# 15-150: Functional Programming, Spring 2014

## Overview

The purpose of this course is to introduce the theory and practice of functional programming (FP). The characteristic feature of FP is the emphasis on computation as evaluation. The traditional distinction between program and data characteristic of imperative programming (IP) is replaced by an emphasis on classifying expressions by types that specify their applicative behavior. Types include familiar (fixed and arbitrary precision) numeric types, tuples and records (structs), classified values (objects), inductive types such as trees, functions with specified inputs and outputs, and commands such as input and output. Well-typed expressions are evaluated to produce values, in a manner that is guaranteed to be type-safe. Because functional programs do not cause side-effects we can take advantage of simple mathematical principles in reasoning about applicative behavior and analyzing the runtime properties of programs.

The advantages of FP are significant:

• Verification: There is a close correspondence between the mathematical reasoning that justifies the correctness of a program and the program itself. Principles of proof by mathematical induction go hand-in-hand with the programming technique of recursion.
• Parallelism: Since expressions have no side-effects, it is natural to use parallel evaluation: the values of independent subexpressions may be determined simultaneously, without fear of interference or conflict, and the final result is not affected by evaluation order. This gives rise to the central concepts of the work (sequential) and span (idealized parallel) complexity of a program, and allows programs to exploit available parallelism without fear of disrupting their correctness.
• Abstraction: FP stresses data-centric computation, with operations that act on compound data structures as whole, rather than via item-by-item processing. More generally, FP emphasizes the isolation of abstract types that clearly separate implementation from interface. Types are used to express and enforce abstraction boundaries, greatly enhancing maintainability of programs, and facilitating team development.

Moreover, FP generalizes IP by treating commands as forms of data that may be executed for their effects.

Upon completion of this course, students will have acquired a mastery of basic functional programming techniques, including the design of programs using types, the development of programs using mathematical techniques for verification and analysis, the use of abstract types and modules to structure code, and the exploitation of parallelism in applications.

Prerequisites: 15-151 or 21-127. Students will require some basic mathematical background, such as the ability to do a proof by mathematical induction, in order to reason about program correctness. In addition, it will be very useful for a student to have developed abstraction skills and to have familarity with the core mathematical structures of Computer Science, such as sets, relations, graphs, and trees.

Successful completion of this course is necessary and sufficient for entry into 15-210 Data Structures and Algorithms, which will build on the functional model of computation to develop a modern account of parallel algorithms for a wide variety of abstract types.

## Past Instances

• Fall 2013, taught by Steve Brookes
• Summer 2013, taught by Iliano Cervesato
• Spring 2013, taught by Michael Erdmann
• Fall 2012, taught by Steve Brookes and Jeannette Wing
• Summer 2012, taught by Ian Voysey
• Spring 2011 through Spring 2012, taught by Dan Licata