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Principles of Programming Languages

Explore programming language design principles, syntax, semantics, and features including functional, logic, and imperative programming. Study Scheme, ML, Prolog, type systems, interpreters, compilers, and more.

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Principles of Programming Languages

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  1. Principles of Programming Languages Lecture 1 Slides by Daniel Deutch, based on lecture notes by Prof. Mira Balaban

  2. 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. An algorithm due to: [Heron of Alexandria] Imperative and Functional Knowledge “How to” • 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

  5. More topics • Types • Type Inference and Type Checking • Static and Dynamic Typing • Different Semantics (e.g. Operational) • Interpreters vs. Compilers • Lazy and applicative evaluation

  6. 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

  7. Administrative Issues • Web-site • Exercises • Mid-term • Exam • Grade

  8. 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

  9. 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 Name Value

  12. Language Elements Syntax Semantics

  13. Expression whose value is a procedure Closing parenthesis Environment Table Other expressions Name Value Opening parenthesis Computing in Scheme ==> 23 23 ==> (+ 3 17 5) 25 ==> (+ 3 (* 5 6) 8 2) score 23 43 ==> (define score 23)

  14. Environment Name Value Computing in Scheme Atomic (can’t decompose) but not primitive ==> score 23 ==> (define total 25) score 23 total 25 ==> (* 100 (/ score total)) 92 percentage 92 ==> (define percentage (* 100 (/ score total)) ==> A name-value pair in the env. is called binding

  15. Evaluation of Expressions To Evaluate a combination:(as opposed to special form) • Evaluate all of the sub-expressions in some order • 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. Special Form (second sub-expression is not evaluated) * + 5 6 - 23 * 2 3 2 11 12 11 121 Using Evaluation Rules ==> (define score 23) ==> (* (+ 5 6 ) (- score (* 2 3 2 )))

  17. formal parameters body To process multiply it by itself something • Special form – creates a “procedure object” and returns it as a “value” Proc (x) (* x x) Internal representation Abstraction – Compound Procedures • How does one describe procedures? • (lambda (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. Proc(x)(* x x) 5 (* 5 5) 25 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)

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

  21. (* 3 3) (* 4 4) + 9 16 25 Using Abstractions ==> (define square (lambda(x)(* x x))) Environment Table ==> (square 3) square Proc (x)(* x x) 9 ==> (+ (square 3) (square 4))

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

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

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

  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,7 replace 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 In scheme almost every expression has a value Examples: • The value of 23 is 23 • The value of + is a primitive procedure for addition • The value of (lambda (x) (* x x)) is the compound procedure proc(x) (* x x) (also denoted <Closure (x) (* x x)> Valueshavetypes. For example: • The type of 23is numeral • The type of + is a primitive procedure • The type of proc (x) (* x x) is a compound procedure • The type of (> x 1) is a boolean (or logical)

  28. 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!

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

  32. (if <predicate> <consequent> <alternative>) • If the value of <predicate> is #t, • Evaluate <consequent> and return it • Otherwise • Evaluate <alternative> and return it The IF special form (if (< 2 3) 2 3) ==> 2 (if (< 2 3) 2 (/ 1 0)) ==> ERROR 2

  33. 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 !

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

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

  36. Some examples: (define twice ) (twice 2) ==> 4 (twice 3) ==> 6 (lambda (x) (* 2 x)) Using “syntactic sugar”: (define (twice x) (* 2 x)) (define second ) (second 2 15 3) ==> 15 (second 34 -5 16) ==> -5 (lambda (x y z) y) Using “syntactic sugar”: (define (second x y z) y)

  37. 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

  38. 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 • Anotherpolymorphic type: arrays of values of type X (e.g. STL vectors in C++)

  39. 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..).

  40. 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

  41. 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

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