CTM06

1
CTM06

• Lecture 1Course Rationale

2
Goals Contents

• The goal is to improve your ability to learn and
  use state-of-the-art high-level programming
  languages.
• It is accomplished by studying some computation
  models, some high-level linguistic abstractions
  useful for programming within these models, and
  some of the design patterns they enable.
• All common paradigms covered, with special
  attention given to different kinds of concurrency
  and techniques for combining several paradigms in
  the same program.

3
The Three Layers
Design Patterns
Computation Model
Linguistic Abstractions
4
Meta Issues for each Layer

• Why do programmers have to care about the layer?
• How is the layer best described/understood?
• What should the layer contain? When should it be
  extended?

5
Computation Models

• Programmers spend a lot of time doing static
  analyses. This requires understanding the
  underlying computation model.
• Commonly described by a formal specification of
  the syntax and semantics for a
• calculus,
• VM assembly language, or a
• kernel language.
• Computation models should almost never be
  extended. They are supposed to be minimal wrt
  some problem domain.

6
Linguistic Abstractions

• Linguistic abstractions are provided by libraries
  and languages. Programming without them is
  hardly ever worth the effort.
• Common approaches to describe them
• Informal description Examples.
• Grammar Rules for translation to kernel
  language.
• Ideally, new linguistic abstractions are
  introduced whenever the result is significantly
  decreased source code complexity. However, the
  value of an abstraction also depends on
• the effort needed to extend the
  languages/libraries involved and,
• run-time overheads introduced by using the new
  language/library constructs.

7
Design Patterns

• By adhering to certain patterns in the way the
  available linguistic abstractions are used, the
  quality of the code (e.g. the maintainability)
  can be improved.
• There is no commonly accepted formalism for
  describing design patterns.
• Design patterns should be introduced whenever
  this improves code quality. Much easier to add
  than linguistic abstractions.

8
Models Studied

• A declarative base model.
• A model providing declarative concurrency.
• A constraint model.
• A model providing explicit state.
• A model providing message-passing concurrency.
• A model providing shared-state concurrency.
• A distribution model.

9
Seminar Structure

• Lectures.
• Exercise sessions.
• Home exam discussions.
• Guest lectures.

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11
CTM06

• Lecture 2Basic Declarative Model

12
Model Export Declaration

• All models presented in the course are extensions
  of the model presented in this lecture.
• In other words, it is a base model from which all
  other models inherits everything.

13
Outline

• Syntax semantics for a kernel language.
• Syntax semantics for some linguistic
  abstractions.
• Some design patterns.
• Some important properties of the kernel language.

14
Kernel Statement Syntax

• skip local in end
  if then else endcase of
  then else end 1
  nraise end !! NewName ?Name
• A-ZA-Za-z_0-9character except

15
Kernel Value Syntax

• proc 1 n end

16
Kernel Record Syntax

• (11
  nn)
• (11
  nn ...)

17
Kernel Literal Syntax

• true false
• a-za-zA-Z0-9_'except ''

18
Record Examples

• yes'if''red dog'
• tree(leftX rightY 2red 1color)tree(color
  red rightY leftX)tree(color leftX red
  rightY)
• ''(a ''(b ''(c nil)))abcnila c b
• 97 100 97 a d a"ada"

19
Procedure Example (1)

• Max proc X Y Z local B in
  Value.' if B then Z Y else Z X end
  end end
• Max proc X Y Z if
  Value.' end
• Max proc X Y Z if X then Z Y else Z X end end

20
Procedure Example (2)

• proc Max X Y Z if X X end end
• proc Max X Y Z Z if X endend
• proc Max X Y if X endend
• fun Max X Y if X

21
Procedure Call Example

• Max X Y Z
• X Max Y Z
• Y Max X Z
• Z Max X Y
• Z Max X Y

22
Expression Syntax

• local in
  end if then else endcase
  of then else end 1
  n 1 n-1
  raise end

23
Kernel Language Semantics

• Defined by a transition relation between the
  states of an abstract machine being an
  interpreter of the kernel language.
• A machine state consists of a constraint store
  and a stack of semantic statements.
• A semantic statement consists of a kernel
  language statement and an environment.

24
Environments

• Environments maps identifiers (variable names) to
  variables and values.
• Variable names may be mapped to unbound
  variables.
• Otherwise, there is nothing unusual in the way
  environments are used. It works like in any
  lexically scoped programming language with
  closures.

25
Constraint Stores

• A store is a logical conjunction of equality
  constraints, each of which constrains a variable
  to be equal to a value or to another variable.
• State transitions treat constraint stores
  monotonously. Information is added and garbage
  collected, but never changed or removed in any
  other way. This is exactly what makes the kernel
  language declarative.
• Whenever the information needed to continue
  execution is unavailable, the current thread is
  suspended until the information has arrived.

26
Execution

• To execute a statement, put it on the stack with
  an empty environment and an empty store and start
  the machine.
• Each transition begins by popping a semantic
  statement from the stack. What happens next
  depends on the statement.
• Execution is done when a transition ends with an
  empty stack or a raise-statement is popped from
  the stack.
• Environment fragments and variables no longer
  reachable from any semantic statement on the
  stack may be garbage-collected at any time.

27
Execution Example (1)
Y
1

• local X in local Y in X Y Y 0end
  end

local X in local Y in X Y Y 0end
end
28
Execution Example (2)
2
X
Y
1

• local Y in X Y Y 0end

local X in local Y in X Y Y
0end end
29
Execution Example (3)
3
Y
2
X
Y
1

• X YY 0

local X in local Y in X Y Y 0end
end
30
Execution Example (4)
3
Y
2
X
Y
1

• X Y

Y 0
local X in local Y in X Y Y 0end
end
31
Execution Example (5)
3
Y
2
X
Y
1

• Y 0

local X in local Y in X Y Y 0end
end
32
Execution Example (6)
3
Y
X
Y
1

• Y 0

local X in local Y in X Y Y 0end
end
33
Execution Example (7)
3
Y
0
X
Y
1

local X in local Y in X Y Y 0
end end
34
Execution Example (8)
Y
0
X
Y
1
local X in local Y in X Y Y 0
end end
35
Execution Example (9)
Y
1
local X in local Y in X Y Y 0 end
end
36
Suspension

• proc CondBind X Y Z if X Y then Z X
  endend
• CondBind A A CCondBind A C 1CondBind A B
  2

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Failure

• proc CondBind X Y Z if X Y then Z
  X endend
• CondBind A A CCondBind A C 1A 2

38
Closure Example

• fun MakeInc X fun Y X Y
  endend
• Inc MakeInc 3Browse Inc 4Browse Inc
  1

39
Local-Statements (1)
local X in local Y in local Z in
... end endend
local X Y Z in ...end
40
Local-Statements (2)

• local Max X Z Q in fun Max X Y if
  X triple(Q, Z, W) Z X Q Max 3 6
  Browse Xend

local fun Max X Y if X else X end end X triple(Q Z W) Z
X Q Max 3 6in Browse X end
41
Nested Local-Statements

• local F G in local Aux in fun Aux
  X ... end fun F X ... end fun
  G X ... end end ... F 9 ... G 3
  ...end

local local fun Aux X ... end
in fun F X ... end fun G X
... end endin ... F 9 ... G 3 ...end
42
Implicit Local-Statements
fun Add Vector1 Vector2 local
vector(X1 Y1 Z1) Vector1 vector(X2 Y2
Z2) Vector2 in vector(X1 X2 Y1
Y2 Z1 Z2) endend fun Add Vector1
Vector2 vector(X1 Y1 Z1) Vector1
vector(X2 Y2 Z2) Vector2in vector(X1 X2
Y1 Y2 Z1 Z2)end fun Add vector(X1 Y1
Z1) vector(X2 Y2 Z2) vector(X1 X2 Y1
Y2 Z1 Z2)end
43
Case-Statements

• fun Map Xs Fun case Xs of nil then
  nil else case Xs of XXs
  then Fun X Map Xs Fun
  else raise noSuchCase end
  end endend

fun Map Xs Fun case Xs of nil then
nil XXs then Fun X Map
Xs Fun endend
44
Wildcards

• fun IsTree X case X of tree(...) then
  true else false endend
• fun IsLeaf X case X of tree(lefttree
  righttree ...) then true else
  false endend

45
Side Conditions
fun Filter Xs Pred case Xs of nil
then nil XYs then if
Pred X then X Filter Ys Pred
else case Xs of XYs
then Filter Ys Pred
end end endend
fun Filter Xs Pred case Xs of nil
then nil XXs andthen Pred X
X Filter Xs Pred _Xs then
Filter Xs Pred endend
46
Inhibited Implicit Declarations
fun After X Xs case Xs of nil then
nil ZXs andthen Z X then
Xs ZXs then After X Xs
endend
fun After X Xs case Xs of nil then
nil !XXs then Xs _Xs
then After X Xs endend
47
The Accumulator Pattern

• fun Sum Ns fun Self Ns Res case
  Ns of NNs then Self
  Ns Res N nil then
  Res end end endin
  Self Ns 0end

fun Sum Ns case Ns of nil then
0 NNs then N Sum Ns
endend
48
Surprisingly Iterative

• proc Map Xs Fun ?Res case Xs of nil
  then Res nil XXs then Tail in
  Res Fun X Tail Map Xs Fun
  Tail endend

fun Map Xs Fun case Xs of nil then
nil XXs then Fun X Map
Xs Fun endend
49
Model Properties

• Fully supports the functional paradigm. In
  addition, provides integrated unification and
  partial values.
• Imperative in the sense that there is a simple
  and predictable order of execution.
• Declarative in the sense that all statements can
  be read as first-order predicate logic formulas.
  More details presented in next lecture.

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CTM06

• Lecture 3Declarative Concurrency

52
Model Import Declaration

• Only the extensions of the base model are
  presented.
• Despite being far more expressive, the extended
  model retains all important properties of the
  base model.

53
Kernel Syntax Extensions

• thread endByNeed Action ?Variable

54
Thread Semantics

• Machine states may contain any number of stacks,
  one for each thread, but all threads share the
  same constraint store.
• Threads can be suspended or active. A thread gets
  suspended when the information needed for its
  continued execution is not yet in the constraint
  store. It gets active again by being notified by
  another thread.
• The precise conditions for suspension and
  notification are specified for each kind of
  kernel language statement. All the programmer has
  to know is that threads do not waste time if no
  progress can be made.

55
Thread Execution

• The machine starts with one stack. Whenever a
  semantic statement of the form (thread end,
  Env) is popped from the stack, a new stack with
  (S, Env) as its only element is added.
• In each machine transition, a stack for an active
  thread is selected, after which a computation
  step is performed as in the base model (plus
  notification).
• Stack selection is fair but otherwise
  unspecified.
• Stacks for threads without hope of becoming
  active may be garbage-collected at any time.
• Execution suspends when only suspended threads
  remain.

56
Termination

• A thread terminates normally when its stack gets
  empty.
• Threads are terminated abruptly by
  raise-statements, external errors and attempts to
  create an inconsistent store.
• Stacks for terminated threads may be
  garbage-collected at any time.
• Execution terminates when all threads have
  terminated. It is considered a normal termination
  if all threads terminated normally.

57
Thread Overhead

• Threads requires little synchronization overhead
  and have very small memory footprints.
• A million threads should not be a problem on a
  standard PC!

58
Threaded Expressions (1)

• thread end

59
Threaded Expressions (2)

• thread if X then 0 else 1 endend
• local Res in thread if X then Res
  0 else Res 1 end end Res end

60
Example
fun Map Xs Fun case Xs of nil then
nil XXs then thread Fun X
end Map Xs Fun endend
61
Trigger Semantics

• In every machine state, there is also a single
  trigger store shared by all threads.
• A trigger store is a set of triggers (P, X) such
  that X is a variable and P a one-argument
  procedure.
• ByNeed P X adds the trigger (P, X) to the
  trigger store.
• Whenever a thread suspends on a variable X and
  there is a trigger (P, X) in the trigger store,
  the trigger is removed and the call P X is
  executed in its own thread.
• A trigger (P, X) is garbage-collected when X is
  garbage-collected.

62
Lazy Functions

• fun lazy Fun ... end
• fun Fun ... ByNeed fun endend

63
Stream Example

• fun lazy IntegersFrom N N IntegersFrom
  N 1end
• fun lazy Map Xs Fun ... end
• Ns IntegersFrom 0Squares Map Ns Square
• Browse SquaresDelay 3000Browse Member
  144 Squares

64
Model Properties

• Fully supports the concurrent functional
  paradigm. In addition, provides integrated
  unification, partial values and dataflow
  variables (both supply-driven and demand-driven).
• Imperative in the sense that there is a simple
  and predictable order of execution for each
  thread.
• Declarative in the sense that all statements can
  be read as first-order predicate logic formulas.
  Consequences follow.

65
The Logical View of a Store
3
0
2
1

• ?1?2?3 2 3 ? 3 0
• ?x?y?z y z ? z 0
• ?y?z y z ? z 0

66
Equivalence Definition

• Two constraint stores are equivalent iff their
  logical views are equivalent.
• A statement produces a constraint store S iff
  there is an execution of the statement without
  garbage collection that terminates or suspends in
  a state containing S.
• A statement C completes a statement S iff the
  execution of the sequence terminates
  normally.
• Two statements S1 S2 are equivalent iff for every
  statement C completing both S1 and S2,
  and produce equivalent stores.

67
Equivalence Properties

• All stores produced by the same statement are
  equivalent.
• If the set of all statements in a statement
  sequence is the same as the set of all statements
  in another sequence, then the sequences are
  equivalent.
• The result of adding "thread ... end" to a
  statement in any way allowed by the grammar is
  equivalent to the original statement.

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Why use declarative models?

• Staying within a declarative model makes writing
  correct programs much easier.
• Declarative components are easier to combine and
  thus more reusable.
• There are no known declarative models fully
  capable of dealing with the fact that the world
  is not declarative.
• But it is probably a good idea to localize the
  use of non-declarative features as much as
  possible.

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CTM06

• Lecture 4A Constraint Model

71
Model Merits

• Programmers specify problems declaratively as
  constraints. Solutions satisfying the constraints
  are found automatically.
• Appealing constraint specification language that
  can easily be extended from within the model.
• Specialized efficient solver algorithms can be
  added from within the model in an interoperable
  manner.
• The overall search strategies and heuristics can
  easily be redefined from within the model.

72
Model Demerits

• Hard to extend to new problem domains, because
  the kind of constraints allowed in stores is
  fixed.
• Not completely declarative, due to some of the
  extensibility features. However, as long as these
  features are not misused, the model stays
  declarative.

73
Model Overview

• Extension of the concurrent declarative model
  presented in the previous lecture.
• Allows several constraint stores in each machine
  state.
• Associates each thread/stack to exactly one
  store. A store and its threads is known as a
  computation space.
• Allows stores to contain domain constraints, each
  of which constrains a single variable to some set
  of values.
• Provides suspension and notification triggered by
  variable domain sizes.
• Provides access to spaces and variable domains
  from within the kernel language.

74
Kernel Syntax Extensions

• FD.reflect.dom Variable ?DomainFD.watch.size
  Variable N ?BoolFD.watch.min Variable N
  ?Bool
• Space.is X ?BoolSpace.new Proc
  ?SpaceSpace.clone Space ?CloneSpace.merge
  Space ?RootSpace.waitStableSpace.askVerbose
  Space ?StatusSpace.commit Space
  ChoiceSpace.choose NumChoices
  ?ChoiceSpace.inject Space Proc

75
The Three Levels

• Basic constraints.
• Propagated constraints.
• Synthesized constraints.

76
Basic Constraints (1)

• Basic constraints are the only constraints stored
  directly in constraint stores.
• They are stored as data structures linked to the
  variables they constrain.
• It is not possible to define new kinds of basic
  constraints from within the model.

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Basic Constraints (2)

• X 33X 3X 3
• Y 37Z 2 5 1099
• W ZW compl(2 2040)

78
Synthesized Constraints (1)

• A synthesized constraint is asserted in a
  computation space by asserting an equivalent set
  of simpler constraints.
• Operators for asserting synthesized constraints
  are defined as declarative procedures.

79
Synthesized Constraints (2)

• proc Between X Y Z X

80
Propagated Constraints (1)

• A propagated constraint exists in a space only by
  being enforced by one or more threads belonging
  to that space. Such threads are known as
  propagators.
• A propagator continuously produces basic
  constraints entailed by the propagated constraint
  in conjunction with the already existing basic
  constraints.
• A propagator should terminate when and only when
  the propagated constraint is entailed by the
  existing basic constraints.
• A propagator must be sound, but is not required
  to be complete.
• Operators for asserting propagated constraints
  are defined as procedures. They are supposed to
  behave declaratively, although they often have to
  use non-declarative features internally.

81
Propagated Constraints (2)

• Browse X Y ZX Y Z 13
• Delay 2000FD.distinctD X Y Z
• Delay 2000X \ 2
• Delay 2000Y \ 2

82
Propagator Example 1

• proc Conj X Y Z X Y Z 01
• thread if X 0 then Z 0 else Y
  Z end end
• thread if Y 0 then Z 0 else X
  Z end end
• thread if Z 1 then X 1 Y 1
  end end
• thread if X Y then Z X end
  endend

83
Propagator Example 2

• proc Conj X Y Z X Y Z 01
• thread cond X 0 then Z
  0 X 1 then Y Z Y 0
  then Z 0 Y 1 then X Z
  Z 1 then X 1 Y 1 X Y then Z
  X end endend

84
Propagator Example 3 (1)

• proc NumDig X Y fun Len N if N
  9 then 1 Len N div 10 else 1 end end
  ... proc Propagator1 ... end proc
  Propagator2 ... endin Y 1(Len FD.sup
  - 1) X 0FD.sup thread Propagator1
  end thread Propagator2 endend

85
Propagator Example 3 (2)

• proc Propagator1 Xsize FD.reflect.size
  Xin Y Ydom FD.reflect.dom X if
  FD.watch.size X Xsize then Propagator1 end
  end
• proc Propagator2 Ysize FD.reflect.size
  Yin X Xdom FD.reflect.dom Y if
  FD.watch.size Y Ysize then Propagator2 endend

86
Propagator Example 3 (3)

• fun Ydom Xdom case Xdom of nil then
  nil (AB)R then (Len
  ALen B)Ydom R NR then Len
  NYdom R endend

87
Propagator Example 3 (4)

• fun Xdom Ydom case Ydom of nil then
  nil (AB)R then (Min
  AMax B)Xdom R NR then Min
  NMax NXdom R endend

88
Propagator Example 3 (5)

• fun Min Len fun Self Len Res if
  Len 1 then Self Len-1 Res10 else Res end
  endin if Len 1 then Self Len 1 else 0
  endend
• fun Max Len Min Len1 - 1end

89
Space States

• A space is failed iff it contains inconsistent
  basic constraints.
• A space is entailed iff it is not failed and
  contains no threads.
• A space is stuck iff it is not failed and all
  contained threads are suspended without any hope
  of ever getting runnable again without external
  intervention.
• A space is unstable unless it is in any of the
  above states.

90
Propagation is not enough (1)

• Even if all involved propagators are complete, a
  space may get stuck, because propagators are not
  aware of each other.
• Therefore a complete solver can not rely on the
  use of a single computation space.
• Hence the need for search and distribution...

91
Propagation is not enough (2)

• X Y Z 13FD.distinctD X Y ZX

92
Search Distribution (1)

• When a space is stuck, a guess has to be made in
  order to resume propagation.
• A thread known as a distributor is responsible
  for constructing a set off possible guesses
• For completeness, the disjunction of all possible
  guesses should be entailed by the basic
  constraints in the space.
• To avoid repeated solutions, guesses should be
  mutually exclusive.

93
Search Distribution (2)

• The choice of which guess should be made is done
  from outside the space by a search engine.
• When the choice is made, the distributor asserts
  the selected guess as a new constraint.

94
Search Distribution (3)

• If the guess turns out to be wrong, it is
  necessary to backtrack to a clone of the original
  space without the guess.
• This is done by the search engine.
• The search engine is also responsible for cloning
  spaces as required for backtracking.

95
Space Operations

• Space.is X ?Bool
• Space.new Proc ?Space
• Space.clone Space ?Clone
• Space.merge Space ?Root
• Space.waitStable
• Space.ask Space ?Status
• Space.commit Space Choice
• Space.choose NumChoices ?Choice
• Space.inject Space Proc

96
A Simple Distributor

• proc Distribute Variables fun Self
  Variables case Variables of nil
  then skip XXs then if
  FD.reflect.size X 1 then case
  Space.choose 2 of 1 then
  X FD.reflect.min X
  2 then X \
  FD.reflect.min X end
  Self Variables else
  Self Xs end end
  endin thread Self Variables endend

97
A Simple Search Engine

• fun Solve Problem fun Self S Res
  case Space.ask S of failed then
  Res succeeded then
  Space.merge S Res alternatives(2)
  then S2 Space.clone S in
  Space.commit S 1
  Space.commit S2 2 Self S2 Self S
  Res end endin Self Space.new
  Problem nilend

98
Problem Example (1)
5 2 63 41
4 6 12 53
5 6 21 43
4 1 63 52
99
Problem Example (2)

• Browse Solve MakeTriangleProblem 5
• Browse SearchAll MakeTriangleProblem 5
• Explorer.object script(MakeTriangleProblem 5)

100
Problem Example (3)

• fun MakeTriangleProblem Width Size Width
  (Width 1) div 2 ...in proc Base
  Triangle in Triangle
  MakeList Size Triangle 1Size
  Nth Triangle Size-2 Size-1 FD.distinct Triangle
  Constrain Triangle Width Distribute
  Reverse Triangle Base List.take
  Triangle Width endend

101
Problem Example (4)

• proc Constrain Triangle Width if Width 1
  then Top List.drop Triangle Width
  in ConstrainBase Triangle Top Width
  Constrain Top Width-1 endend
• proc ConstrainBase XYYs ZZs Width
  FD.distance X Y '' Z if Width 2 then
  ConstrainBase YYs Zs Width-1 endend

102
Space Inheritance (1)

• Whenever a new space is created, it becomes a
  child of the space to which the creating thread
  belongs.
• A space may have at most one parent.
• A space may have any number of children.
• All threads, constraints and variables created by
  a thread running in a space S will also belong to
  S.
• A thread running in a space S sees all and only
  constraints and variables belonging to S or an
  ancestor of S.

103
Space Inheritance (2)

• proc Or C1 C2 S1 Space.new C1 S2
  Space.new C2
• proc Loop Status case Status
  of succeeded(entailed)_ then skip
  _succeeded(entailed) then
  skip failedfailed then
  fail failed_ then
  Space.merge S2 _ _failed then
  Space.merge S1 _
  suspended(X)suspended(Y) then Loop
  XY endin thread Loop
  Space.askVerbose S1Space.askVerbose S2
  endend

104
Space Inheritance (3)

• Browse X Y Z
• X 1099Y 12Z 39
• Or proc X FD.distance X Y '' Z end

105
Epilogue on Prolog

• The extensibility of the Mozart system goes far
  beyond what is provided by the Sicstus Prolog
  system.
• Prolog is based on resolution rather than
  computation spaces. An annoying consequence of
  this is that the order in which constraints are
  asserted matters.
• Conclusion Use Mozart instead of Prolog.

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