1. CSE 425: Functional Programming I Programs as Functions Some programs act like mathematical functions –Associate a set of input values from the function’s domain with a set of output values from the function’s range –E.g., written as y = f(x) or f : X → Y … … where X is the domain, Y is the range, x  X is the independent variable, and y  Y is the dependent variable No assignment, so no loops in purely functional code –Instead, rely on recursion to perform iteration Referential transparency –Function’s value depends only on arguments (+ global state) Value semantics –No local state

2. CSE 425: Functional Programming I Intro to Lambda Calculus Syntax expression → constant | variable | ‘(‘ expression expression ‘)’ | ‘(‘ ‘λ’ variable ‘.’ expression ‘)’ Lambda expressions: function, parameters, arguments –E.g., (λx. + 1 x), written (lambda (x) (+ 1 x)) in Scheme Can apply a lambda expression (“beta reduction”) –E.g., (λx. + 1 x) 2 replaces x with 2, evaluates to 3 Can parameterize an expression (“beta astraction”) –E.g., can parameterize expression (+ 1 2) as (λx. + 1 x) 2 Can also rename variables (“alpha conversion”) and remove redundant expressions (“eta conversion”)

3. CSE 425: Functional Programming I Intro to Scheme (a Dialect of Lisp) General syntactic structure of Scheme is very simple expression → atom | ‘(‘ {expression} ‘)’ atom → literal | symbol literal → number | string | character | boolean Atomic literals evaluate to themselves –100, “world”, #\z, #T, #f, Symbols are treated as identifiers –Which are then looked up in a symbol table for the current environment, replaced by the values that are found there –If a symbol names a function, it is applied to other values

4. CSE 425: Functional Programming I Expressions in Scheme All are either special forms or function applications –Special forms begin with a Scheme keyword (e.g., car, cdr, cond, cons, define, display, if, lambda, let, letrec, quote, etc.) –Function application (call) is prefix: name then arguments Predefined operators for many basic functions –Such as + (addition), * (multiplication), / (division), etc. Selection expressions for if, if-else, and if-elseif logic –Use if form for single selection, vs. cond form for multiple Binding lists (using the let or letrec keywords) –Associate values with variables before applying a function Lambda expressions (using the lambda keyword) –Define formal parameter lists for (anonymous) functions

5. CSE 425: Functional Programming I Data Structures in Scheme Basic construct is a list node (box and arrow notation) –Lists are concatenations of list (or list of list …) nodes –Functions car and cdr select the head vs. the rest of a list The cons function constructs a list from two others –Concatenates them with the first in front of the second The null? primitive tests whether or not a list is empty –Useful for recursive operations on lists (“cdr down, cons up”) L car Lcar cdr Lcdr L “hello, ”“world!” cdr cdr L

6. CSE 425: Functional Programming I Evaluation, Type Checking, and Scopes Scheme uses applicative order evaluation –Arguments evaluated first, then function is applied to them –Recursively, expression tree is evaluated leaves-to-root Special forms use delayed evaluation –E.g., else part of a cond expression may not evaluate at all Can prevent evaluation using the quote keyword –Identifies a list as being a literal rather than an expression Scheme type checks only when absolutely necessary –E.g., just before a primitive function is applied Scoping is static in Scheme, with hiding with nesting –E.g., an inner let hides an outer let for same symbol name

7. CSE 425: Functional Programming I Today’s Studio Exercises We’ll explore ideas from Scott Chapter 10.1-3 –Looking at basic functional programming features in C++ –Using them in ways similar to Scheme/Lisp features Today’s required exercises are again in C++ –Please take advantage of the on-line tutorial and reference manual pages that are linked in the lab machines –As always, please ask us for help as needed When done, email your answers to the course account with subject line “Functional Programming Studio I” –Send to cse425@seas.wustl.edu