Introduction

Willamette Mathematics Colloquium • Fall 2002

Introduction

Traditional computing: not the best tool for math
traditional finite representations do not respect mathematical accounts of numbers:
• when integers grow "too large" they can become negative
• floating point values represent real numbers inaccurately
(see Prof. Janeba's Numerical Analysis course)

Willamette Mathematics Colloquium • Fall 2002

Introduction

Traditional computing: not the best tool for math

Computing: more than just a tool for doing math
computing can have a better relationship with math:
• computational style can reflect math sensibilities
• computation can be studied from a mathematical perspective

Willamette Mathematics Colloquium • Fall 2002

Introduction

Traditional computing: not the best tool for math

Computing: more than just a tool for doing math

What are "mathematical sensibilities"?

• proof, equational reasoning
• concise, stylized language
• what, not how (i.e., results, not process)
• focus on relevance, suppress distractions
• abstraction and generality
• conceptual elegance (e.g., symmetry, duality)

Willamette Mathematics Colloquium • Fall 2002

Introduction

Traditional computing: not the best tool for math

Computing: more than just a tool for doing math

What are "mathematical sensibilities"?

Functional programming
an alternative style (or "paradigm"), outside the mainstream, which stresses sound mathematical semantics and encourages formal methods

Willamette Mathematics Colloquium • Fall 2002

Introduction

Traditional computing: not the best tool for math

Computing: more than just a tool for doing math

What are "mathematical sensibilities"?

Functional programming

The Haskell programming language
a purely functional language with a math-friendly syntax and a sophisticated, flexible type system
(other functional languages: Clean, SML, Caml, Scheme, LISP, APL, ...)

	Traditional computing: not the best tool for math
	*Computing: more than just a tool for doing* math** computing can have a better relationship with math: • computational style can reflect math sensibilities • computation can be studied from a mathematical perspective

	Traditional computing: not the best tool for math
	Computing: more than just a tool for doing math
	What are "mathematical sensibilities"? • proof, equational reasoning • concise, stylized language • what, not how (i.e., results, not process) • focus on relevance, suppress distractions • abstraction and generality • conceptual elegance (e.g., symmetry, duality)

	Traditional computing: not the best tool for math
	Computing: more than just a tool for doing math
	What are "mathematical sensibilities"?
	Functional programming an alternative style (or "paradigm"), outside the mainstream, which stresses sound mathematical semantics and encourages formal methods