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Programming Languages
Meeting 10
November 4/5, 2014
Planning Ahead
Next week: short exam
– FOR loops in all their forms
• NEXT functions
– Program functions
– Parameter passing
• Value, return, value-return, reference, name
– Real numbers: syntax, parsing
– Functional programming
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Formal notation
Objects
Primitives
Functionals
Primitives
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first
last
head
tail
atom?
nil?
list?
More Primitives
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appendr
appendl
length
The arithmetic functions
The comparison functions
Functional Forms
The four Cs
• constant
– denoted by overbar
– depends on one object
• composition
– denoted by centered small circle
– depends on two functions
Functional Forms (2)
• construction
– denoted by [ ]
– depends on n functions
– [f]:x <−> <f:x> (n=1)
• conditional
– denoted using −> and ;
– depends on a predicate and two functions
Functional Forms (3)
• apply to all
– denoted by αf
– depends on one function
– works only on lists
• insert (also known as reduce)
– denoted by /f
– depends on one function with a number of
properties
Enhanced apply-to-all
• αf applies f to each element of a list
• Called apply-to-all
• apply-to-all1 applies a dyadic function (two
arguments) to a fixed object and a list of objects
• apply-to-all2 applies a dyadic function to a
pair of equal length lists
Exploring apply-to-all
Exploring reduce
Exploring LispWorks
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car
cdr
reverse
length
cons
append
defun
cond
error
funcall
mapcar
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and, or, not
fixp
zerop
plusp
minusp
equal
atom
null
mod
/
times
Creating Functions
Write these functions in Lisp using only our
primitives.
1. IG, a function that takes a positive integer as
an argument and returns (1 2 … n)
2. second, the function that returns the second
element of a list.
3. ALLTRUE?, a function that takes a list as an
argument and returns T if each element of
the list is T, and false otherwise.