CS6202: Advanced Topics in Standard ML Standard ML Programming Languages and Systems Lecture 2/3 : Standard ML • Great programming language – reusability, abstraction, quite efficient. • Expression-Oriented. • Values, Types and Effects A type-safe language that embodies • Polymorphic Types and Inference many innovative ideas in language • Products, Records and Algebraic Types design. • Higher-Order Functions • Exceptions and Reference Types • Rich Module Language Reference --- Programming in Standard ML: http://www.cs.cmu.edu/~rwh/introsml/ CS6202 ML 1 CS6202 ML 2 Example ML Program Example ML Program Signature Signature • Problem – matching string against a regular expression. • Signature – describe interface of modules. • Signature Expression : sigexp ::= sig specs end • Contains basic specifications for type, datatype, exception, values. • Signature binding : signature sigid = sigexp • Structure is implementation , while signature denotes interface . CS6202 ML 3 CS6202 ML 4
Implementation Structure Implementation Structure • Implementation of signature is called structure. • A unit of program with declarations for types, exceptions and values. • Structure Expression : strexp ::= struct decs end • Components referred by long identifiers. • Contains definitions for type, datatype, exception, values. • Structure binding : structure strid = strexp CS6202 ML 5 CS6202 ML 6 Computation Model Computation Model Values Values • Emphasis is on evaluation of expressions rather than • Expression has a type, denoted by exp : typ command. • Each expression has three characteristics : (i) type , (ii) value and (iii) possible effect . • Type is a description of the value it is supposed to yield. • Can be evaluated to a value, denoted by exp ⇓ val • Evaluation may cause an effect, such as input/output , exception or mutation . • Pure expression (e.g. mathematical functions) does not have side-effects. CS6202 ML 7 CS6202 ML 8
Types Declarations Types Declarations • Some examples of base types : • Any type may be given a name through type binding • A value may be given a name through a value binding. Such bindings are type-checked, and rejected if ill-typed. CS6202 ML 9 CS6202 ML 10 Limiting Scope Limiting Scope Functions Functions • Two main aspects : • Scope of a type variable or type constructor may be • algorithmic – how it is computed delimited, as follows : • extensional – what is being computed • Each function has a type : typ -> typ’ • An Example. • Anonymous function written using syntax : Example : CS6202 ML 11 CS6202 ML 12
Functions Tuple and Product Type and Product Type Functions Tuple • Function is also a value : • Aggregate data structures, such as tuples, lists, can be easily created and manipulated. • An n-tuple is a finite ordered sequence : : • An example of function value : product type tuple value Example CS6202 ML 13 CS6202 ML 14 Tuple Pattern Tuple Pattern Record Types Record Types • Allows easy access of components. General form : • Record type allows a label to be associated with each component. • A record value and its type : • Permitted form of tuple pattern : : record type record value • Record binding. • Example : CS6202 ML 15 CS6202 ML 16
Record Example Selectors Record Example Selectors record binding • A list of predefined selection function for the i-th record type component of a tuple. • Predefined selector for record fields : ellipsis as shorthand expanded • Use sparingly as patterns are typically clearer. CS6202 ML 17 CS6202 ML 18 Case Analysis Case Analysis Recursive Function Recursive Function • Clausal function expression useful for cases. • Use rec to indicate recursive value binding. • An example : • Or use fun notation directly : • Alternative form : ≡ CS6202 ML 19 CS6202 ML 20
General Recursion Iteration via Tail- -Recursion Recursion General Recursion Iteration via Tail • Requires linear stack space. • Loop is equivalent to tail-recursive code • Example : • Example : • What is a tail call, and why is it more efficient? CS6202 ML 21 CS6202 ML 22 Algebraic Data Types Algebraic Data Types Polymorphism / Overloading Polymorphism / Overloading • Some functions have generic type. For example, the • Data type declaration via datatype contains : identity function has a principal type ‘a -> ‘a • Type constructor • Value constructor(s) • Examples of non-recursive data types. • Overloading uses the same name for a class of operator. type constructor value constructors • Hard problem: CS6202 ML 23 CS6202 ML 24
Algebraic Data Types Algebraic Data Types Algebraic Data Types Algebraic Data Types • Some may have type parameters, e.g. • Recursive functions : • An example of its use : • Mutual recursive data types (a bit contrived): • Recursive type is also possible : • Disjoint union types : CS6202 ML 25 CS6202 ML 26 Abstract Syntax Tree Lists Abstract Syntax Tree Lists • Easy to model symbolic data structures : • A built-in data type with 2 value constructors. abbreviated • An interpreter : • Some functions on list : infix version of append CS6202 ML 27 CS6202 ML 28
Higher Higher- -Order Functions Order Functions Higher- Higher -Order Functions Order Functions • Functions are first-class : pass as arguments , return as • Returning function as result : result , contain inside data structures , has a type . • Key main uses : • abstracting control • Curry function to untupled argument • staging computation • Example – applies a function to every element of list tupled curried CS6202 ML 29 CS6202 ML 30 Abstracting Control Staging Abstracting Control Staging • Distinguish early from late arguments : • Abstracting similar patterns of control early argument late argument • Improve by early evaluation and then sharing. staged_append [v 1 ,…,v n ] • What is the principal type of this reduction? CS6202 ML 31 CS6202 ML 32
Exceptions Exceptions Exceptions Exceptions • Are useful to catch runtime errors. • Exception handler can be used to catch a raised exception. This can make software more robust. • An example of user-defined exception : • Handler has the syntax: exp handle match match ::= pat => exp CS6202 ML 33 CS6202 ML 34 Exceptions Mutable Store Exceptions Mutable Store • Exception can implement back-tracking. • Mutable cell contains a value that may change : • Create a mutable cell with an initial value : ref : ‘a -> ‘a ref • Contents can be retrieved using : ! : ‘a ref -> ‘a Can use a ref pattern : • Exception may carry values. • How is equality implemented for reference? declare raise catch CS6202 ML 35 CS6202 ML 36
Bad Imperative Programming Bad Imperative Programming OO Programming Style OO Programming Style • A factorial function : can you follow? • An single counter : • A class of counters : type of new_counter CS6202 ML 37 CS6202 ML 38 Mutable Array Memoization Mutable Array Memoization • Mutable array as a primitive data structure : • Repeated calls are retrieved rather than recomputed. • Can be used for memoization where many redundant calls, e.g n-th Catalan number : sum f n = (f 0) + … + (f n) CS6202 ML 39 CS6202 ML 40
Memoization Memoization Tupling Tupling • Apply the same idea to computing fibonacci efficiently. • Is there no hope for purity? Use tupled function local val limit : int = 1000 fibtup n = (fib(n+1), fib(n)) val memo : int option array = Array.array(limit,NONE) in fun fib’ 0 = 1 Optimised code with reuse : | fib’ 1 = 1 | fib’ n = fib(n-1) + fib(n-2) and fib n = fun fibtup 0 = (1,1) if n<limit then | fibtup n = case fibtup(n-1) of case Array.sub (memo,n) of (u,v) => (u+v,u) SOMR r => r and fib n = snd(fibtup(n)) | None => let r=fib’ n in end Array.update(memo,n,SOME r) end More optimization – tail recursion ? logarithmic time? else fib’ n end CS6202 ML 41 CS6202 ML 42 Input/Output Lazy Data Structures Input/Output Lazy Data Structures • Standard input/output organized as streams. • ML philosophy – laziness us a special case of eagerness. Can treat an unevaluated expression as a value. • Read a line from an input stream. • Applications (i) infinite structures (e.g. streams) inputLine : instream -> string (ii) interactive system activate SML/NJ option (iii) better termination property • Write a line to stdout stream. print : string -> unit • Write a line to a specific stream. • Infinite stream and acceses: output : outstream * string -> unit flushout : outstream -> unit • A blocking input that reads current available string input : instream -> string • Non-blocking input that reads upto n-char string caninput : instream * int -> string CS6202 ML 43 CS6202 ML 44
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