The Jo ys of Sc heme Daniel P F riedman Computer - - PDF document
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The Jo ys of Sc heme Daniel P F riedman Computer Science Depa rtmert Indiana Universit y XX Conferencia Latinoamericana de Info rmatica P ANEL Mexico Cit y The Jo ys of Sc
SLIDE 1
The
Jo ys
f
Sc heme Daniel P
F
riedman Computer Science Depa rtmert Indiana Universit y XX Conferencia Latinoamericana de Info rmatica P ANEL
Mexico
Cit y The Jo ys
f
Sc heme
SLIDE 2
Desiderata
Keep
it in y
ur
head
Simple
Syn tax
Simple
Seman tics
F
reedom
f
Expression
Tink
erto ys
High
P aradigmicit y
Dynamically
but Strongly T yp ed
W
e shouldnt ha v e to do that
Automatic
Memory Managemen t
In
teractiv e Program Dev elopmen t The Jo ys
f
Sc heme
SLIDE 3
Outline
Ov
erview
f
the language
Iden
tifying Characteristics
Basic
Data T yp es
Basic
Con trol Structures
Simple
Program St yles
Quic
ksort
An
illustration
f
basic features
The
algorithm
A
list implemen tation
Adv
anced F eatures
Syn
tax Extensions
FixedP
in
ts
Another
Example
Con
tin uations
Milestones
Devils and Angels
Using
Con tin uations
Exception
Handling
Engines
Am
b simple v ersion
Numeric
Multiple In tegration The Jo ys
f
Sc heme
SLIDE 4
An
Ov erview
f
Sc heme The Jo ys
f
Sc heme
SLIDE 5
Iden
tifying Characteristics
Ev
erything is data
Pro
cedures
Con
tin uations
All
b
jects ha v e indenite exten t
Pro
cedures
Dynamic
Strong T yping
Listbased
syn tax The Jo ys
f
Sc heme
SLIDE 6
Syn
tax expr ession
liter
al
variable
expr
ession
lamb
da variable
expr
ession
set
variable expr ession
if
expr ession expr ession expr ession
There
are also additional sp e cial forms
They
denote
ther
language constructs
But
are built from this small set The Jo ys
f
Sc heme
SLIDE 7
W
riting Recursiv e Programs dene
lamb
da n m cond zero n
else
sub
n m
What
is the value
f
W
e reason as follo ws
Ho
w do w e ll in
to
turn
into
Simple
w e add
to
it
Lucky
fo r us m is
What
is the value
f
It
must b e the identit y
f
that
is
The
Jo ys
f
Sc heme
SLIDE 8
Multiplication
dene
lamb
da n m cond zero n
else
m
sub
n m
The
Jo ys
f
Sc heme
SLIDE 9
Y
ure
not con vinced dene facto rial lamb da n cond zero n
else
facto
rial sub n
What
is the value
f
W
e reason as follo ws
facto
rial
facto
rial
Ho
w do w e ll in
to
turn
into
Simple
w e multiply it b y
Lucky
fo r us n is
What
is the value
f
It
must b e the identit y
f
that
is
The
Jo ys
f
Sc heme
SLIDE 10
F
actorial dene facto rial lamb da n cond zero n
else
n
facto rial sub n facto rial
The
Jo ys
f
Sc heme
SLIDE 11
Y
ure
still not con vinced dene p
w
erset lamb da set cond null set
else
p
w
erset cdr set
What
is the value
f
W
e reason as follo ws
p
w
erset a b c
a
b c a b a c a b c b c
p
w
erset b c
b
c b c
Ho
w do w e ll in
to
turn little set into big set
Simple
W e fo rm the union
f
adding a to each element
f
the little set and the little set itself
Lucky
fo r us ca r set is a
What
is the value
f
b
y denition
The
Jo ys
f
Sc heme
SLIDE 12
P
w
er Set dene p
w
erset lamb da set cond null set
else
extend ca r set p
w
erset cdr set dene extend lamb da item p
w
erset app end map lamb da set cons item set p
w
erset p
w
erset The Jo ys
f
Sc heme
SLIDE 13
Simple
Programs dene facto rialaps lamb da n a cond zero n a else facto rialaps sub n
n
a dene facto rial lamb da n facto rialaps n
dene
facto rialcps lamb da n k cond zero n k
else
facto rialcps sub n lamb da v k
v
n dene facto rial lamb da n facto rialcps n lamb da x x The Jo ys
f
Sc heme
SLIDE 14
F
actorial using letrec dene facto rial letrec facto ralaps lamb da n a cond zero n a else facto rialaps sub n
n
a lamb da n facto rialaps n
dene
facto rial letrec facto rialcps lamb da n k cond zero n k
else
facto rialcps sub n lamb da v k
n
v lamb da n facto rialcps n lamb da v v The Jo ys
f
Sc heme
SLIDE 15
Basic
Data T yp es A tomic Data T yp es
Num
b ers
e
Characters
n a
n
newline
Sym
b
ls
video cdpla y er radio Comp
und
Ob jects
Lists
Constructors
cons
list AccessorsMutators ca r cdr setca r setcdr Predicates null pair list The Jo ys
f
Sc heme
SLIDE 16
Basic
Data T yp es
V
ectors Constructor vecto r AccessorMutator vecto rref vecto rset Predicate vecto r
Strings
Constructor string AccessorMutator stringref stringset Predicate string The Jo ys
f
Sc heme
SLIDE 17
Basic
Data T yp es Unprin table Data T yp es
Pro
cedures Constructor lamb da formals b
dy
Accessor
p
er ator
p
er ands
Application
Predicate p ro cedure
Con
tin uations Constructor callcc Accessor Applic ation Predicate p ro cedure The Jo ys
f
Sc heme
SLIDE 18
Basic
Con trol Structures
Conditionals
if
testexp thenexp elseexp
cond
testexp exp
Sequencing
b egin E
E
n
Lo
ping
and Iteration By Recursion The Jo ys
f
Sc heme
SLIDE 19
An
Illustration Quic ksort Problem Sort a giv en set sa y X
f
n um b ers in ascend ing
rder
F
r
example
Boundary
Condition
If
empt y set sorted v ersion is the empt y sequence Step
Cho
se
a piv
t
n st n
X
Step
P
artition the list hA B i st A
fx
X
j x
ng
and B
fx
X
j x
ng
Step
Sort
partitions and join them A
n
B
where
A
and
B
are
sorted v ersions
f
A and B
The
Jo ys
f
Sc heme
SLIDE 20
An
Illustration Quic ksort Represen t sets as lists dene quickso rt lamb da ls cond null ls
else
let pivot ca r ls app end quickso rt lo w erpa rtition pivot cdr ls list pivot quickso rt upp erpa rtition pivot cdr ls
cond
is a conditional
let
is a binding construct
app
end joins t w
lists
The Jo ys
f
Sc heme
SLIDE 21
An
Illustration Quic ksort dene lo w erpa rtition lamb da pivot ls lterin lamb da x
pivot
x ls dene upp erpa rtition lamb da pivot ls lterin lamb da x
pivot
x ls dene lterin lamb da test ls cond null ls
test
ca r ls cons ca r ls lterin test cdr ls else lterin test cdr ls The Jo ys
f
Sc heme
SLIDE 22
Using
Con tin uation P assing St yle dene quickso rt lamb da ls cond null ls
else
let pivot ca r ls pa rtition pivot cdr ls lamb da lo w erpa rtition upp erpa rtition app end quickso rt lo w erpa rtition list pivot quickso rt upp erpa rtition The Jo ys
f
Sc heme
SLIDE 23
Using
Con tin uation P assing St yle dene pa rtition lamb da pivot ls k cond null ls k
else
pa rtition pivot cdr ls lamb da lo w erpa rtition upp erpa rtition if
ca
r ls pivot k cons ca r ls lo w erpa rtition upp erpa rtition k lo w erpa rtition cons ca r ls upp erpa rtition The Jo ys
f
Sc heme
SLIDE 24
Seman
tics
f
some sp ecial forms
In
terms
f
the basic syn tax let v e
b
dy
b
dy
lamb
da v
b
dy
b
dy
e
blo
ck v
b
dy
b
dy
let
v
b
dy
b
dy
letrec
v e
b
dy
b
dy
blo
ck v
set
v e
b
dy
b
dy
b
egin e e
lamb
da
e
e
while
testexp e e
letrec
lo
p
lamb da
if
testexp b egin e e
lo
p
lo
p
The Jo ys
f
Sc heme
SLIDE 25
FixedP
in
ts
Another
Example Fixedp
in
t algorithms are fairly common
Numerical
Algorithms
Set
Equations
Program
Analyses etc Rep eat a certain computation un til c hanges in the so lution are within a certain b
und
F
r
example let us compute the v alue
f
tan
tan
dene
pi letrecequations x
x
expt
n
add
n
n
add
n lamb da x y t
x
The Jo ys
f
Sc heme
SLIDE 26
FixedP
in
ts
Another
Example In suc h cases
ne
usually b egins with an initial solution and then iterates
letrecequations
is a sp ecial form
It
is not in standard Sc heme
It
is a great abstraction for a fairly common st yle
f
programming
Ho
w general is this abstraction The Jo ys
f
Sc heme
SLIDE 27
FixedP
in
ts
Another
Example Set equations are useful in man y con texts F
r
example The Philosophers P art y
A
philosopher will attend the part y i his friends will
Find
a suitable guestlist dene guestlist lamb da inits letrecequations guests inits union guests friends guests
guests
guestlist a ristotle
The
Jo ys
f
Sc heme
SLIDE 28
FixedP
in
ts
Another
Example
W
e can add letrecequations to Sc heme
Macros
r
syn tax extensions allo w syn tactic forms to b e added to the language
Macros
are not y et a part
f
standard Sc heme but will so
n
b e The Jo ys
f
Sc heme
SLIDE 29
FixedP
in
ts
Another
Example letrecequations va r init exp bina rytest
b
dy
b
dy
letrec
lo
p
lamb da va r
if
and bina rytest va r exp
b
egin b
dy
b
dy
lo
p
exp
lo
p
init
The
Jo ys
f
Sc heme
SLIDE 30
FixedP
in
ts
Another
Example dene friends let lo
kuplist
a ristotle plato alexander plato so crates so crates alexander ptolemy homer virgil sopho cles virgil dante ho race dante p etrach p etrach sidney shak esp ea re lamb da guests mapunion lamb da g let ans assq g lo
kuplist
if ans cdr ans
guests
The Jo ys
f
Sc heme
SLIDE 31
Con
tin uations
A
generalized Goto
A
con tin uation is a pro cedure that represen ts the rest
f
the computation
A
con tin uation can b e captured
If
a con tin uation is restored it resets the computation bac k to the p
in
t the con tin uation w as captured
Primary
Uses
Nonstandard
con trol constructs coroutines
Exception
Handling
Bac
ktrac king as in prolog The Jo ys
f
Sc heme
SLIDE 32
Escaping
Pro cedures Pro cedures that ab
rt
when applied Examples
v
v
v
v
f
v
v
F
r
any f
f
v
g
v
g
The
Jo ys
f
Sc heme
SLIDE 33
CallccBasics
cons
callcc
lamb da k k cons
k
v v callcc lamb da k k cons
k
v v
cons
callcc lamb da k k
k
v cons v
The
Jo ys
f
Sc heme
SLIDE 34
CallccBasics
cons
callcc
lamb da k k
k
v cons
v
cons
callcc
lamb da k k
k
v cons
v
cons
callcc
lamb da k k
k
v cons
v
The
Jo ys
f
Sc heme
SLIDE 35
Milestones
Devils and Angels Milestone An imp
rtan
t ev en tw
rth
getting bac k to Devil T ak es y
u
bac k to y
ur
last milestone in exc hange for y
ur
soul Angel Undo es the w
rk
f
the devil
The
devils job is to k eep the computation from hap p ening Errors and exceptions
A
milestone is a place where the computation go es bac k to reco v er
An
angel causes the computation to reco v er The Jo ys
f
Sc heme
SLIDE 36
Milestones
Devils and Angels dene mda lamb da
cond
a
b
milestone
b
egin writeln here
c
angel allisw ell
d
e
milestone
f
angel
g
devil
else
b egin writeln made it to
h
devil
In
b
In
a
f
In e
In
d
f
made it to In e
In
d
t
In b
In
a
t
here In g
allisw
ell In h
allisw
ell allisw ell The Jo ys
f
Sc heme
SLIDE 37
Milestones
Devils and Angels dene past
dene
future
push
s v
set
s cons v s p
p
s
if
null s erro r Cannot p
p
empt y stack let v ca r s set s cdr s v The Jo ys
f
Sc heme
SLIDE 38
Milestones
Devils and Angels dene milestone lamb da v callcc lamb da k push past k v dene devil lamb da v callcc lamb da k push future k p
p
past v dene angel lamb da v p
p
future v The Jo ys
f
Sc heme
SLIDE 39
Using
Con tin uationsException Handling W e w an t to con trol ho w errors are handled dene div lamb da x if
x
raise
divideb yzero
x
dene fo
lamb
da n div n dene test withhandler divideb yzero lamb da exn f
fo
f
raise
raises the exception
withhandler
traps it The Jo ys
f
Sc heme
SLIDE 40
Using
Con tin uationsException Handling Handlers ha v e uid sc
p
e ie the last handler established at the time the error
ccured
m ust b e c hosen
Stac
k
f
handlers
Handlers
should kno w where to resume execution dene handlers
withhandler
name handler b
dy
b
dy
callcc
lamb da k uidlet handlers cons list name k handler handlers b
dy
b
dy
The
Jo ys
f
Sc heme
SLIDE 41
Using
Con tin uationsException Handling dene raise lamb da exn let res assq exn handlers cond pair res apply lamb da name k handler k handler exn res else erro r Exception is not handled exn The Jo ys
f
Sc heme
SLIDE 42
EnginesAm
b Simple V ersion Engines An abstraction
f
async hronous con trol Am b Return the v alue
f
the expression that returns rst
am
b factorial
factorial
am
b factorial
factorial
am
b factorial
factorial
am
b factorial
factorial
am
b factorial
factorial
The
Jo ys
f
Sc heme
SLIDE 43
EnginesAm
b Simple V ersion
aneng
ticks success failure
ticks
is an integer
success
is a a rgument p ro cedure
Its
rst a rgument is the value
f
the
riginal
a rgument to engine
Its
second a rgument is the unused ticks
failure
is a a rgument p ro cedure
Its
nly
a rgument is a new engine
If
it is invok ed it sta rts where the
ld
ne
quit The Jo ys
f
Sc heme
SLIDE 44
EnginesAm
b Simple V ersion amb e e
ambengines
engine e engine e dene ambengines lamb da engine engine engine random
cons
lamb da engine engine random
cons
lamb da engine ambengines engine engine What if cons is replaced b y lamb da value ticks value
What
if cons is replaced b y lamb da value ticks ticks
The
Jo ys
f
Sc heme
SLIDE 45
Gaussian
Quadrature
p
in
t Gaussian Quadrature algorithm for nding denite in tegrals
The
algorithm is exact to the th degree mo dulo the inexactness
f
the co ecien ts used
Sc
hemes elegance is brough t
ut
as usual b y lamb da
The
follo wing algorithm computes denite in tegrals
v
er the in terv al
so
in general a trans lation
f
the in terv al is needed
An
y
rdinary
language lik e C
r
P ascal w
uld
require us to dene a help function dened
n
the in terv al
but
with Sc hemes supp
rt
f
anon ymous pro cedures via lamb da this isnt necessary
The
substitution is done
n
the y The Jo ys
f
Sc heme
SLIDE 46
Gaussian
Quadrature p
int
Gaussian quadrature Exact to the
th
degree dene int let ro
ts
ro
ts
f
th
Legendre p
ly
co
es
co
es fo r its resp ective ro
t
The
Jo ys
f
Sc heme
SLIDE 47
Gaussian
Quadrature let intfromnegto lamb da f
letrec
lo
p
lamb da co es ro
ts
cond null co es
else
ca
r co es f ca r ro
ts
lo
p
cdr co es cdr ro
ts
lo
p
co es ro
ts
lamb da f limitpair intfromnegto translate f limitpair cons
The
Jo ys
f
Sc heme
SLIDE 48
Gaussian
Quadrature dene translate lamb da f limitpair limitpair let from ca r limitpair to cdr limitpair from ca r limitpair to cdr limitpair let m
to
from
to
from lamb da x
m
f
m
x
from from The Jo ys
f
Sc heme
SLIDE 49
Gaussian
Quadrature R
x
dx
int
lamb da x
x
x cons
T
compute
a double in tegral w e need to mak e sure w e get the v ariables assigned correctly R
R
xy
dydx
int
lamb da x int lamb da y
x
y cons
cons
The
Jo ys
f
Sc heme
SLIDE 50
Gaussian
Quadrature But with Sc hemes abilit y to curry s w e can surely do b etter
dene
f lamb da x lamb da y
x
y
int
lamb da x int lamb da y f x y cons
cons
W
e can no w dene doubleint as follo ws dene doubleint lamb da f limitpair limitpair int lamb da x int lamb da y f x y limitpair limitpair The Jo ys
f
Sc heme
SLIDE 51
Gaussian
Quadrature
doubleint
lamb da x lamb da y
x
y
W
e can write an integrato r that tak es multiple integrations dene nint lamb da f limitpairs cond null limitpairs f
else
int lamb da x nint f x cdr limitpairs ca r limitpairs
nint
lamb da x lamb da y
x
y
The
Jo ys
f
Sc heme
SLIDE 52
Gaussian
Quadrature W e can abstract
ver
int allo wing any integrato r dene nintmak er lamb da int letrec nint lamb da f limitpairs cond null limitpairs f
else
int lamb da x nint f x cdr limitpairs ca r limitpairs nint dene gaussianquadraturenint nintmak er int The Jo ys
f
Sc heme
SLIDE 53
Gaussian
Quadrature Or w e can asso ciate a dierent integration metho d with each limit pair b y fo rming a new data structure that has b
th
the integrato r and its limit pair dene sup ernint lamb da f intlimitspairs cond null intlimitspairs f
else
ca r ca r intlimitspairs lamb da x sup ernint f x cdr intlimitspairs cdr ca r intlimitspairs
sup
ernint lamb da x lamb da y
x
y list cons int
cons
int
The
Jo ys
f
Sc heme
SLIDE 54
The
Simplicit y
f
Sc heme
va
riable reference lamb da application
set
if
callcc
engines
Primitiv
es
n
data structures
dene
The
Jo ys
f
Sc heme
SLIDE 55
Wh
y Sc heme
P
aradigmatic Considerations
Simplicit
y
Minimalit
y
Flexibilit
y
Wide
range
f
concepts can b e realized with just a few constructs
