Scheme : variant of LISP LISP : John McCarthy (1958) Scheme : Steele and Sussman (1973) Those who do not learn from history are doomed to repeat it. - George Santayana C/Pascal : Procedural / Imperative Java/C++: Object-oriented style Scheme/LISP : Functional style General purpose languages vs scripting languages cs3180(Prasad) L12Scm

Scheme (now called Racket) Scheme = LISP + ALGOL symbolic list manipulation block structure; static scoping Symbolic Computation Translation Parsers, Compilers, Interpreters. Querying / Reasoning Natural language understanding systems Database querying Searching / Question-Answering Reasoners: make explicit information implicit in the facts and rules First-order logic deduction, common-sense reasoning cs3180(Prasad) L12Scm

“Striking” Features Simple and uniform syntax Support for convenient list processing (Automatic) Garbage Collection Environment for Rapid Prototyping Intrinsically generic functions Dynamic typing (flexible but inefficient) Compositionality through extensive use of lists. (minimizing impedance mismatch) Trivial syntax, minimal punctuations --- useful for meta-programming Code a solution before getting an optimal one : rapid prototyping no extra syntax for generics : other languages overspecific reliability not sacrificed. cf. static typing, OOPL’s polymorphic type system cs3180(Prasad) L12Scm

Expressions Literals Variables Procedure calls Literals Variables numerals(2), strings( “abc” ), boolean( #t ), etc. Variables Identifier represents a variable. Variable reference denotes the value of its binding. x Cf. Java reference types ref 5 cs3180(Prasad) L12Scm

Scheme Identifiers E.g., y, x5, +, two+two, zero?, list->string, etc (Illegal) 5x, y)2, ab c, etc Identifiers reserved keywords variables pre-defined functions/constants ordinary functions = procedures Not case sensitive In Java : two+two counts as 3 tokens (two, +, two). Blanks mandatory. ABC= AbC = abc = abC = … In Scheme: two+two is just one token. cs3180(Prasad) L12Scm

Procedure Call (application) (operator-expr operand-expr ...) prefix expression (proc/op arg1 arg2 arg3 ...) (+ x (p 2 3)) Function value ( (f 2 3) 5 6) f is Higher-order function The operator-expression must yield a function value compatible with the operand expressions. (f 2 3) must return a binary function on integers. Higher-order functions. Order of evaluation of the sub-expressions is “explicitly” left unspecified by Scheme. cf. C is silent about it. cf. Java specifies a left to right processing. cs3180(Prasad) L12Scm

Simple Scheme Expressions (+  12  13)    = 25 (/  12  14)    = 6/7 (+ 2.2+1.1i 2.2+1.1i ) = 4.4+2.2i (* 2.2+1.1i   0+i ) = (-1.1+2.2i) (< 2.2 3 4.4 5) = #t (positive? 25) = #t (negative? (- 1 0)) = #f (expt 2 10) = 1024 (sqrt 144) = 12 (string->number “12” 8) = 10 (string->number “AB” 16) = 171 (string->number “ABC”) = #f 10*16 + 11 = 171 cs3180(Prasad) L12Scm

Scheme Evaluation Rule (REPL) Expression blank separated, parentheses delimited, nested list structure Evaluation Evaluate each element of the outerlist recursively. Apply the result of the operator expression (of function type) to the results of zero or more operand expressions. The syntax of a program is well-matched with the basic data structure the programs manipulate to facilitate META-PROGRAMMING. “program-manipulating programs” REPL: Read Eval Print Loop cs3180(Prasad) L12Scm

(+ (* 2 3) (- 4 (/ 6 3) )) (+ (* 2 3) (- 4 2) ) (+ 6 2) 8 Simple Example (+ (* 2 3) (- 4 (/ 6 3) )) (+ (* 2 3) (- 4 2) ) (+ 6 2) 8 cs3180(Prasad) L12Scm

Lists Ordered sequence of elements of arbitrary type (Heterogeneous) Empty List : () 3-element list : (a b 3) Nested list : (1 (2.3 x) 4) Sets vs lists Duplication matters: (a) =/= (a a) Order matters: (a b) =/= (b a) Nesting-level matters: ( a ) =/= ( (a) ) cs3180(Prasad) L12Scm

Key Point Syntax of Scheme programs has been deliberately designed to match syntax of lists -- its most prominent data structure Important consequence: Supports meta-programming Enables program manipulating programs cs3180(Prasad) L12Scm

Special Forms Definition Conditional (define <var> <expr>) E.g., (define false #f) Conditional (if <test> <then> <else>) E.g., (if (number? 5) (zero? “a”) (/ 10 0) ) define takes the first argument as is. Need: do not evaluate all the arguments. conditional evaluates either the then-expr or the else-expr but not both. (if ’() ’1 ’2) => 1 (if (symbol? 'a) (zero? 5) (/ 1 0)) => #f cs3180(Prasad) L12Scm

Symbols Identifiers treated as primitive values. Distinct from identifiers that name variables in program text. Distinct from strings (sequence of characters). Some meta-programming primitives quote symbol? cs3180(Prasad) L12Scm

Symbolic Data : quote function “say your name aloud” “say ‘your name’ aloud” variable vs symbolic data (to be taken literally) (define x 2) x = 2 (quote x) = x ’x = x (+ 3 6) = 9 ’(+ 3 6) -> list value cs3180(Prasad) L12Scm

Pairs (cons ’a ’b) (cons ’a (cons ’b ’()) ) Printed as: (a . b) a b cs3180(Prasad) L12Scm

(cont’d) (cons ’a (cons ’a (cons ’b ’()))) Printed as: (a a b) a () a cs3180(Prasad) L12Scm

List Functions Operations Expressions car, cdr, cons, null?, ... list, append, ... cadr, caddr, caaar, ... Expressions ( length (quote (quote a)) ) ( length ’’’a ) = 2 ( length ’’’’’’’quote ) (cadar X) = (car (cdr (car X))) The first implementation of LISP was on an IBM 704 by Steve Russell, who read McCarthy's paper and coded the eval function he described in machine code. The familiar (but puzzling to newcomers) names CAR and CDR used in LISP to describe the head element of a list and its tail, evolved from two IBM 704 assembly language commands: Contents of Address Register and Contents of Decrement Register, each of which returned the contents of a 15-bit register corresponding to segments of a 36-bit IBM 704 instruction word. cs3180(Prasad) L12Scm

{ allocate storage for the list and initialize xl} (define xl ’(a b c)) { allocate storage for the list and initialize xl} car, first : list -> element (car xl) = a cdr : list -> list (cdr xl) = (b c) { non-destructive } cons : element x list -> list (cons ’a ’(b c)) = (a b c) car: contents of address register cdr : contents of decrement register cons: construct IBM 704 m/c implementation cs3180(Prasad) L12Scm

(cons (car xl) (cdr xl)) = xl For all non-empty lists xl: (cons (car xl) (cdr xl)) = xl For all x and lists xl: (car (cons x xl)) = x (cdr (cons x xl)) = xl car : first element of the outermost list. cdr : list that remains after removing car. (cons ’() ’()) = ?? (cons ’() ’()) = (()) Wrong alternatives: () (()()) cs3180(Prasad) L12Scm

null? : list -> boolean (null? ’()) = #t (null? ’(a)) = #f (null? 25) = #f list : elements x ... -> list (list ’a ’(a) ’ab) = (a (a) ab) append : list x ...-> list (append ’() (list ’a) ’(0)) = (a 0) { variable arity functions } cs3180(Prasad) L12Scm

Role of parentheses Program Data Extra call to interpreter (list ’append) = (append) (list (append)) = (()) (list (append) (append)) = ? = (()()) Data Extra level of nesting (car ’(a)) = a (car ’((a))) = (a) (list append append) = ? = (@fn @fn) cs3180(Prasad) L12Scm

Equivalence Test (define a (cons 3 ’())) (define b (cons 3 ’())) (eq? (cons 3 ’()) (cons 3 ’())) = #f (define a (cons 3 ’())) (define b (cons 3 ’())) (eq? a b) = #f (define c a) (eq? a c) = #t cs3180(Prasad) L12Scm

Equivalent Scheme Expressions ( (car (list append list)) (cons ’a ’()) ’(1 2 3) ) = ( append ’(a) ’(1 2 3) ) = ’(a 1 2 3) ( (cdr (cons car cdr)) (cons ’car ’cdr) ) = ( cdr ’(car . cdr) ) = ’cdr cs3180(Prasad) L12Scm