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Programming Languages
Meeting 10
November 8/9, 2016
Planning Ahead
• Next week: Short Exam 2
– Program functions
– Control structures
– Parameter passing
– Foundations of functional programming
• Definitions
• Syntax
• Semantic specification
Reflections on Homework
• Program function, II.4, variables in range
0..maxint
– What is the value of x when a while loop that has
condition x<>b terminates?
• If sum(1,25,1,k,A[k]) sums the first 25
elements of the array A, by pattern matching
sum( _ , _ , _ , _ , ___ ) sums the first 7 powers
of 3.
Example 3 (6)
int A,B;
A := 3;
// Show Env element
B := AV(IV(A));
// Show Env element
A := 3;
B := AV(IN(A));
// Show Env element
A := 3;
B := AN(IV(A));
// Show Env element
A := 3;
B := AN(IN(A));
// Show Env element
and Store element
and Store element
and Store element
and Store element
and Store element
Primitives
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•
•
•
•
•
•
first
last
head
tail
atom?
nil?
list?
More Primitives
•
•
•
•
•
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
Exploring reduce
• Evaluate /f on the list <1,2,3,4,5,6> when f is
o
o
o
o
o
o
+
*
/
^
max
Exploring apply-to-all
• Evaluate αf on the list <0, -1, 1, 2, -2> when f is
o sgn, the function that returns 1 if its argument is
positive, -1 if its argument is negative, and 0
otherwise.
o pow2, where pow2(x) = x^2
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
Theorems about Functions
• Lengths of lists
• Equivalent compositions of functions
Programming in LISP
Our approach; our rules
• Functions may only use our primitives and userdefined functions.
• Primitives and functionals may use built-in functions
• Functions must not use the LISP equivalents of
assignment statements or loops
Hints:
1. Think recursively
2. Think in parallel
3. Think with composition
Built-In Lisp Functions
•
•
•
•
•
•
•
•
•
•
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car
cdr
reverse
length
cons
append
defun
cond
error
funcall
mapcar
•
•
•
•
•
•
•
•
•
•
and, or, not
fixp
numberp
zerop, plusp, minusp
equal
atom
null
mod
+, - , *, /
times
Your Turn
1. Create a file using a text editor that contains the
LISP definitions of the primitives. Use only the
built-in LISP functions listed above.
2. Load your primitives file and test each function
thoroughly
3. Create a second file using a text editor that
contains the LISP definitions of the functionals.
Note: You do not have define composition or
condition; they are built into the LISP system.
Your Turn (2)
4. Test your functionals thoroughly.
5. Using the primitives and functionals, define
concat, a function that concatenates two lists.
6. Using the primitives and functionals, define IG,
the index generator function. (IG n) creates a
list of length n containing the first n positive
integers. E.g. (IG 5) returns (1 2 3 4 5)
For next time
Complete the Your Turn activities.