1 functional programming & standard ml hossein hojjat et al
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Functional Programming & Standard ML
Hossein Hojjat et al.
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By doing it mathematically, you provide a firm foundation which will enable people
to go further.Robin Milner,
Turing Award Lecturer(1991) and the ML designer
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Outline
• Introduction
• Why functional programming?
• Some History
• Standard ML
• ML Syntax
• Programming in Standard ML
• Some Good References
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Introduction
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Introduction
• We use a zillion different programming languages:
• general purpose programming: Fortran, Lisp, Basic, C, Pascal, C++, Java, etc.
• scripting: Visual Basic, awk, sed, perl, tcl, sh, csh, bash, REXX, Scheme, etc.
• search: regular expressions, browser queries, SQL, etc.
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Introduction
• display and rendering: PostScript, HTML, XML, VRML, etc.
• hardware: SystemC, VHDL, Esterelle
• theorem proving and mathematics: Mathematica, Maple, Matlab, NuPRL, Coq
• others?
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Introduction
• ML is very different from what most of us have seen: it is functional
• Before considering ML, we will summarize the imperative languages properties
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Introduction
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Introduction
• Design of imperative languages is based directly on the von Neumann architecture
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Introduction
• Programs in imperative languages rely heavily on modifying the values of a collection of variables, called the state
• Before execution, the state has some initial value σ
• During execution, each command changes the state
'...210 n
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Introduction
• Example: – In a sorting program, the state initially
includes an array of values
• When the program has finished, the state has been modified in such a way that these values are sorted
• Intermediate states represent progress towards this goal
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Introduction
• The state is typically modified by assignment commands
• By using control structures, one can execute these commands conditionally, or repeatedly, depending on other properties of the current state
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Introduction
• But …
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Introduction
• Functional programs don’t use variables - there is no state
• Therefore they cannot use assignments : there is nothing to assign to
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Introduction
• The idea of executing commands in sequence is meaningless
• The first command can make no difference to the second : there are not any state between them
• They are based on Mathematical functions
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Introduction
• Functions can be treated in exactly the same way as simpler objects like integers
• They can be passed to other functions as arguments and returned as results
• Most traditional languages provide poor facilities in these areas
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Introduction
• Instead of sequencing and looping, functional languages use recursive functions
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Introduction
• Example:
f(n) =
1 if n=1
f(5*n-1) if n is odd, n≠1
f(n/4-3) if n is even
• Question: You said there are not any variables, but what about “n”?
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Introduction
• “n” is an identifier• In a Functional Language, the
identifier bind to values• Variable is something that can
be assigned a value• Functions have no side effect
– They do not update any variables– It is easy to define the semantics
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Introduction
• Haskell is an example of a pure functional language.
• Haskell is, as of 2002, the functional language on which the most research is being performed.
• ML is not a pure functional language in that it is possible to write procedural programs (with assignments and side-effects)
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Why Functional Programming?
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Why Functional Programming?
The von Neumann bottleneck
• Backus' famous paper encouraged much interest in functional languages as a means of breaking the von-Neumann bottleneck
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Why Functional Programming?
• Von Neumann bottleneck: pumping single words back and forth between CPU and store
• Task of a program: change store in some major way.
• It has kept us tied to word-at-a-time thinking instead of of encouraging us to think in terms of the larger conceptual units of the task at hand.
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Why Functional Programming?
• The assignment statement is the von Neumann bottleneck of programming languages
• Pure functional programming languages remove state and assignments
• Concurrency possible: order of evaluation doesn’t matter
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Why Functional Programming?
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Why Functional Programming?
• System is referentially transparent if, in a fixed context, the meaning of the whole can be determined solely by the meaning of its parts.
• Independent of the surrounding expression.
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Why Functional Programming?
• Do we have such property in imperative languages?
• If the function has side-effects (updating a global variable, doing input or output), then f(3) + f(3) may not be the same as 2 * f(3).– The second f(3) has a different
meaning than the rst
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Why Functional Programming?
• Purely declarative languages guarantee referential transparency
• It makes it easier to understand how a program works
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Why Functional Programming?
• Many features of imperative languages have arisen by a process of abstraction from typical computer hardware
• Perhaps the right approach is not to start from the hardware and work upwards
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Why Functional Programming?
• “Start with programming languages as an abstract notation for specifying algorithms and then work down to the hardware.” (Dijkstra 1976)
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Why Functional Programming?
• Makes programming into an engineering discipline rather than a trial-and-error process
• The Formalism Principle: “Correctness should be confirmed by reasoning and not by experiment”- Marjan Sirjani
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Why Functional Programming?
• As a matter of fact, it is unlikely that programmers will have the patience to perform such proofs: the proofs are usually long and boring
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• “Beware of bugs in the above code; I have only proved it correct, not tried it.” ,Donald Knuth
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Why Functional Programming?
• Functional Programming is an area of current research
• ACM Conference on LISP and Functional Programming
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Some History
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Some History
• 1940s:– Alonzo Church and Haskell Curry
developed the lambda calculus, a simple but powerful mathematical theory of functions.
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Some History
• Alonzo Church is a famous computer scientist
• He had many doctoral students , such as Stephen C. Kleene or Alan Turing
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Some History
• 1960s:– John McCarthy developed Lisp, the
first functional language. Some influences from the lambda calculus, but still retained variable assignments.
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Some History
• 1978:– John Backus publishes award
winning article on FP, a functional language that emphasizes higher-order functions and calculating with programs.
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Some History
• Mid 1970s:– Robin Milner develops ML, the first of
the modern functional languages, which introduced type inference and polymorphic types.
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Some History
• Late 1970s - 1980s:– David Turner develops a number of
lazy functional languages leading up to Miranda, a commercial product.
• 1988:– A committee of prominent researchers
publishes the first definition of Haskell, a standard lazy functional language.
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Some History
• 1999:– The committee publishes the definition
of Haskell 98, providing a long-awaited stable version of the language.
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Standard ML
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Standard ML
• Historically, ML stands for metalanguage
• General-purpose functional programming language
• Developed by Robin Milner and others in the late 1970s at Edinburgh University
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Standard ML
• In 1969 Dana Scott introduced LCF, his Logic for Computable Functions
• It was a core higher-order call-by-name functional programming language with arithmetic, booleans and recursion at all types
• That lead to Milner et al's LCF system and then the programming language ML
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ML Syntax
• A program in ML, like any other language, is made up of various kinds of expressions.
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ML Syntax
syntactic class syntactic variable(s) and grammar rule(s) examples
identifiers x, y a, x, y, x_y, ...
constants c
...~2, ~1, 0, 1, 2 (integers) 1.0, ~0.001, 3.141 (reals)true, false (booleans)"hello", "", "!" (strings)#"A", #" " (characters)
unary operator u ~, not, size, ...
binary operators b +, *, -, >, <, >=, <=, ^, ...
expressions (terms)
e ::= x | c | u e | e1 b e2 | if e then e else e |
let d1...dn in e end | e (e1, ..., en)foo, ~0.001, not b, 2 + 2,
declarations d ::= val x = e | fun y (x1:t1, ..., xn:tn): t = e val one = 1fun square(x: int): int
typest ::= int | real | bool | string | char | t1*...*tn->t
int, string, int->int, bool*int->bool
Adapted from Cornell lectures
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Programming in Standard ML
• Example: A simple function declaration that computes the absolute value of a real number:
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Programming in Standard ML
• The SML prompt lets you type either a term or a declaration that binds a variable to a term
• Running an ML program is just evaluating a term– The ML evaluator takes the left-most
expression that is not a value and reduces it to some simpler expression. Eventually the whole expression is a value and then evaluation stops: the program is done
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Programming in Standard ML
• For example consider evaluating abs(2.0+1.0):
abs(2.0+1.0) →
abs(3.0) →
if 3.0 < 0.0 then ~3.0 else 3.0 →
if false then ~3.0 else 3.0 →
3.0
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Programming in Standard ML
• The let expression works by:– Evaluating all of its bindings.– Those bindings are substituted into
the body of the let expression (the expression in between in...end)
• Example:let val x = 1+4 in x*3 →let val x = 5 in x*3 → 5*3 → 15
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Programming in Standard ML
• Rather big example…
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Programming in Standard ML
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Some Good References
• Functional Programming Using Standard ML : Ake Wikstrom
• Introduction to Functional Programming : John Harrison
• Introduction to Standard ML,Robert Harper
• Cornell CS312 lectures
• And lots more …
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Any Questions ?!
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