# Practice Scheme Assignment

### Functional Programming in Scheme

This assignment provides an introduction to functional programming and the lambda calculus. You will write several simple recursive functions in the scheme programming language.

### Background Information

Background information is obtained in lecture on functional programming and the documentation for MIT/GNU Scheme.

### What to do

Implement, document (i.e. specifications), and test the following functions in scheme. Scheme has implemented some of the constructs below (iota, association lists) - you may not use these implementations, but rather must implement them yourself. Make sure all functions are thoroughly tested.
1. The Matlab language supports a convenient notation for specifying ranges of numbers. The notation start:step:end denotes the range of integers start, start+step, start+2*step,...,start+n*step, where n is the largest integer such that start+n*step &le end and start+(n+1)*step > end. Note that the range may be empty if start > end. Write a scheme function (range (start step end)), which returns the list of integers equal to start:step:end.
Example: (range '(0 2 7)) => (0 2 4 6), (range '(2 2 0)) => ()
2. The Maple computer algeba system has a command seq(f, i = m..n, step), which returns the sequence fm,...fn, where fi is the expression f with all occurrences of the symbol i replaced by the numeric value of i in the sequence of integers from m to n. Implement a scheme function (seq f (start step end)), and produces a list of values (f(start),f(start+step),...,f(start+n*step)), where n is the largest integer such that start+n*step &le end and start+(n+1)*step > end.
Example: (seq (lambda (x) (* x x)) '(0 2 7)) => (0 4 16 36)
3. Write a scheme function (iterator (start step end)) which returns a function which when repeatedly called returns the numbers in the sequence (range (start step end)). When the sequence is exhausted the returned function should return ().
Example: (define next (iterator '(0 2 7))), (begin (next) (next) (next) (next) (next)) => 0, 2, 4, 6, ()
4. An association list is a list of bindings of names to values: ((name1 val1) ... (namet valuet)). This data structure can be used to implement a symbol table. An environment can be represented by a list of association lists (i.e. a list of symbol tables), where the first element in the list is nearest scope, the second the next surrounding scope, and the last the outermost scope.
1. Write recursive scheme function (lookup name assoc_list) that returns the binding (pair) whose name equals the given name. If no such binding is found return the null list.
2. Write a recursive function (lookup-env name environment), which returns the binding with the specified name in an environment (i.e. list of association lists) and null if no such binding is found.