Dependently Typed Functional Programming with Idris

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1 Dependently Typed Functional Programming with Idris Lecture 2: Embedded Domain Specific Languages Edwin Brady University of St

2 Introduction In this lecture: Some history Programming Languages and Abstraction A well-typed interpreter Embedding languages with syntax overloading OS interaction and foreign functions Managing resources

3 Abstraction Computer Scientists often talk of abstraction English definition: the process of considering something independently of its associations or attributes In Computer Science:... a process of extracting the general structure to allow the inessential details to be ignored Ron Morrison, PhD Thesis Separation of what a program or system does from how

4 Abstraction Computer Scientists often talk of abstraction English definition: the process of considering something independently of its associations or attributes In Computer Science:... a process of extracting the general structure to allow the inessential details to be ignored Ron Morrison, PhD Thesis Separation of what a program or system does from how We can view a computer system as a number of layers of abstraction

5 Some History

6 Some History 1946 ENIAC, the first general purpose electronic computer Turing Complete meaning it could run any computable function But... no abstraction! Programmed by manipulating switches and cables on the machine

7 Some History 1949 EDSAC, the first practical stored program computer Programs stored in memory as binary data

8 Some History 1949 EDSAC, the first practical stored program computer Programs stored in memory as binary data 1950 (approx) Assembly Language Mnemonics for machine instructions MOV A, R4 ADD B, R4 MOV R4, C HALT New abstraction: human readable notation for machine language

9 Some History

10 Some History 1952 A-0, the first compiler Arithmetic Language version 0 Converted a specification into machine code Created by Grace Hopper

11 Some History 1952 A-0, the first compiler Arithmetic Language version 0 Converted a specification into machine code Created by Grace Hopper She did this, she said, because she was lazy and hoped that the programmer may return to being a mathematician. (

12 Some History

13 Some History 1957 FORTRAN (FORmula TRANslator) Intended as a more practical alternative to hand-writing assembly language Invented by a team led by John Backus New abstraction: Familiar mathematical notation C = A + B

14 Some History 1957 FORTRAN (FORmula TRANslator) Intended as a more practical alternative to hand-writing assembly language Invented by a team led by John Backus New abstraction: Familiar mathematical notation C = A + B Much of my work has come from being lazy. I didn t like writing programs, and so, when I was working on the IBM 701, writing programs for computing missile trajectories, I started work on a programming system to make it easier to write programs. John Backus

15 High Level Languages Since FORTRAN, many new high level languages have been designed providing new abstractions, targetting new application domains. A selection: LISP (1958), ALGOL (1960), C (1973), ML (1973), C++ (1983), Haskell (1990), Java (1995), Go (2009)

16 High Level Languages Since FORTRAN, many new high level languages have been designed providing new abstractions, targetting new application domains. A selection: LISP (1958), ALGOL (1960), C (1973), ML (1973), C++ (1983), Haskell (1990), Java (1995), Go (2009) Most programming languages are partly a way of expressing things in terms of other things and partly a basic set of given things. Peter Landin, The next 700 programming languages (1966)

17 Domain Specific Languages A Domain Specific Language (DSL) is a language designed for a particular problem domain Very high level of abstraction Typically declarative, i.e. say what, not how Often not Turing Complete Examples: Database and Internet applications HTML, XML, SQL,... Scientific programming R, Mathematica Computer games UnrealScript Hardware description Verilog Spreadsheet formulas

18 Domain Specific Languages A Domain Specific Language (DSL) is a language designed for a particular problem domain Very high level of abstraction Typically declarative, i.e. say what, not how Often not Turing Complete filtering:

19 Domain Specific Languages A Domain Specific Language (DSL) is a language designed for a particular problem domain Very high level of abstraction Typically declarative, i.e. say what, not how Often not Turing Complete Music playlists

20 DSLs in Idris Idris aims to support the implementation of verified domain specific languages. To illustrate this, we begin with an interpreter for the simply typed λ-calculus.

21 First Attempt Expressions data Expr = Val Int Add Expr Expr

22 First Attempt Expressions data Expr = Val Int Add Expr Expr Evaluator interp : Expr -> Int interp (Val x) = x interp (Add l r) = interp l + interp r

23 First Attempt Expressions data Expr = Val Int Var String Add Expr Expr

24 First Attempt Expressions data Expr = Val Int Var String Add Expr Expr Evaluator interp : List (String, Int) -> Expr -> Maybe Int interp env (Val x) = x interp env (Var n) = case lookup n env of Nothing => Nothing Just val => val interp env (Add l r) = interp env l + interp env r

25 Preliminaries Types data Ty = TyInt TyBool TyFun Ty Ty

26 Preliminaries Types data Ty = TyInt TyBool TyFun Ty Ty Interpreting types interpty : Ty -> Type interpty TyInt = Int interpty TyBool = Bool interpty (TyFun s t) = interpty s -> interpty t

27 Preliminaries The Finite Sets data Fin : Nat -> Type where fo : Fin (S k) fs : Fin k -> Fin (S k)

28 Preliminaries The Finite Sets data Fin : Nat -> Type where fo : Fin (S k) fs : Fin k -> Fin (S k) Example: Bounds Safe Vector Lookup total index : Fin n -> Vect a n -> a index fo (x::xs) = x index (fs k) (x::xs) = index k xs

29 Preliminaries We can represent variables as a de Bruijn index Nameless A number, counting binders since the variable was bound λxy.x + y = λxy.1 + 0

30 Preliminaries We can represent variables as a de Bruijn index Nameless A number, counting binders since the variable was bound λxy.x + y = λxy If there are n variables: Fin n represents a bounded de Bruijn index index i G is a bounds safe lookup of variable i in context G.

31 Preliminaries Environments using (G : Vect Ty n) data Env : Vect Ty n -> Type where Nil : Env Nil (::) : interpty a -> Env G -> Env (a :: G) data HasType : (i : Fin n) -> Vect Ty n -> Ty -> Type where stop : HasType fo (t :: G) t pop : HasType k G t -> HasType (fs k) (u :: G) t

32 Preliminaries Environment Example ctxt : Vect Ty (S (S O)) ctxt = [TyInt, TyBool] env : Env ctxt env = [42, True] isbool : HasType (fs fo) ctxt TyBool isbool = pop stop

33 Demonstration: the Interpreter

34 Syntax Overloading dsl notation dsl expr lambda = Lam variable = Var index_first = stop index_next = pop

35 Syntax Overloading syntax rules syntax IF [x] THEN [t] ELSE [e] = If x t e forloop : List a -> (a -> IO ()) -> IO () syntax for {x} "in" [xs] ":" [body] = forloop xs (\x => body)

36 Syntax Overloading Implicit conversions data Lang : Vect Ty n -> Ty -> Type where Val : interpty a -> Lang G a... implicit MkVal : interpty a -> Lang G a MkVal = Val

37 Interlude: Foreign Function Calls Foreign Types data FTy = FInt FFloat FChar FString FPtr FAny Type FUnit

38 Interlude: Foreign Function Calls Foreign Types data FTy = FInt FFloat FChar FString FPtr FAny Type FUnit Foreign Types to Idris interpfty : FTy -> Type interpfty FInt = Int interpfty FFloat = Float interpfty FChar = Char interpfty FString = String interpfty FPtr = Ptr interpfty (FAny t) = t interpfty FUnit = ()

39 Interlude: Foreign Function Calls Building Foreign Function Calls ForeignTy : (xs:list FTy) -> (t:fty) -> Type data Foreign : Type -> Type where FFun : String -> (xs:list FTy) -> (t:fty) -> Foreign (ForeignTy xs t) mkforeign : Foreign x -> x

40 Interlude: Foreign Function Calls Examples putstr : String -> IO () putstr x = mkforeign (FFun "putstr" [FString] FUnit) x getchar : IO Char getchar = mkforeign (FFun "getchar" [] FChar)

41 Interlude: Foreign Function Calls Examples data File = FHandler Ptr do_fopen : String -> String -> IO Ptr do_fopen f m = mkforeign (FFun "fileopen" [FString, FString] FPtr) f m openfile : String -> Mode -> IO File openfile f m = fopen f (modestr m) where modestr Read = "r" modestr Write = "w" modestr ReadWrite = "r+"

42 Extra-functional Correctness Nobody in industry really cares whether a program does what it s supposed to what they are really concerned with is how the program behaves when it s run. Joe Armstrong (designer of Erlang programming language)

43 Extra-functional Correctness We make a distinction between: Functional correctness Does the program do what it is supposed to do? e.g. Does sort produce an ordered permutation of its input? Extra-functional correctness Does the program run within the required resource constraints? e.g. Does the program run within 1 Mb RAM? Does it respond to input within 1 second?

44 Resource Example: Files A program which manages files must conform to a resource usage protocol. Informally: Files must be opened succesfully before they are read or written A file open for reading may not be written to, and vice versa Files must be closed when processing is finished We have developed a domain specific language for encoding, in general, resource usage protocols

45 Demonstration: Resources Resource Safe File Management readh : String -> RES () readh fn = res (do let x = open fn Reading if opened x then do str <- rreadline x rputstrln str rclose x else rputstrln "Error")

Embedded Domain Specific Languages in Idris Lecture 3: State, Side Effects and Resources

Embedded Domain Specific Languages in Idris Lecture 3: State, Side Effects and Resources Edwin Brady (ecb10@st-andrews.ac.uk) University of St Andrews, Scotland, UK @edwinbrady SSGEP, Oxford, 9th July