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The Functional Paradigm
Joseph Spring
7COM1023 Programming Paradigms
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Discussion
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Introduction
Functions and the λ Calculus
Lisp
Haskell
Summary
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The Functional Paradigm
• Emerged as a distinct paradigm during the 1960’s
• Motivated by :
– researchers in (AI) Artificial Intelligence and related subfields
• Symbolic computation
• Theorem proving
• Rule based systems
• Natural language processing
• The needs of the above were not well met by
imperative paradigm languages during the 60’s
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The Functional Paradigm
• First functional language was Lisp
– Developed by John McCarthy in 1960
– Described in Lisp 1.5 Programmers Manual in 1965
• Notable for clarity and brevity (just 116 pages)
• ‘The Lisp language is primarily for symbolic data
processing.
– It has been used for symbolic calculations in:
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Differential and integral calculus
Electrical circuit design
Mathematical logic
Game playing and other fields in AI
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The Functional Paradigm
• In Functional Programming
– Computations are viewed as mathematical
functions mapping inputs to outputs
– In imperative programming we work with the
notion of state
• need to work with assignment statements
– In Functional programming
• we do not work with the notion of a state
– Hence no need for assignment statements
• Implication for control structures?
– Loops? No way to increment or decrement variables i in a state
– Use recursion
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The Functional Paradigm
• In practice most Functional Programming languages
– Support the notions of variable, assignment and
looping
– Such languages are referred to as ‘impure’
functional programming languages
• Point:
– The notions of variable, assignment and (non
recursive) looping are NOT part of the ‘pure’
functional programming model
• Functional paradigm seen by some as a more reliable
paradigm for software design than the imperative
paradigm
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The Functional Paradigm
• For a comparison of the imperative and functional
paradigms see for example
– John Hughes ‘Why Functional Programming
Matters’, The Computer Journal, 32, 2, (1989) pp 98
– 107
Exercise
Compare and contrast the Imperative Paradigm
with the Functional Paradigm
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Lisp
We have seen examples of syntax and semantics used
in Lisp through DrRacket and Racket. In particular:
• Documentation Window
• Debug Window
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Lisp
We have:
• Input and Evaluated
– Data
– Expressions
– Constants
• Explored a range of Lisp functions
• Defined and Evaluated
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Constants
Expressions
Functions
Functional Composition
Conditionals
• And are currently exploring
– Recursion
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Functional Paradigm
We now formally review:
– Sets and Relations
– Source, Domain, Target, Range and Codomain
– Types of Relation
– Relations and Functions
– Functional Composition
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Haskell
We will discuss Haskell
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References
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McCarthy, John et al, ‘Lisp 1.5 Programmers
Manual’ MIT Press, 1965
John Hughes ‘Why Functional Programming
Matters’, The Computer Journal, 32, 2, (1989)
pp 98 – 107
Church, Alonzo ‘The Calculi of Lambda
Conversion’, Princeton University Press, (1941)
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