modules

cs776(Prasad) L112Modules 1

Modules

value : type : function ::

structure : signature : functor


SML features • Programming in the

small– Reliability

• Correctness (types)

• Robustness (exceptions)

– Efficiency• Data Structures and

Algorithms (lists, arrays)

– Abstraction• Data (patterns)

• Control (higher-order functions)

Declarative (enhances programmer productivity)

• Programming in the large– Cluster related definitions;

hierarchical organization of programs (structures)

– Encapsulation (localization) of implementation details, for clarity and modifiability (abstype, signatures)

– Reusability and interchangeability of parts (functors).

• Separate compilation.

• Standard libraries.


Customization of Modules

• Controlling visibility of names (Managing environments)– To avoid potential name conflicts.

• Multiple implementations of an ADT (e.g, Table).• Similar operations on different ADTs (e.g., delete

on Set, List, Table, etc).• Programmer choice of names, to conform to domain

vocabulary.

– To encapsulate representation details.• To enable transparent changes to the impl.• To preserve data integrity (invariants)

• Instantiation (Specializing w.r.t. types)


SML Constructs

• Structure – Collection of definitions

• E.g., Ada/Java packages, C++/Java classes, etc

• Signature– Type declarations of the names

• E.g., Ada package specification, Java interfaces, etc

• Functor – Maps a structure to another structure

– Parameterized structures • E.g., Ada generic units, C++ templates, Java functions with

interface/class parameters, etc


structurestructure QueueImpl = structstruct datatype 'a t = Q of ('a list * 'a list); exception E;

val empty = Q([],[]); fun norm (Q([],ts)) = Q(rev ts, []) | norm q = q; fun enq(Q(hs,ts), x) = norm(Q(hs, x::ts)); fun null(Q([],[])) = true | null _ = false; fun hd(Q(x::_,_)) = x | hd(Q([],_)) = raise E; fun deq(Q(x::hs,ts)) = norm(Q(hs,ts)) | deq(Q([],_)) = raise E; endend;


structurestructure QueueImpl : sigsig datatype 'a t = Q of 'a list * 'a list exception E val deq : 'a t -> 'a t val empty : 'a t val enq : 'a t * 'a -> 'a t val hd : 'a t -> 'a val norm : 'a t -> 'a t val null : 'a t -> bool end;end;


Information Hiding Concerns

• The implementation details of QueueImpl are exported. – Client code can use pattern matching to

manipulate queues.• Client code can break if the implementation of QueueImpl is changed.

– Client code can ignore the FIFO discipline.• Semantics of queue (invariants) can be violated.

• Possible Solution : Restrict the view


Transparent Signature Constraints

signaturesignature Qtip = sigsig type ’a t val deq : 'a t -> 'a t val empty : 'a t val enq : 'a t * 'a -> 'a t val hd : 'a t -> 'a val null : 'a t -> bool end;end;

structure structure Queue : Qtip = QueueImpl;Queue : Qtip = QueueImpl;


- QueueImpl.norm; val it = fn : 'a QueueImpl.t -> 'a QueueImpl.t

- Queue.norm; (* error *)

- Queue.hd; val it = fn : 'a QueueImpl.t -> 'a

- Queue.Q; (* error *)

- Queue.empty = QueueImpl.Q ([],[]);- open QueueImpl;- norm(Queue.enq(Queue.empty, “a”)); val it = Q (["a"],[]) : string t


Opaque Signature Constraints

structure structure Queue :> Qtip = QueueImpl;;

• This enforces data abstraction.– Only operations that are explicitly defined on Queue can be invoked on Queue-values.

QueueImpl.norm(Queue.enq(Queue.empty,“a”)); (* error *)

– Equality tests (based on the representation) are banned.

Queue.empty = QueueImpl.Q ([],[])); (* error *)

• To allow equality tests, use eqtype ’a t instead of type ’a t.

(Cf. Ada’s Limited Private Types and Private Types)


signature SIG = sig val i : int; type t; val x : t val f:t*t -> bool end;

structure STRUC = struct val i = 3; type t = int; val x = 4; fun f(a,b) = (a=b) end;

open STRUC;

f(x,x);

f(i,x); (*val it = false : bool*)

structure STRUC’:> SIG = STRUC;

open STRUC’;f(i,x); (* type error *)

• Type t created using opaque signatures is regarded as distinct from any other type (including int and other type t created from the same structure.)


signature SIG = sig val i : int; type t; val x : t val f:t*t -> bool end;

structure STRUC = struct val i = 3; type t = int; val x = 4; fun f(a,b) = (a=b) end;

signature SIG’ = SIG where type t = int;structure STRUC’:> SIG’

= STRUC;open STRUC’;

f(i,x);

(* val it = false : bool*)

• Type t being int is visible because where-clause explicitly exports it.


Signature Matching

structure strId : sigExp = strExp ; (* target candidate *)

Target signature expresses a set of constraints that the candidate structure must satisfy.

Informally, the candidate’s signature may have more components than are required by the target, may have more definitions of types than are required, and may have value components with more general types.


QUEUE_WITH_EMPTY matches QUEUE

signature QUEUE = sig type 'a queue exception Empty val empty : 'a queue val insert : 'a * 'a queue -> 'a queue val remove : 'a queue -> 'a * 'a queue end

signature QUEUE_WITH_EMPTY = sig include QUEUE val is_empty : 'a queue -> bool end


QUEUE_AS_LISTS matches QUEUE

signature QUEUE = sig type 'a queue exception Empty val empty : 'a queue val insert : 'a * 'a queue -> 'a queue val remove : 'a queue -> 'a * 'a queue end

signature QUEUE_AS_LISTS = QUEUE where type 'a queue = 'a list *

'a list


Equivalent: QUEUE_AS_LIST and QUEUE_AS_LIST0

signature QUEUE = sig type 'a queue exception Empty val empty : 'a queue val insert : 'a * 'a queue ->

'a queue val remove : 'a queue -> 'a * 'a queue end

signature QUEUE_AS_LIST0 = QUEUE where type

'a queue = 'a list

signature QUEUE_AS_LIST = sig type 'a queue = 'a list exception Empty val empty : 'a list val insert : 'a * 'a list -> 'a list val remove : 'a list -> 'a * 'a listend


MERGEABLE_QUEUE matches MERGEABLE_INT_QUEUE

signature MERGEABLE_QUEUE = sig include QUEUE val merge : 'a queue * 'a queue -> 'a queue end

signature MERGEABLE_INT_QUEUE = sig include QUEUE val merge : int queue * int queue -> int queue end


RBT_DT matches RBT

signature RBT_DT = sig datatype 'a rbt = Empty | Red of 'a rbt * 'a * 'a rbt | Black of 'a rbt * 'a * 'a rbt end

signature RBT = sig type 'a rbt val Empty : 'a rbt val Red : 'a rbt * 'a * 'a rbt -> 'a rbt end


(cont’d)

• Every type specification (resp. datatype definition) in the target must have a matching (resp. equivalent) type specification (resp. datatype definition) in the candidate.

• Every exception specification in the target must have an equivalent exception specification in the candidate.

• Every value specification in the target must be matched by a value specification in the candidate with at least as general a type.


Relationship between Structures and Signatures

• In ML, a signature may serve as an interface for many different structures, and that a structure may implement many different signatures.

(interchangeability of componentsinterchangeability of components)• ML, C++, Java† : many-to-many

• Modula-2 : one-to-one

• Ada-95 : many-to-one.

• Every structure has a principal signature, with the property that all other signatures for that structure are more restrictive than the principal signature.


Functors

• A functorfunctor maps structures to structure.– A functor can be viewed as a reusable unit that

contains well-defined “sockets for plug-ins”.– Parameterized/Generic modules.– Useful in “client-server paradigm” applications

exploiting interchangeability of parts with common interface.

• Developing floating point libraries that work with different precision implementations.

• Building common test harness to verify various implementations of an abstract data type.


Example

signature Order = sig eqtype et ; val le : et -> et -> boolend;

functor MkOrdSet(Ord:Order) = struct exception EmptySetEX; datatype set = SET of (Ord.et list) val empty = SET nil fun insert (SET s) n = SET (n::s) fun member (SET s) n = (List.exists (fn x => (x = n)) s)

fun min (SET s) = if (null(s)) then raise EmptySetEX

else foldr (fn (x,r) => if (Ord.le r x) then r else x) (hd s) (tl s);

end;


structure OrdInt: Order = struct type et = int;

fun le (x:et) y = x <= yend;

structure intset = MkOrdSet(OrdInt);

open intset; (min empty); (* uncaught exception *) val s1 = (insert empty 5);

val s2 = (insert s1 3); (* val s2 = SET [3,5] : set *) (min (insert s2 8)); (* val it = 3 : OrdInt.et *)


Example Functor (Component Reuse) signature ORDER = sig type t; val compare: t*t -> bool end;structure StringOrder: ORDER = struct type t = string; val compare = String.compare end;

...

structure StringDict = Dictionary (StringOrder);

(* structure StringDict : sig type key = StringOrder.t type 'a t exception E of key val empty : 'a t val lookup : 'a t * Key.t -> 'a val update : 'a t * key * 'a -> 'a t end *)


functor Dictionary (Key: ORDER) = struct type key = Key.t; abstype 'a t = Lf | B of key *'a*'a t *'a t with

exception E of key; val empty = Lf; fun lookup (B(a,x,t1,t2), b) = (case Key.compare(a,b) of GREATER => lookup(t1, b) | EQUAL => x | LESS => lookup(t2, b)) | lookup (Lf, b) = raise E b; fun update (Lf, b, y) = B(b, y, Lf, Lf) | update (B(a,x,t1,t2), b, y) = (case Key.compare(a,b) of GREATER => B(a, x, update(t1,b,y), t2)

| EQUAL => B(a, y, t1, t2) | LESS => B(a, x,t1,update(t2,b,y)));

end end;


(cont’d)

infix |< ;

fun (d |< (k,x)) =

StringDict.update(d,k,x);

val dict = StringDict.empty

|< (“abc”, 2) |< (“nbc”, 11)

|< (“dsc”, 53) |< (“tlc”,54);

(* val dict = - : int StringDict.t *)

StringDict.lookup(dict, “dsc”);

(* val it = 53 : int *)

StringDict.lookup(dict, “cnn”);

(* uncaught exception E *)


signature INT = sig val i: int end; signature REAL = sig val r: real end;

functor Foo(structure I:INT and R: REAL; val x : int) = struct end;

structure Int = struct val i = 0 end; structure Real= struct val r = 0.0 end;

structure Bar = Foo(structure I = Int and R = Real; val x = 2);

Multi-argument Functor


Sharing Constraints (for combining / integrating modules)

To express equality constraints among types names.• Type sharing

sharing type <type> = … = <type>

• Structure sharingsharing <structure> = … = < structure>

Shorthand for sharing of identically named types within the equated structures.


signature ELEMENT = sig type element; val similar : element * element -> bool; end;

signature BTREE = sig structure Element: ELEMENT; eqtype elt; sharing type elt = Element.element; datatype bt = Empty | Node of elt * bt * bt; val leaf : elt -> bt; val build : elt * bt * bt -> bt; val lookup : elt * bt -> bool end;

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