Transcript Lecture 7: Data Abstraction It is better to have 100 functions operate on one data structure than 10 functions on 10 data.

Lecture 7: Data Abstraction
It is better to have 100 functions operate on one data
structure than 10 functions on 10 data structures.
Alan Perlis
Menu
• Data Abstraction before CLU
• Data Abstraction in CLU
• Reasoning about Data Abstractions
– Abstraction Functions
– Rep Invariants
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University of Virginia CS 655
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What is a type?
• Last time: a set of values
• Today: an abstraction for decomposing
a program that provides a set of
operations
• Sets of values don’t work because you
are tied to the representation
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University of Virginia CS 655
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Data Abstraction in C/Pascal?
• User-defined types:
typedef enum { red = 0, green, blue } color;
typedef struct { int locx; int locy; } location;
• Type checking either:
– By structure (e.g., color dumb = 23)
– By name (maybe in Pascal, ambiguous)
• Only way to use type, is to access its
representation; no restrictions on where
you can do this.
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Data Abstraction in BLISS?
• User specifies accessing algorithm for
structure elements
• May modify either structure definition or
algorithms without affecting the other
structure array[i, j] = (.array + .i * 10 + .j)
• May define memory allocation routines
• But: only arrays, no typed elements
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Data Abstraction in Simula67
• Define a class with hidden attributes (visible
only in the class implementation) and protected
attributes (visible in subclass implementations
also)
• Unfortunately, not widely known:
– From Sweden
– Few Publications (mostly in Swedish), no language
Report, no decent textbook until 1986
• Alan Kay learned about Simula by reading the source code,
thinking it was an Algol compiler!
– Big influence on Smalltalk and C++; small influence
on CLU
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Providing Data Abstraction
• Type check by name
• Restrict what code can access the
representation of a data type
– CLU, Alphard: only operations of the type
– Other (possibly) reasonable answers:
• C++: allow functions outside the type that are declared
friends to access representation
• LCLint: in files and functions according to a naming
convention, elsewhere when explicitly annotated
• [Stata97]: operations can access the only some of the
representation
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Data Abstraction in CLU
Rest of program sees black box described by specification.
intmap = data type is create, insert, lookup
Operations
create = proc () returns (intset)
effects Returns a new, empty intmap.
insert = proc (s: intmap, k: string, val: int)
requires s does not have a key k.
modifies s
effects spost maps k to val.
lookup = proc (s: intmap, k: string) returns (int)
requires There is a key k in s.
effects Returns value associated with key in s.
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Black-box Interface
intmap
down (intmap)
returns (rep)
up (rep)
returns (intmap)
rep = representation of intmap
Only code in the cluster implementing intmap can call
intmap$up or intmap$down.
There is nothing else special about code in the cluster!
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Parameterized Data Abstractions
• Don’t want to implement stringintmap,
stringrealmap, intintmap, etc.
• Value Parameters:
– Don’t want to implement Factorial2 (), Factorial3
(), Factorial4 (), ...
– Implement Factorial (n: int)
• Type Parameters:
– Implement map[tkey: type, tval: type]
• Problem: how will we implement lookup if we
don’t know anything about tkey?
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Specification
map = data type [tkey: type, tval: type] is create, insert, lookup
Requires tkey has an operation
equal: proctype (t, t) returns (bool)
that is an equivalence relation on t.
Operations
create = proc () returns (map)
effects Returns a new, empty map.
insert = proc (s: map, k: tkey, val: tval)
requires s has no key k’ such that tkey$equal (k, k’).
modifies s
effects lookup (spost. k) = val.
lookup = proc (s: map, k: tkey) returns (tval)
requires s has a key k’ in s such that tkey$equal (k, k’).
effects Returns value associated with k in s.
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Where Clauses
map = cluster [tkey: type, tval: type] is
create, insert, lookup
where tkey has
equal: proctype (tkey, tkey) returns bool
Used in implementation, not specification.
Checked by compiler.
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Implementing Data Abstractions
• Need a concrete representation
map = cluster [tkey: type, tval: type] is create, insert,
lookup where tkey has
equal: proctype (tkey, tkey) returns (bool)
pair = record [key: tkey, value: tval]
rep = array [pair]
create = proc () returns (map)
return up(rep$new ())
end create
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Implementing map
insert = proc (m: map, k: tkey, v: tval)
% Better spec would remove requires
% clause and signal exception if key
% is already in the map.
down (m).addh (pair${key: k, value: v})
end insert
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Printing maps
map = cluster [tkey: type, tval] is ... unparse
...
unparse = proc (m: map) returns (string)
where
tkey has unparse: proctype (tkey) returns (string)
tval has unparse: proctype (tval) returns (string)
Why put the where clause about equal on the
cluster instead of member operation?
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• bool
CLU: Special Types
– Language control structures (if, while) depend
on type bool
• int, char, real, string, null
– Built-in language support for literals
• record, struct, variant, oneof, array,
sequence
– Special constructor syntax T${ … }
• any
– Union of all possible types, use force to
convert (with checking) to actual type
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CLU Operators
• Assignment (:=)
– Always means sharing (recall immutable types)
– Types by name must match
• Everything else is syntactic sugar, all types
can use:
3 + 2  int$add (3, 2)
m1,m2: map[string,int] m1 + m2 
map[string,int]$add (m1, m2)
ai: array[int] ai[n] := ai[n-1] 
array[int]$store (ai, n, array[int]$fetch (ai, n-1))
• Four exceptions: up, down, cand, cor
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Reasoning about Data Abstractions
• They are abstractions – need to invent a
formal notation (A) for describing them
• They have representations – need to
define a mapping from concrete
representation to that formal notation
• Abstraction Function:
A: rep  A
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Describing maps
A map can be described by a sequence
of (key, value) pairs with unique keys:
[ (key0, value0), (key1, value1), … ]
such that if key = keyi the value
associated with key is valuei .
A: rep  [(key0, value0), (key1, value1), …]
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Abstraction Function
A: array [record [key: tkey, value: tval]]
 [(key0, value0), (key1, value1), …]
A(r) = [(r[rep$low(r)].key, r[rep$low(r)].value),
(r[rep$low(r) + 1].key, r[rep$low(r)+1].value),
...
(r[rep$high(r)].key, r[rep$high(r)].value)]
Problem: What if r contains duplicate keys?
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Rep Invariant
• “It better not!”
• I: rep  Boolean
I(r) = (r[i].key = r[k].key implies i = k)
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Reasoning with Rep Invariants
Prove by induction, for a datatype t:
1. For each operation that creates new t: prove that
returned reps r of returned t satisfies I(r)
2. For each cluster operation: assume all t objects
passed as parameters satisfy have reps r that satisfy
I(r), prove they do at all cluster exit points.
Argue that only cluster operations can alter the rep, so
if you can prove invariant holds for all cluster
operations, it must always hold.
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What can go wrong?
map = cluster [tkey: type, tval: type] is ...
choose = proc (m: map) returns (pair)
% requires m is not empty.
% effects Returns a (key, value) pair in m.
return (down (m)[rep$low (down(m))]
end choose
p = proc (m: map[string, int])
map[string,int]$insert (m, “duplicate”, 3)
pair p := map[string,int]$choose (m)
p.key = “duplicate”
end p
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Rep Exposure
• Can’t share mutable objects in data
representations
• Sharing immutable objects is okay
• Could compiler prevent this?
– Yes, pretty easy
• Why doesn’t CLU compiler prevent this?
– Sometimes efficiency requires rep exposure
– e.g., create a map by passing in an array of
pairs
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Next Time
Would adding syntactic sugar make CLU
object-oriented?
x.operation (args) 
typeof (x)$operation (x, args)
e.g.:
m.insert (s, v) 
map[string, int]$insert (m, s, v)
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Charge
• Read Stroustrup
paper before
class Thursday
• Project
Proposals by
midnight
tomorrow
• Be ready to give
elevator
speeches in
class Thursday
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University of Virginia CS 655
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