# format Presentation by nikeborome

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```									Table of Content
   Basic Definitions
   Basic statements
   Predicate transformer
   Monotonicity
   Operational interpretation of
Statements
   Derived Statements
   Correctness & Refinements
Basic statements

   Defining a simple programming
language
   capture the interaction between a
computing system and its user
   Statements
Basic Definitions
   State predicate
   State transformer
   State relation
   statements are interpreted as predicate
transformers
   interpret predicate as a set of states
Basic Definitions
Basic Definitions
Basic Lattices
   The predicates on a state space form a
complete boolean lattice
   The predicate transformers form a
complete boolean lattice
Basic Lattices (cont)
True                            magic

{p} and [p]
q1            qn                 q1           qn

False                           abort
Basic Definitions
   Monotonicity of predicate transformers

   Form a complete (but not boolean)
lattice
   Basic statements are all monotonic
   Any monotonic predicate transformer
can be expressed as statements
   Statements  Normal Form
Operational interpretation of
Statements

Global Shared Memory

A program statement describes the way in
which the interaction between the user and
system takes place.
Operational interpretation of
Statements (cont)
   Changing the state
   Skip : dose not change the state
   Deterministic update :   computes a new
state from present state

   Sequential Composition
   Describes the order of progression in the
computation
Operational interpretation of
Statements (cont)
   Failure
   abort : user loses control of the
computation
   assert : {q} , qualifies the aborting
statement
   Selecting alternative
   angelic choice :           , user choose
one.
   Input statements
   angelic update statement : {Q} , a
request for an input value
Operational interpretation of
Statements (cont)
   Waiting
    magic : waiting for a miracle (deadlock)
    guard : [g], wait when the condition g is not true
   Uncertainty
    demoniac choice :          ,user do not know
which one will actually be chosen by the system.
   Specification
    demonic update :[Q] ,nondeterministic
assignment
Operational interpretation of
Statements (cont)

   Conditional statements
Operational interpretation of
Statements (cont)

   Iteration

Doi is the ith approximation of the loop
Refinement
   angelic construct