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.

3 Declarative Knowledge “What is true”

4 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..

10 Scheme LISP = LISt Processing – Invented in 1959 by John McCarthy – Scheme is a dialect of LISP – invented by Gerry Sussman and Guy Steele

11 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

12 Language Elements Means of Abstraction (define score 23) Associates score with 23 in environment table Syntax Semantics Means of Combination (composites) ( ) Application of proc to arguments Result = 25 Primitives 23 + * #t, #f 23 Primitive Proc (add) Primitive Proc (mult) Boolean

13 Computing in Scheme ==> ==> ( ) 25 ==> (+ 3 (* 5 6) 8 2) 43 ==> (define score 23) Name Value Environment Table 23score Opening parenthesis Expression whose value is a procedure Other expressions Closing parenthesis

14 Computing in Scheme ==> score 23 ==> (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

15 Evaluation of Expressions To Evaluate a combination: (as opposed to special form) a.Evaluate all of the sub-expressions in some order b.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: number The value of a built-in operator: machine instructions to execute The value of any name: the associated value in the environment

16 Using Evaluation Rules ==> (define score 23) ==> (* (+ 5 6 ) (- score (* ))) Special Form (second sub- expression is not evaluated) * *

17 Abstraction – Compound Procedures How does one describe procedures? (lambda (x) (* x x)) To process something multiply it by itself formal parametersbody Internal representation Special form – creates a “procedure object” and returns it as a “value” Proc (x) (* x x)

18 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?

19 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 ==> ((lambda(x)(* x x)) 5) Proc(x)(* x x) 5 (* 5 5) 25

20 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) a.Evaluate all of the sub-expressions in any order b.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: number The value of a built-in operator: machine instructions to execute The value of any name: the associated object in the environment

21 Using Abstractions ==> (square 3) 9 ==> (+ (square 3) (square 4)) ==> (define square (lambda(x)(* x x))) (* 3 3) (* 4 4) Environment Table NameValue squareProc (x)(* x x)

22 Yet More Abstractions ==> (define f (lambda(a) (sum-of-two-squares (+ a 3) (* a 3)))) ==> (sum-of-two-squares 3 4) 25 ==> (define sum-of-two-squares (lambda(x y)(+ (square x) (square y)))) Try it out…compute (f 3) on your own

23 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) a.Evaluate all of the sub-expressions in any order b.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: number The value of a built-in operator: machine instructions to execute The value of any name: the associated object in the environment

24 Lets not forget The Environment ==> (define x 8) ==> (+ x 1) 9 ==> (define x 5) ==> (+ x 1) 6 The value of (+ x 1) depends on the environment!

25 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

26 Booleans Two distinguished values denoted by the constants #t and #f The type of these values is boolean ==> (< 2 3) #t ==> (< 4 3) #f

27 Values and types Values have types. For example: In scheme almost every expression has a value Examples: 1)The value of 23 is 23 2)The value of + is a primitive procedure for addition 3)The value of (lambda (x) (* x x)) is the compound procedure proc(x) (* x x) (also denoted 1)The type of 23 is numeral 2)The type of + is a primitive procedure 3)The type of proc (x) (* x x) is a compound procedure 4)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

29 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 ]

31 More examples ==> (define x 8) Name Value Environment Table 8x ==> (define x (* x 2)) ==> x 16 ==> (define x y) reference to undefined identifier: y ==> (define + -) # + ==> (+ 2 2) 0 Bad practice, disalowed by some interpreters

32 The IF special form ERROR2 (if ) If the value of is #t, Evaluate and return it Otherwise Evaluate and return it (if ( 2 (if (

33 IF is a special form In a general form, we first evaluate all arguments and then apply the function (if ) is different: determines whether we evaluate or. We evaluate only one of them !

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

35 Syntactic Sugar for naming procedures (define square (lambda (x) (* x x)) (define (square x) (* x x)) Instead of writing: We can write:

36 (define second ) (second ) ==> 15 (second ) ==> -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 > ’a a > (define a ’a) > a a > b a > (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-variable Atomic --> ’Number’ | ’Boolean’ | ’Symbol’ Composite --> Procedure | Union Procedure --> ’Unit ’->’ Type | ’[’ (Non-Unit ’*’)* Non-Unit ’->’ Type ’]’ Union --> Type ’union’ Type Type-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