Programming Languages. Example 5. Example 4. CSE 130 : Fall type, can reuse code for all types! let rec cat l = match l with

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1 CSE 130 : Fall 2008 Programming Languages Lecture 9: s and Signatures Ranjit Jhala UC San Diego Previously: Polymorphism enables Reuse Can reuse generic functions: map : a * b b * a filter: ( a bool * a list) a list rev: a list a list length: a list int swap: a * b b * a sort: ( a a bool * a list) a list compose: ( a b * c b) c a If function (algorithm) is indepent of type, can reuse code for all types! Example 4 let rec cat l = [] -> h::t -> h^(cat t) ML doesn t know what the function does, or even that it finishes only its type! string list -> string let rec cat l = [] -> cat [] h::t -> h^(cat t) Example 5 ( a (a-> b) -> a list -> b list let rec map f l = [] -> [] h::t ->(map h)::(map f t) Introduce unknown tyvar: Unify,solve, Remaining tyvar gets a forall

2 Example 6 ( b (b-> c) * ( a -> b) -> ( a -> c) Example 7 ( a (a* b -> b) -> b -> a list -> b let compose (f,g) x = f (g x) let rec fold f cur l = [] -> cur h::t -> fold f (f h cur) t let foo1 f g x = if f x then x else g x let foo2 f g x = if f x then x else foo2 f g (g x)

3 Today: Divide-Conquer Programming We ve seen very small programs so far 4 yr education chopped into quarters Typical software is thousands, millions LOC How can a PL help to manage complexity? Only one technique humans know about Divide-Conquer Programming Interfaces : Rational Numbers Say you want a software package that uses rational numbers heavily Remember rationals? Ratio of two integers: m/n Well, seems simple enough: Use a pair of integers to represent rationals! OCaml type: int * int Rational Numbers Well, every pair of isn t a rational (5,0)? 2nd elem denominator must not be zero How do we print a rational? When are two rationals equal? (6,4) and (30,20)? Need to normalize rationals But need to fix to_string

4 Many functions related to type Many functions related to type module Name = Pack into a module Types, Values, Exceptions bound in Name are: Name.t, Name.x, Name.f Bind module to diff name module NewName = Rational;; NewName.add;; NewName.to_string;; module Name = Pack into a module Types, Values, Exceptions bound in Name are: Name.t, Name.x, Name.f Can open module Everything comes tumbling out open Rational;; add;; to_string;; Many functions related to type Information Hiding ure Name = Can pack into a module Variables, functions, exceptions bound in Name are: Name.x, Name.f Bind module to diff name Open module Not much better than diff files! Whats the problem? Prevent the client from passing in any pair Hide implementation from client Control usage by restricting the interface Interface: what any client needs to know

5 Specify Interfaces by Signatures module type SIGNAME = Signature = Type of a module type- module Name: SIGNAME = Specifies what module provides types values and their types exceptions and their types Name : SIGNAME Name implements SIGNAME Code using Name knows only the entities in nature Implementing a Signature ML checks if Name:SIGNAME Name implements SIGNAME Name must contain all the in SIGNAME May and usually will, have more module type RATIONAL = type rational = val from_int : val to_string : val add : module Rational = type rational = int * int let gcd (x,y) = let normalize (x,y) = let from_int (x,y) = let to_string = let add r1 r2 = Hiding SIGNAME can hide of Name Bindings not in SIGNAME are hidden (private) That is, invisible to clients outside Name module type RATIONAL = type rational = val from_int : val to_string : val add : module Rational = type rational = int * int let gcd (x,y) = let normalize (x,y) = let from_int (x,y) = let to_string = let add r1 r2 = Still doesn t solve problem Inept client: Rational.add (2,3) (0,0);; Loops forever Solution: Make types abstract Client knows name of type, not implementation! Cannot directly access or create values of abs type Restrictthe interface to enforce invariants