modules
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cs776(Prasad) L112Modules 1
Modules
value : type : function ::
structure : signature : functor
cs776(Prasad) L112Modules 2
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.
cs776(Prasad) L112Modules 3
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)
cs776(Prasad) L112Modules 4
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
cs776(Prasad) L112Modules 5
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;
cs776(Prasad) L112Modules 6
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;
cs776(Prasad) L112Modules 7
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
cs776(Prasad) L112Modules 8
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;
cs776(Prasad) L112Modules 9
- 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
cs776(Prasad) L112Modules 10
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)
cs776(Prasad) L112Modules 11
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.)
cs776(Prasad) L112Modules 12
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.
cs776(Prasad) L112Modules 13
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.
cs776(Prasad) L112Modules 14
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
cs776(Prasad) L112Modules 15
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
cs776(Prasad) L112Modules 16
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
cs776(Prasad) L112Modules 17
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
cs776(Prasad) L112Modules 18
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
cs776(Prasad) L112Modules 19
(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.
cs776(Prasad) L112Modules 20
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.
cs776(Prasad) L112Modules 21
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.
cs776(Prasad) L112Modules 22
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;
cs776(Prasad) L112Modules 23
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 *)
cs776(Prasad) L112Modules 24
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 *)
cs776(Prasad) L112Modules 25
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;
cs776(Prasad) L112Modules 26
(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 *)
cs776(Prasad) L112Modules 27
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
cs776(Prasad) L112Modules 28
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.
cs776(Prasad) L112Modules 29
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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