code>typecheck_patterns</code> should have type <code>((string * string * typ) list) * (pattern list) -> typ option</code>. | <code>typecheck_patterns</code> should have type <code>((string * string * typ) list) * (pattern list) -> typ option</code>. | ||
Line 202: | Line 204: | ||
=Type Summary= | =Type Summary= | ||
− | + | <syntaxhighlight lang="sml"> | |
+ | val g = fn : (unit -> int) -> (string -> int) -> pattern -> int | ||
val only_capitals = fn : string list -> string list | val only_capitals = fn : string list -> string list | ||
val longest_string1 = fn : string list -> string | val longest_string1 = fn : string list -> string | ||
Line 219: | Line 222: | ||
val match = fn : valu * pattern -> (string * valu) list option | val match = fn : valu * pattern -> (string * valu) list option | ||
val first_match = fn : valu -> pattern list -> (string * valu) list option | val first_match = fn : valu -> pattern list -> (string * valu) list option | ||
− | val typecheck_patterns = fn : (string * string * typ) list * pattern list -> typ option</ | + | val typecheck_patterns = fn : (string * string * typ) list * pattern list -> typ option |
+ | </syntaxhighlight> | ||
=Test= | =Test= |
Latest revision as of 19:25, 10 July 2023
Contents
Hints and Gotchas
Credit
All credit for this assignment goes to Prof. Grossman and his team at UW. UW or Coursera
Code To Implement
You will define several SML functions. Many will be very short because they will use other higher-order functions. You may use functions in ML’s library; the problems point you toward the useful functions and often require that you use them. The sample solution is about 120 lines, including the provided code, but not including the challenge problem. This assignment is probably more difficult than Homework 2 even though (perhaps because) many of the problems have 1-line answers.
String Functions
1) only_capitals
Write a function only_capitals
that takes a string list
and returns a string list
that has only
the strings in the argument that start with an uppercase letter. Assume all strings have at least 1
character. Use List.filter, Char.isUpper, and String.sub to make a 1-2 line solution.
2) longest_string1
Write a function longest_string1
that takes a string list
and returns the longest string
in the
list. If the list is empty, return "". In the case of a tie, return the string closest to the beginning of the
list. Use foldl, String.size, and no recursion (other than the implementation of foldl is recursive).
3) longest_string2
Write a function longest_string2
that is exactly like longest_string1
except in the case of ties
it returns the string closest to the end of the list. Your solution should be almost an exact copy of
longest_string1. Still use foldl and String.size.
4) longest_string_helper, longest_string3, and longest_string4
Write functions longest_string_helper
, longest_string3
, and longest_string4
such that:
longest_string3
has the same behavior aslongest_string1
andlongest_string4
has the same behavior aslongest_string2
.longest_string_helper
has type(int * int -> bool) -> string list -> string
(notice the currying). This function will look a lot likelongest_string1
andlongest_string2
but is more general because it takes a function as an argument.- If
longest_string_helper
is passed a function that behaves like > (so it returns true exactly when its first argument is strictly greater than its second), then the function returned has the same behavior aslongest_string1
. longest_string3
andlongest_string4
are defined with val-bindings and partial applications oflongest_string_helper
.
5) longest_capitalized
Write a function longest_capitalized
that takes a string list
and returns the longest string in
the list that begins with an uppercase letter, or "" if there are no such strings. Assume all strings
have at least 1 character. Use a val-binding and the ML library’s o operator for composing functions.
Resolve ties like in problem 2.
6) rev_string
Write a function rev_string
that takes a string
and returns the string
that is the same characters in
reverse order. Use ML’s o operator, the library function rev for reversing lists, and two library functions
in the String module. (Browse the module documentation to find the most useful functions.)
Utilities For Pattern Matching
The next two problems involve writing functions over lists that will be useful in later problems.
7) first_answer
Write a function first_answer
of type (’a -> ’b option) -> ’a list -> ’b
(notice the 2 arguments are curried). The first argument should be applied to elements of the second argument in order
until the first time it returns SOME v
for some v and then v is the result of the call to first_answer
.
If the first argument returns NONE
for all list elements, then first_answer
should raise the exception
NoAnswer
. Hints: Sample solution is 5 lines and does nothing fancy.
8) all_answers
Write a function all_answers
of type (’a -> ’b list option) -> ’a list -> ’b list option
(notice the 2 arguments are curried). The first argument should be applied to elements of the second
argument. If it returns NONE
for any element, then the result for all_answers
is NONE
. Else the
calls to the first argument will have produced SOME lst1, SOME lst2, ... SOME lstn
and the result of
all_answers
is SOME lst
where lst
is lst1, lst2, ..., lstn
appended together (order doesn’t matter).
Hints: The sample solution is 8 lines. It uses a helper function with an accumulator and uses @. Note
all_answers f []
should evaluate to SOME []
.
Pattern And Valu Datatypes
The remaining problems use these type definitions, which are inspired by the type definitions an ML implementation would use to implement pattern matching:
datatype pattern = Wildcard
| Variable of string
| UnitP
| ConstP of int
| TupleP of pattern list
| ConstructorP of string * pattern
datatype valu = Const of int
| Unit
| Tuple of valu list
| Constructor of string * valu</nowiki>
Given valu v and pattern p, either p matches v or not. If it does, the match produces a list of string * valu pairs; order in the list does not matter. The rules for matching should be unsurprising:
Wildcard
matches everything and produces the empty list of bindings.Variable s
matches any value v and produces the one-element list holding (s,v).UnitP
matches onlyUnit
and produces the empty list of bindings.ConstP 17
matches onlyConst 17
and produces the empty list of bindings (and similarly for other integers).TupleP ps
matches a value of the formTuple vs
if ps and vs have the same length and for all i, the ith element of ps matches the ith element of vs. The list of bindings produced is all the lists from the nested pattern matches appended together.ConstructorP(s1,p)
matchesConstructor(s2,v)
if s1 and s2 are the same string (you can compare them with =) and p matches v. The list of bindings produced is the list from the nested pattern match. We call the strings s1 and s2 the constructor name.- Nothing else matches.
Pattern Matching Rosetta Stone
datatype pattern = Wildcard
| Variable of string
| UnitP
| ConstP of int
| TupleP of pattern list
| ConstructorP of string * pattern
type point = (int * int)
type circle = (point * int)
fun is_overlapping_with_origin(circle_option : circle option) : bool =
case circle_option of
NONE (* pattern_a *) => false
| SOME((x,y),radius) (* pattern_b *) => x*x + y*y <= radius*radius
val false_none = is_overlapping_with_origin(NONE)
val true_r6 = is_overlapping_with_origin(SOME((3,4),6))
val true_r5 = is_overlapping_with_origin(SOME((3,4),5))
val false_r4 = is_overlapping_with_origin(SOME((3,4),4))
val pattern_a = ConstructorP("NONE", UnitP)
val pattern_b = ConstructorP("SOME",
TupleP([
TupleP([Variable("x"), Variable("y")]),
Variable("radius")
])
)
fun is_radius_42(circle_option : circle option) : bool =
case circle_option of
SOME(_,42) (* pattern_c *) => true
| _ (* pattern_d *) => false
val b = is_radius_42(SOME((1,2),42))
val pattern_c = ConstructorP("SOME",
TupleP([
Wildcard,
ConstP(42)
])
)
val pattern_d = Wildcard
Pattern Matching Functions
9) count_wildcards, count_wild_and_variable_lengths, and count_some_var
(This problem uses the pattern datatype but is not really about pattern-matching.) A function g
has been provided to you.
9a) count_wildcards
Use g
to define a function count_wildcards
that takes a pattern and returns how many Wildcard
patterns it contains.
9b) count_wild_and_variable_lengths
Use g
to define a function count_wild_and_variable_lengths
that takes a pattern and returns
the number of Wildcard
patterns it contains plus the sum of the string lengths of all the variables
in the variable patterns it contains. (Use String.size. We care only about variable names; the
constructor names are not relevant.)
9c) count_some_var
Use g
to define a function count_some_var
that takes a string and a pattern (as a pair) and
returns the number of times the string appears as a variable in the pattern. We care only about
variable names; the constructor names are not relevant.
10) check_pat
Write a function check_pat
that takes a pattern and returns true if and only if all the variables
appearing in the pattern are distinct from each other (i.e., use different strings). The constructor
names are not relevant. Hints: The sample solution uses two helper functions. The first takes a
pattern and returns a list of all the strings it uses for variables. Using foldl with a function that uses
@ is useful in one case. The second takes a list of strings and decides if it has repeats. List.exists may
be useful. Sample solution is 15 lines. These are hints: We are not requiring foldl and List.exists
here, but they make it easier.
11) match
Write a function match
that takes a valu * pattern
and returns a (string * valu) list option
,
namely NONE
if the pattern does not match and SOME lst
where lst is the list of bindings if it does.
Note that if the value matches but the pattern has no patterns of the form Variable s
, then the result
is SOME []
. Hints: Sample solution has one case expression with 7 branches. The branch for tuples
uses all_answers
and ListPair.zip. Sample solution is 13 lines. Remember to look above for the
rules for what patterns match what values, and what bindings they produce. These are hints: We are
not requiring all_answers
and ListPair.zip here, but they make it easier.
12) first_match
Write a function first_match
that takes a value and a list of patterns and returns a
(string * valu) list option
, namely NONE
if no pattern in the list matches or SOME lst
where
lst is the list of bindings for the first pattern in the list that matches. Use first_answer
and a
handle-expression. Hints: Sample solution is 3 lines.
Challenge Problem
13) typecheck_patterns
Write a function typecheck_patterns
that “type-checks” a pattern list. Types
for our made-up pattern language are defined by:
datatype typ = Anything (* any type of value is okay *)
| UnitT (* type for Unit *)
| IntT (* type for integers *)
| TupleT of typ list (* tuple types *)
| Datatype of string (* some named datatype *)</nowiki>
typecheck_patterns
should have type ((string * string * typ) list) * (pattern list) -> typ option
.
The first argument contains elements that look like ("foo","bar",IntT), which means constructor foo
makes a value of type Datatype "bar" given a value of type IntT. Assume list elements all have different
first fields (the constructor name), but there are probably elements with the same second field (the datatype
name). Under the assumptions this list provides, you “type-check” the pattern list to see if there exists
some typ (call it t) that all the patterns in the list can have. If so, return SOME t
, else return NONE
.
You must return the “most lenient” type that all the patterns can have. For example, given patterns
TupleP[Variable("x"),Variable("y")]
and TupleP[Wildcard,Wildcard]
, return TupleT[Anything,Anything]
even though they could both have type TupleT[IntT,IntT]
. As another example, if the only patterns
are TupleP[Wildcard,Wildcard]
and TupleP[Wildcard,TupleP[Wildcard,Wildcard]]
, you must return
TupleT[Anything,TupleT[Anything,Anything]]
.
Type Summary
val g = fn : (unit -> int) -> (string -> int) -> pattern -> int
val only_capitals = fn : string list -> string list
val longest_string1 = fn : string list -> string
val longest_string2 = fn : string list -> string
val longest_string_helper = fn : (int * int -> bool) -> string list -> string
val longest_string3 = fn : string list -> string
val longest_string4 = fn : string list -> string
val longest_capitalized = fn : string list -> string
val rev_string = fn : string -> string
val first_answer = fn : (’a -> ’b option) -> ’a list -> ’b
val all_answers = fn : (’a -> ’b list option) -> ’a list -> ’b list option
val count_wildcards = fn : pattern -> int
val count_wild_and_variable_lengths = fn : pattern -> int
val count_some_var = fn : string * pattern -> int
val check_pat = fn : pattern -> bool
val match = fn : valu * pattern -> (string * valu) list option
val first_match = fn : valu -> pattern list -> (string * valu) list option
val typecheck_patterns = fn : (string * string * typ) list * pattern list -> typ option
Test
source folder: | src/test/sml/uw3 |
how to run with CM.make verbosity off: | sml -Ccm.verbose=false run_uw3_testing.sml |
how to run with CM.make verbosity on: | sml run_uw3_testing.sml |
note: ensure that you have removed all printing to receive credit for any assignment.
Test your functions. The unit tests you have been provided by UW are intentionally minimal.
Pledge, Acknowledgments, Citations
file: | uw3-pattern-matching-pledge-acknowledgments-citations.txt |
More info about the Honor Pledge