Principles of Programming Languages

Lecture 1

Slides by Daniel Deutch, based on lecture notes by Prof. Mira Balaban

Introduction• We will study Modeling and Programming Computational Processes• Design Principles

– Modularity, abstraction, contracts…• Programming languages features

– Functional Programming• E.g. Scheme, ML• Functions are first-class objects

– Logic Programming• E.g. Prolog• “Declarative Programming”

– Imperative Programming• E.g. C,Java, Pascal• Focuses on change of state

– Not always a crisp distinction – for instance scheme can be used for imperative programming.

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Declarative Knowledge

0 and such that theis 2 yxyyx

“What is true”

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To find an approximation of x:

• Make a guess G• Improve the guess by averaging G and x/G• Keep improving the guess until it is good enough

Imperative and Functional Knowledge

“How to”

An algorithm due to:

[Heron of Alexandria]

More topics

• Types– Type Inference and Type Checking– Static and Dynamic Typing

• Different Semantics (e.g. Operational)

• Interpreters vs. Compilers– Lazy and applicative evaluation

Languages that will be studied• Scheme

– Dynamically Typed– Functions are first-class citizens– Simple (though lots of parenthesis ) and allows to show different programming styles

• ML– Statically typed language– Polymorphic types

• Prolog– Declarative, Logic programming language

• Languages are important, but we will focus on the principles

Administrative Issues

•Web-site•Exercises•Mid-term•Exam •Grade

Use of Slides

• Slides are teaching-aids, i.e. by nature incomplete

• Compulsory material include everything taught in class, practical sessions as well as compulsory reading if mentioned

Today

• Scheme basics– Syntax and Semantics– The interpreter– Expressions, values, types..

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Scheme

• LISP = LISt Processing– Invented in 1959 by John McCarthy– Scheme is a dialect of LISP – invented by Gerry

Sussman and Guy Steele

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The Scheme Interpreter

• The Read/Evaluate/Print Loop– Read an expression– Compute its value– Print the result

– Repeat the above

• The (Global) Environment

– Mapping of names to values

score23

total25

percentage92

Name Value

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Language Elements

Means of Abstraction

(define score 23)Associates score with 23 in environment table

Syntax Semantics

Means of Combination

(composites)

(+ 3 17 5)Application of proc to arguments

Result = 25

Primitives23+*#t, #f

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Primitive Proc (add)

Primitive Proc (mult)

Boolean

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Computing in Scheme

>==23

23

+( >==3 17 5)

25

+( >==3 *( 5 6 )8 2)

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( >==define score 23)

Name Value

Environment Table

23score

Opening parenthesis

Expression whose value is a procedure

Other expressions

Closing parenthesis

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Computing in Scheme

>==score

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( >==define total 25)

*( >==100 /( score total))

92

( >==define percentage (* 100 (/ score total))

Name Value

Environment

23score

25total

92percentage

>==

Atomic (can’t decompose) but not primitive

A name-value pair in the env. is called binding

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Evaluation of Expressions

To Evaluate a combination: (as opposed to special form)a. Evaluate all of the sub-expressions in some orderb. Apply the procedure that is the value of the leftmost

sub-expression to the arguments (the values of the other sub-expressions)

The value of a numeral: numberThe value of a built-in operator: machine instructions to executeThe value of any name: the associated value in the environment

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Using Evaluation Rules

( >==define score 23)

+( *( >==5 6 -( ) score (* 2 3 2 )))

Special Form (second sub-expression is not evaluated)

* + 5 6

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- 23 * 3 22

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11

121

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Abstraction – Compound Procedures

•How does one describe procedures?

•(lambda (x) (* x x))

To process something multiply it by itself

formal parameters

body

Internal representation

• Special form – creates a “procedure object” and returns it as a “value”

Proc (x) (* x x)

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More on lambdas

• The use of the word “lambda” is taken from lambda calculus.

• A lambda body can consist of a sequence of expressions

• The value returned is the value of the last one

• So why have multiple expressions at all?

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Evaluation of An ExpressionTo Apply a compound procedure: (to a list of arguments) Evaluate the body of the procedure with the formal parameters

replaced by the corresponding actual values

(( >==lambda(x)(* x x) )5)

Proc(x)(* x x) 5

*( 5 5)

25

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Evaluation of An Expression

To Apply a compound procedure: (to a list of arguments) Evaluate the body of the procedure with the formal parameters

replaced by the corresponding actual values

To Evaluate a combination: (other than special form).aEvaluate all of the sub-expressions in any order.bApply the procedure that is the value of the leftmost sub-expression to the

arguments (the values of the other sub-expressions)

The value of a numeral: numberThe value of a built-in operator: machine instructions to executeThe value of any name: the associated object in the environment

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Using Abstractions

( >==square 3)

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( +( >==square 3( )square 4))

( >==define square (lambda(x)(* x x)))

*( 3 3 *( )4 4)

9 16+

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Environment Table

NameValuesquare Proc (x)(* x x)

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Yet More Abstractions

==> (define f (lambda(a) (sum-of-two-squares (+ a 3) (* a 3))))

( >==sum-of-two-squares 3 4)

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==> (define sum-of-two-squares (lambda(x y)(+ (square x) (square y))))

Try it out…compute (f 3) on your own

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Evaluation of An Expression (reminder)

To Apply a compound procedure: (to a list of arguments) Evaluate the body of the procedure with the formal parameters

substituted by the corresponding actual values

To Evaluate a combination: (other than special form).aEvaluate all of the sub-expressions in any order.bApply the procedure that is the value of the leftmost sub-expression to the

arguments (the values of the other sub-expressions)

The value of a numeral: numberThe value of a built-in operator: machine instructions to executeThe value of any name: the associated object in the environment

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Lets not forget The Environment

( >==define x 8 )

+( >==x 1 )

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( >==define x 5 )

+( >==x 1 )

6The value of (+ x 1) depends

on the environment !

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Using the substitution model

)define square (lambda (x) (* x x))()define average (lambda (x y) (/ (+ x y) 2))(

)average 5 (square 3)()average 5 (* 3 3)(

)average 5 9(first evaluate operands,then substitute

+) /)5 9 (2( /)14 2(if operator is a primitive procedure,

7replace by result of operation

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Booleans

Two distinguished values denoted by the constants

#t and #f

The type of these values is boolean

<( >==2 3 )

#t

<( >==4 3 )

#f

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Values and types

Values have types. For example:

In scheme almost every expression has a value

Examples:

1) The value of 23 is 232) The value of + is a primitive procedure for addition3) The value of (lambda (x) (* x x)) is the compound

procedure proc(x) (* x x) (also denoted <Closure (x) (* x x)>

1) The type of 23 is numeral 2) The type of + is a primitive procedure3) The type of proc (x) (* x x) is a compound procedure4) The type of (> x 1) is a boolean (or logical)

Atomic and Compound Types

• Atomic types– Numbers, Booleans, Symbols (TBD)

• Composite types– Types composed of other types– So far: only procedures– We will see others later

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No Value?• In scheme most expressions have values• Not all! Those that don’t usually have side effects

Example : what is the value of the expression(define x 8)And of (display x) [display is a primitive func., prints the value of its argument to the screen]

• In scheme, the value of a define, display expression is “undefined” . This means “implementation-dependent”

• Never write code that relies on such value!

Dynamic Typing

• Note that we never specify explicitly types of variables

• However primitive functions expect values of a certain type!– E.g. “+” expects numeral values

• So will our procedures (To be discussed soon)• The Scheme interpreter checks type correctness

at run-time: dynamic typing– [As opposed to static typing verified by a compiler ]

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More examples

( >==define x 8 )

Name Value

Environment Table

8x

( >==define x (* x 2) )

>==x

16 16

( >==define x y )

reference to undefined identifier: y

( >==define )- +

>-<#+

+( >==2 2)

0

Bad practice, disalowed by some interpreters

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The IF special form

ERROR2

(if <predicate> <consequent> <alternative)>

If the value of <predicate> is #t,

Evaluate <consequent> and return it

Otherwise

Evaluate <alternative> and return it

(if (< 2 3) 2 3 >== )2

(if (< 2 3) 2 (/ 1 0) >== )

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IF is a special form

•In a general form, we first evaluate all arguments and then apply the function

•(if <predicate> <consequent> <alternative>) is different:

<predicate> determines whether we evaluate <consequent> or <alternative>.

We evaluate only one of them !

Conditionals

(lambda (a b) (cond ( (> a b) a) ( (< a b) b) (else -1 )))

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Syntactic Sugar for naming procedures

(define square (lambda (x) (* x x))

(define (square x) (* x x) )

Instead of writing:

We can write:

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(define second )

(second 2 15 3 >== )15

(second 34 -5 16- >== )5

Some examples:

(lambda (x) (* 2 x))

(lambda (x y z) y)

Using “syntactic sugar:”

(define (twice x) (* 2 x))

Using “syntactic sugar:”

(define (second x y z) y)

(define twice )

(twice 2) ==> 4

(twice 3) ==> 6

Symbols> (quote a)a> ’aa> (define a ’a)> aa> ba> (define b a)> (eq? a b)#t> (symbol? a)#t> (define c 1)> (symbol? c)#f> (number? c)#t

Symbols are atomic types, their values

unbreakable:‘abc is just a symbol

More on Types

• A procedure type is a composite type, as it is composed of the types of its inputs (domain) and output (range)

• In fact, the procedure type can be instantiated with any type for domain and range, resulting in a different type for the procedure (=data)

• Such types are called polymorphic– Another polymorphic type: arrays of values of

type X (e.g. STL vectors in C++)

Type constructor• Defines a composite type out of other types

• The type constructor for functions is denoted “->”

• Example: [Number X Number –> Number] is the type of all procedures that get as input two numbers, and return a number

• If all types are allowed we use a type variable:– [T –> T] is the type of all procs. That return the same type as they get

as input

• Note: there is nothing in the syntax for defining types! This is a convention we manually enforce (for now..).

Scheme Type Grammar

Type --> ’Unit’ | Non-Unit [Unit=Void]Non-unit -> Atomic | Composite | Type-variableAtomic --> ’Number’ | ’Boolean’ | ’Symbol’Composite --> Procedure | UnionProcedure --> ’Unit ’->’ Type | ’[’ (Non-Unit ’*’)* Non-Unit ’->’ Type ’]’Union --> Type ’union’ TypeType-variable -> A symbol starting with an upper case letter

Value constructor

• Means of defining an instance of a particular type.

• The value constructors for procedures is lambda– Each lambda expression generates a new

procedure