Listoflectures
TDDA69DataandProgramStructure
Evaluation
CyrilleBerger
1IntroductionandFunctionalProgramming
2ImperativeProgrammingandDataStructures
3Parsing
4Evaluation
5ObjectOrientedProgrammingandtypessystem
6Macrosanddecorators
7VirtualMachinesandBytecode
8GarbageCollectionandNativeCode
9ConcurrentComputing
10DeclarativeProgramming
11LogicProgramming
12Summary
2/62
Howisaprograminterpreted?
Lecturecontent
Sourcecode
SubstitutionModel
EnvironmentModel
Parser
Parser
Environment
Evaluationrules
EvaluationandEnvironment
AssignmentandEnvironment
FunctionsandEnvironment
Scope
TheScopeTrap
Writinganevaluator
3/62
AbstractSyntaxTree
Treevisitor
Generator
Sourcecode
Bytecode
VirtualMachine
Assembler
Assembly
...
OperatingSystem
CPU
4/62
SubstitutionModel-Example(1/2)
(define(squarex)(*xx))
(define(sum-of-squaresxy)
(+(squarex)(squarey)))
(define(fa)
(sum-of-squares(+a1)(*a2)))
Howtoevaluate(f(+14))?
SubstitutionModel
6
SubstitutionModel-Example(2/2)
SubstitutionModel
Toevaluate:
Toevaluateacombinationwitha
compoundprocedureasoperator:
(f(+14)
Evaluatethearguments
(f5)
Fetchthevalueoff
evaluatetheelementsofthecombination
applytheprocedure(i.e.valueftheoperator)
tothearguments(i.e.valuesoftheoperands):
evaluatethebodyoftheprocedurewhere
eachformalparameterisreplacedbythe
correspondingargument
(sum-of-squares(+a1)(*a2)))
Replaceaby5
(sum-of-squares(+51)(*52))
Evaluatethearguments
(sum-of-squares610)
Fetchthevalueofsum-of-squaresandreplacethearguments:
(+(square6)(square10))
Andsoon:
(+(*66)(*1010))
(+36100)
136
Thisisthesubstitutionmodelintheapplicativeorder
7
8
ApplicativevsNormal-Example(1/2)
ApplicativevsNormal
(define(squarex)(*xx))
Recursivelyevaluateallthe
subexpressions,butinwhatorder?
Applicative
order
Applicativeorder:evaluatetheargumentsand
thenapply.Evaluatetheprocedurebodywith
everyformalparameterreplacedwiththe
correspondingargumentvalue
Normalorder:fullyexpandandthenreduce.
Recursivelyexpandeveryprocedureuntilonly
primitiveoperatorsareleft.Evaluate(reduce)
theresult.
(square(*42))
(square(*8))
(*88)
64
Normalorder
(square(*42))
(*(*42)(*42))
(*88)
64
Forprocedureapplicationsthatcanbemodeledwiththe
substitutionmodelthatterminatewithlegitimatevalues,
applicativeandnormalorderproducethesamevalue.
9
ApplicativevsNormal-Example(2/2)
Normalorderandlazyevaluation
if(objectandobject.count()
andobject.sum()/
object.count()>0.90):
print('Highsuccessrate!')
(define(fooxy
(if(=x0)y(*2x))))
Applicative
order
(foo10(/200))
error:divisionby
zero
10
Normalorder
(foo10(/200))
(if(=100)(/200)
(*210))
(*210)
20
Whatistheresult?www.govote.at253312
start
11
12
Assignmentandthesubstitutionmodel(1/2)
(define(make-withdrawbalance)
(lambda(amount)
(set!balance(-balanceamount))
balance))
(defineW(make-withdraw25))
(W20)
5
(W10)
-5
Assignmentandthesubstitutionmodel(2/2)
(define(make-withdrawbalance)
(lambda(amount)
(set!balance(-balanceamount))
balance))
(defineW(make-withdraw25))
(W20)
((make-withdraw25)20)
((lambda(amount)(set!balance(-balanceamount))
25)20)
((set!balance(-2520))25)
25
13
14
Whydoesn’tthesubstitutionmodelwork?
Substitutionisbasedonthenotion
thatsymbolsarenamesforvalues
Usingset!changessymbolstoplaces
wherevaluescanbestored
Thevalueinsuchaplacecanchange
usingassignmentwithset!
Anewmodelofevaluationisneeded:
theenvironmentmodelofevaluation.
15
EnvironmentModel
Assignment
Bindsnamestovalues
a
:=
2
Nowahasthevalue2
Environment
a
plus
2
evaluatesto4
Thisimplythataisstored
somewhere!
18
Environment
FromtheSICPBook,section3.2:
Bindingsassociatevariablestovalues(in
assignmentexpression)
Aframeisasetofbindings
Anenvironmentisasequenceofframes
Environmentsdescribecontextswhere
expressionsareevaluated
Everyframepointstothefollowingframein
theenvironment
Allenvironmentshaveaglobalframeas
thelastframeinthesequence
Theglobalenvironmentisaframewithall
predefinedbindings
Scopetherangeinwhichavariablecanbe
referenced
nil:...
pi:3.14...
...
EnvironmentDiagram
(global)I
nil:...
pi:3.14...
...
II
a:6
f:[34]
...
VI
a:2
m:4
...
19
f:6
m:{'key':1}
...
(global)I
a:6
f:[34]
...
II
m:1
y:2
...
III
IV
a:1
...
V
a:2
m:4
...
VI
20
EnvironmentsDiagrams
Environment
diagramsvisualize
theinterpreter's
process
nil:...
pi:3.14...
...
(global)I
II
a:6
f:[34]
...
a:2
m:4
...
Evaluationrules
VI
21
Evaluationrules-Example
Evaluationrules
Afunctionisevaluated,bycreatinganew
frameandbindingtheargumentsintheframe
Afunctionisstoredasalambdarepresenting
thefunctionbodyandapointertothe
environmentwherethefunctioniscreated
http://tinyurl.com/z9mabuh
23
24
NameshavenoMeaningwithoutEnvironments
Variables(andhenceexpressions)
donothavemeaningsin
themselves
Variablesforwhichthereisno
bindinginanenvironmentaresaid
tobeunbound
Avariablecanhaveatmostone
bindingperframe
EvaluationandEnvironment
26
Evaluationofanexpression
Namelook-up(1/2)
NameshavenoMeaningwithout
Environments...
...soexpressionsneedtobe
associatedtoanenvironment
Buthowdowegetthevalueof
'a'?
Ifseveralbindingsexistforthe
samevariableinanenvironment
a
plus
thenthevariableisassociatedtotheclosest
binding
thatbindingissaidtoshadowtheother
bindingsofthevariable
2
27
28
Namelook-up(2/2)
Whatisthevalueofa?
Whatisthevalueoff?
Govoteat(forframeII)
www.govote.at737756
Govoteat(forframeVI)
www.govote.at228098
nil:...
a:3...
...
(global)I
start
f:6
m:{'key':1}
...
a:6
f:2
...
II
m:1
y:2
...
III
IV
a:1
...
V
a:2
m:4
...
VI
AssignmentandEnvironment
29
AssignmentStatement(1/2)
Startinaclean
state
a=1
b=2
b,a=a+b,b
Question
(global)I
Whatisthevalueofthefinal
expressioninthissequence?
a=2
b=3
>>>f=min
>>>g=max
>>>g,h=min,max
>>>max=g
>>>max(f(2,g(h(1,5),3)),4)
www.govote.atentercode821391
31
32
AssignmentStatement(2/2)
f=min
g=max
g,h=min,max
max=g
max(f(2,g(h(1,5),3)),4)
->2
Inwhichframetobind?
(global)I
WeareinFrameII:
a=2
b=1
Whereshouldthe
bindingofaandb
bedone?
min=funcmin(...)
max=funcmax(...)
(global)I
a:0
c:34
II
b:3
33
34
CallingUser-DefinedFunctions(1/2)
Procedureforcallinguser-defined
functions:
FunctionsandEnvironment
Addalocalframe
Bindthefunction'sformalparameterstoits
argumentsinthatframe
Executethebodyofthefunctioninthatnew
frame
36
NamesHaveDifferentMeaningsinDifferentEnvironments
CallingUser-DefinedFunctions(2/2)
(global)I
fromoperatorimportmul
defsquare(x):
returnmul(x,x)
square(-2)
fromoperatorimportmul
defsquare(square):
⠀⠀returnmul(square,square)
square(-2)
(square)II
(global)I
mul:funcmul(...)
square:funcsquare(...)
(square)II
square:-2
x:-2
37
38
RecursioninEnvironmentDiagram
Recursion
deffact(n):
n:3
ifn==0:
return1
else:
returnn*fact(n-1)
fact(3)
⠀↳fact(2)
⠀⠀↳fact(1)
⠀⠀⠀↳fact(0)
Thesamefunctioniscalled
multipletime
Differentframeskeeptrackofthe
differentargumentsineachcall.
Whatnevaluatestodepends
uponwhichisthecurrentcontext.
n:1
39
(fact)II
(fact)III
n:2
(global)I
mul:funcmul(...)
square:funcsquare(...)
(fact)IV
(fact)V
n:0
40
LocalvsGlobal(1/4)
deff():
print(s)
s='World'
f()
Scope
(global)I
f:funcf(...)
s:'World'
(f)II
42
LocalvsGlobal(2/4)
deff():
s='Hello'
print(s)
s='World'
f()
LocalvsGlobal(3/4)
(global)I
f:funcf(...)
s:'World'
(f)II
s:'Hello'
43
deff():
print(s)
s='Hello'
print(s)
s='World'
f()
UnboundLocalError:local
variable's'referenced
beforeassignment
(global)I
f:funcf(...)
s:'World'
(f)II
s:undefined
44
LocalvsGlobal(4/4)
deff():
globals
print(s)
s='Hello'
print(s)
s='World'
f()
InJavaScript
(global)I
f:funcf(...)
s:'Hello'
(f)II
functionf()
{
vars='Hello'
console.log(s)
}
s='World'
f()
console.log(s)
functionf()
{
console.log(s)
s='Hello'
console.log(s)
}
s='World'
f()
45
46
Functions-scopevsBlock-scope
Python,JavaScript,Lisp...have
function-scope
C,C++,Java...haveblock-scope
ForinstanceinC++:
TheScopeTrap
inta=1;
{
inta=2
}
std::cout<<a<<std::endl;
47
TheScopetrap
OutoftheScopeTrap
functioncreate_arr()
{
vararr=[]
for(vari=0;i<4;++i)
{
arr[i]=function(){console.log(i)}
}
returnarr;
}
functioncreate_arr()
{
vararr=[]
for(vari=0;i<4;++i)
{
arr[i]=(function(value){returnfunction(){console.log(value)}})(i)
}
returnarr;
}
arr=create_arr()
arr=create_arr()
for(vari=0;i<4;++i)
{
arr[i]()
}
for(vari=0;i<4;++i)
{
arr[i]()
}
Whatisprinted?www.govote.at910291
http://tinyurl.com/h7b7r4c
Howtosolve?www.govote.at327070
http://tinyurl.com/z7rqfrt
49
50
TheScopeTrapinC++
#include<vector>
#include<functional>
#include<iostream>
([i](){...})I
i:1
std::vector<std::function<void()>>create_arr()
{
std::vector<std::function<void()>>val;
for(inti=0;i<4;++i)
{
val.push_back([i](){std::cout<<i<<std::endl;});
}
returnval;
}
intmain(intargc,char**argv)
{
std::vector<std::function<void()>>arr=create_arr();
for(std::function<void()>v:arr)
{
v();
}
}
Writinganevaluator
(global)I
(for(...))II
i:1
InC++,capturedvariablesarecopiedinthelambdaframe
51
Usingthevisitorpatternforevaluation
Howdoes
interpeterwork
inpractice?
Wecanusethe
visitorpattern.
+
['+'[1
['*'[4
['/'[5
['+'[23]
]]]]]]]
*
1
defevaluate(node):
ifnotisinstance(node,list):
returnnode
elifnode[0]=='+':
returnevaluate(node[1][0])
+evaluate(node[1][1])
elifnode[0]=='-':
returnevaluate(node[1][0])
-evaluate(node[1][1])
elifnode[0]=='*':
returnevaluate(node[1][0])
*evaluate(node[1][1])
elifnode[0]=='/':
returnevaluate(node[1][0])
/evaluate(node[1][1])
else:
raiseError()
/
4
Visitorinterpreter
5
+
2
3
+
*
1
/
4
5
+
2
3
http://tinyurl.com/z8o234q
53
Definingvalue
54
Setvalue
['define'['x'10]]
defevaluate(node):
...
elifnode[0]=='define':
currentFrame.define(
node[1][0],
evaluate(node[1][1]))
['set'['x'10]]
defevaluate(node):
...
elifnode[0]=='set':
currentFrame.set(
node[1][0],
evaluate(node[1][1]))
55
56
Getvalue
Condstatement
[+['x'10]]
defevaluate(node):
ifnotisinstance(node,list):
returnnode
elifnode[0]=='+':
...
defevaluate(node):
ifnotisinstance(node,list):
if(currentFrame.has(node)):
returncurrentFrame.get(node)
returnnode
elifnode[0]=='+':
...
['cond'[[[<'x'0]['-'x]]],
[[='x'0]0],
['T''x']]]]
defevaluate(node):
...
elifnode[0]=='cond':
foreltinnode[1]:
ifelt[0]=='T'
orevaluate(elt[0]):
returnevaluate(elt[2])
57
Whilestatement
58
DefiningaLambda
['while'[<'x'10]
['set'['x'['+'['x'1]]]
defevaluate(node):
...
elifnode[0]=='while':
whileevaluate(node[1][0]):
evaluate(node[1][1])
['lambda'[['x']['+''x'1]]]
defevaluate(node):
...
elifnode[0]=='lambda':
return(array[1][0],
array[1][1],
currentFrame)
59
60
CallingaLambda
Summary
['increment''x']
defevaluate(node):
...
else:
(args,body,frame)=currentFrame.get(node[0])
previousFrame=currentFrame
currentFrame=createFrame(frame)
foriinrange(0,len(args)):
name=args[i]
value=evaluate(node[1][i])
currentFrame.define(name,value)
ret=evaluate(body)
currentFrame=previousFrame
returnret
ParserandAbstractSyntaxTree
EvaluationModels
Howtobuildasimpleinterpreter
61
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