500 CIS Software Foundations Fall 2003 8 September
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Administrivia
Recitations start this week: Wednesday, 3:30-5:00PM Wednesday, 6:00-7:30PM Thursday, 6:00-7:30PM Thursday, 5:00-6:30PM Thursday, 6:30-8:00PM Thursday, 6:00-7:30PM Friday, 9:00-10:30AM Levine 612 T owne 309 T owne 309 T owne 305 T owne 305 T owne 303 Moore 212 Advanced Advanced Review Review Advanced Review Review
Permanent assignments to recitations will be made next week. For this week, attend any recitation you like.
CIS 500, 8 September
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Study Groups
How many have already organized into study groups?? We will help organize study groups for the rest, beginning Wednesday.
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Homework 2
Homework 1 was due at noon today. Homework 2 will be due next Monday at noon. Read Chapter 6 of Jason Hickeys Introduction to the Objective Caml Programming Language before starting Homework submission process is different this week!
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Questions from last time...
Are there any?
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Basic Pattern Matching
Recursive functions on lists tend to have a standard shape: we test whether the list is empty, and if it is not we do something involving the head element and the tail.
% % " ! $ # " !
OCaml provides a convenient pattern-matching construct that bundles the emptiness test and the extraction of the head and tail into a single syntactic form:
% % 2 $ 1 ' ) ) ( ( 2 1 & 0
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CIS 500, 8 September
Pattern matching can be used with types other than lists. For example, here it is used on integers:
& % % ( & ' ) ) ( ( & 0
The
pattern here is a wildcard that matches any value.
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The basic elements (constants, variable binders, wildcards, , , etc.) may be combined in arbitrarily complex ways in expressions:
Complex Patterns
& ) ( ' % % & 2 % % # ) ( 0 ) ) ( 2 & % % % % 2 ( % % % % % 2
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& 2 ) 1 ) ( 2 1 0 # ( % % % % % % 2 & (
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Type Inference
One pleasant feature of OCaml is a powerful type inference mechanism that allows the compiler to calculate the types of variables from the way in which they are used.
&
The compiler can tell that takes an integer argument because used as an argument to the integer and functions.
& (
% % ( & ' ) ) ( ( & 0 ) ) ( & &
is
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% % 2 $ 1 ' ) ) ( ( 2 1 & 0
) ) ( &
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Similarly:
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Polymorphism
Suppose we ask the OCaml system to infer the type of the following very similar denition:
The here, pronounced alpha, is a type variable, standing for an arbitrary type. The inferred type tells us that the function can take a list with elements of any type (i.e., a list with elements of type alpha, for any choice of alpha). Well have more to say about polymorphism later.
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% % 2 $ ' ) ) ( ( 2 & 0 & & ) ) (
CIS 500, 8 September
&
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% % &
& (
% % &
& ( % % & % # % #
& % # % # (
items connected by commas are tuples
T uples
% % 2 1 2 1
) ) ( &
How many arguments does
take?
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& 2 '
CIS 500, 8 September
% % # '
# ' & % % % # % ' % # % ' &
% % # " !
# 2 & 1 % % # " ! ' ( % % ' ' & % % ' % 2 ' # 2 & 1
T uples are not lists
Please do not confuse them!
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T uples and Pattern Matching
T uples can be deconstructed by pattern matching:
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& & & ' & &
% % & % % ) ( & & (
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Example: Finding words
Suppose we want to take a list of characters and return a list of lists of characters, where each element of the nal list is a word from the original list.
% % % % # % % % ' % % % % % % %
(Note that character constants are written with single quotes.)
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& ( % % # % % ' % % % % % %
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'
' ) ( ' ' ) ( & 0 ' ) ( 0
% %
) % & % ) ( & &
[N.b.: this version is cleaner than the one in the photocopied slides!]
Note the use of both tuple patterns and nested patterns (as well as wildcards).
) & ) ( & ) ( & &
An implementation of
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Aside: Local function denitions
The function is completely local to : there is no reason for anybody else to use it or even, for anybody else to be able to see it! It is good style in OCaml to write such denitions as local bindings:
' ' ) ( ' ' ) ( & 0 ' ) ( 0 % %
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In general, any let denition that can appear at the top level
% % " " " % % %
can also appear in a
form.
" " " " " "
% % % " " "
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A Better Split
Our function worked ne for the example we tried it on. But here are some other tests:
% % % % % & % % & & (
Could we rene lists in the result?
% % % & % & & (
so that it would leave out these spurious empty
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Sure. First rewrite the pattern match a little (without changing its behavior):
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' ' ' ) ( ' & % %
' ) ( 0 ' ) ( 0
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Then add a couple of clauses:
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' ' ) ( ) ( ' & 0
'
) ( 0 ' ) ( % % 0
' ) ( 0 % % % & & & ( % % %
% % % # % % % % % % & # % % % & & ( & (
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Basic Exceptions
OCamls exception mechanism is roughly similar to that found in, for example, Java. We begin by dening an exception:
% % # & 1
Now, encountering will immediately terminate evaluation and return control to the top level:
# & & & # % & % ( & & % % ( & " # & 1
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Naturally, exceptions can also be caught within a program (using the form), but lets leave that for another day.
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" " " ' " " " 2
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Data Types
We have seen a number of data types:
&
Ocaml has a few other built-in data types in particular, operations like , , etc. One can also create completely new data types.
" " $
, with
&
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The need for new types
The ability to construct new types is an essential part of most programming languages. Suppose we are building a (very simple) graphics program that displays circles and squares. We can represent each of these with three real numbers.
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A circle is represented by the co-ordinates of its center and its radius. A square is represented by the co-ordinates of its bottom left corner and its width. So we can represent both shapes as elements of the type:
& & &
However, there are two problems with using this type to represent circles and squares. First, it is a bit long and unwieldy, both to write and to read. Second, because their types are identical, there is nothing to prevent us from mixing circles and squares. For example, if we write
% % # " # # & & &
we might accidentally apply the a nonsensical result.
function to a circle and get
(Recall that numerical operations on the type are written differently from the corresponding operations on e.g., instead of . See the OCaml manual for more information.)
& " $ $
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& & &
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Data Types
We can improve matters by dening as a new type:
&
This does two things: It creates a new type called type in the system. that is different from any other
&
% % & & & & & 2
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It creates a constructor called a (with capital ) that can be used to create a from three oats. For example:
& & % % " " " & " " " & & (
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T aking data types apart
We take types apart with (surprise, surprise...) pattern matching.
& & &
So we can use constructors like
Constructors are recognized by being capitalized (the rst letter is upper case).
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' & % % # " # ) ( # & ) & ) ( & & & & & # ! ' & % % 2 1 ) ( 2 1 & ) & & ) ( & # ! &
both as functions and as patterns.
&
These functions can be written a little more concisely by combining the pattern matching with the function header:
% % # " # # & & & & % % 2 1 2 1 & # !
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Continuing, we can dene a data type for circles in the same way.
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% % " " " % % & & " & (
We cannot now apply a function intended for type type :
% % & & & 2 % % 2 1 2 1 # % % & & & &
% % " " " & &
" & 2 ' # 2 & 1
to a value of
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Variant types
Going back to the idea of a graphics program, we obviously want to have several shapes on the screen at once. For this wed probably want to keep a list of circles and squares, but such a list would be heterogenous. How do we make such a list? The solution is to build a type that can be either a circle or a square.
& & & & 2 % % & & & & 0
Now both constructors For example:
and
create values of type
.
A type that can have more than one form is often called a variant type.
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&
&
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% % " " " & " & & ( " "
We can also write functions that do the right thing on all forms of a variant type. Again we use pattern matching:
& & ' & " " " ) ( % % # " # ) ( # & 0 " & & " & (
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% % " "
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% " " " & % " " " % " " " % % # " ! & & " & ( "
% % " "
A heterogeneous list:
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Mixed-mode Arithmetic
Many programming languages (Lisp, Basic, Perl, database query languages) use variant types internally to represent numbers that can be either integers or oats. This amounts to tagging each numeric value with an indicator that says what kind of number it is.
% % & & 0 2 # # & ' & & " $ $ & ) ) ( ( & 0 0 " & (
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" $ & & ) ( &
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% % " $ & ) ( & & 0 % % " & # # &
follows exactly the same pattern:
& " & ) ) ( ( ' & 0 & 0 % % " & ) ( & & 0
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Multiplication,
" & & ) ( &
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Some Higher-Level Mixed-Mode Functions
% % " ( & ) ( & 0 ( ) ( ' & 2 & & % % 2 & # # & % % & % % & (
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A Data Type for Optional Values
Suppose we are implementing a simple lookup function for a telephone directory. We want to give it a string and get back a number (say an integer). We expect to have a function whose type is
) ( 2 # ) (
where the directory.
is a (yet to be decided) type that well use to represent
However, this isnt quite enough. What happens if a given string isnt in the directory? What should return? There are several ways to deal with this issue. One is to raise an exception. Another is based on the following data type:
% % 0 2 & 2
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2 #
T see how this type is used, lets represent our directory as a list of o pairs:
% & & % % % # % & 2 # ) ( ' ) ( & 0 % % 2 # & 2 & ( % % 2 # & 2 & ( % %
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Built-in options
Because options are often useful in functional programming, OCaml provides a built-in type for each type . Its constructors are (corresponding to ) and (for ).
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) ( ' ) ( & 0 % % % % 2 # & 2 & (
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