From Interpreter to Compiler and Virtual Machine

Size: px

Start display at page:

Download "From Interpreter to Compiler and Virtual Machine"

Agatha Robbins
7 years ago
Views:

1 BRICS From Interpreter to Compiler and Virtual Machine Mads Sig Ager BRICS, University of Aarhus, Denmark Joint work with Dariusz Biernacki, Olivier Danvy, and Jan Midtgaard 1 Examples of machines Krivine s machine CEK CLS CAM SECD ZAM JVM VEC 2

Dariusz Biernacki, Olivier Danvy, and Jan Midtgaard 1

2 What is the difference between an abstract machine and a virtual machine? 3 What is the difference between an abstract machine and a virtual machine? A virtual machine has an instruction set. An abstract machine does not. 4

A virtual machine has an instruction set.

3 This work: From Interpreter to Compiler and Virtual Machine Compiler Interpreter Virtual Machine 5 Related work Lotsofit 6

4 This talk A methodology. Two examples: an evaluation function for the λ-calculus; a normalization function for the λ-calculus. 7 Methodology Defunctionalization. Closure conversion. CPS transformation. Factorization. 8

5 Defunctionalization (Reynolds, 1972) Who inhabits a function space? Answer: instances of lambda abstractions. Let us enumerate them and represent a function space as a sum: function declaration: sum constructor; function application: case. 9 A simple example (1/2) (* aux : (int -> int) -> int *) fun aux f = f 100 fun main x = aux (fn n => n+1) + aux (fn n => x+n) 10

Let us enumerate them and represent a function space as a sum: function declaration: sum

6 A simple example (2/2) datatype lam = L0 L1 of int fun apply (L0, n) = n+1 apply (L1 x, n) = x+n fun aux f = apply (f, 100) fun main x = aux L0 + aux (L1 x) 11 Closure conversion Special case of defunctionalization: only one summand; apply function inlined. 12

fun main x = aux L0 + aux (L1 x) 11 Closure conversion Special

7 CPS transformation 1. Names intermediate results. 2. Sequentializes their computation. 3. Introduces continuations. Or again: transforms into monadic normal form and picks the continuation monad. Or again: λ-counterpart of double negation. 13 Factorization [ ] maps source program to endofunction. We factorize into composition of combinators and recursive calls to [ ]. We name combinators. 14

Or again: transforms into monadic normal form and picks the continuation monad.

8 Example Before factorization: eval (LAM t) = (fn (e, (c, e ) :: s) => eval t ((c, e ) :: e, s)) After factorization: eval (LAM t) = (eval t) o grab val grab = (fn (e, (c, e ) :: s) => ((c, e ) :: e, s)) 15 Evaluation function, call-by-name 16

9 Evaluation function, call-by-name Closure convert. Call-by-name CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system. 17 Evaluation function, call-by-name Closure convert. Call-by-name CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system.... Krivine s machine. 18

10 Evaluation function, call-by-value 19 Evaluation function, call-by-value Closure convert. Call-by-value CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system. 20

11 Evaluation function, call-by-value Closure convert. Call-by-value CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system.... CEK machine. 21 Assessment Krivine: the simplest derivation we know of. CEK: new reconstruction. 22

Factorize. Result: compiler and transition system.... CEK machine.

12 Assessment Krivine: the simplest derivation we know of. CEK: new reconstruction. They are two sides of the same coin. 23 Normalization function, call-by-name 24

13 Normalization function, call-by-name Closure convert. Call-by-name CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system. 25 Normalization function, call-by-name Closure convert. Call-by-name CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system.... a generalization of Krivine s machine. 26

25 ... a generalization of Krivine s machine. 26

14 Normalization function, call-by-value 27 Normalization function, call-by-value Closure convert. Call-by-value CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system. 28

15 Normalization function, call-by-value Closure convert. Call-by-value CPS transform. Defunctionalize continuations. Factorize. Result: compiler and transition system.... a generalization of the CEK machine. 29 Assessment Two new virtual machines for strong normalization. Derived rather than discovered or invented. 30

Result: compiler and transition system.... a generalization of the CEK machine.

16 Reynolds, 1972 Self-interpreters depend on the evaluation order of their meta-language. 31 Reynolds, 1972 Self-interpreters depend on the evaluation order of their meta-language. Case in point: Krivine s machine and CEK machine. 32

31 Case in point: Krivine s machine and CEK machine. 32

17 Reynolds, 1972 Self-interpreters depend on the evaluation order of their meta-language. Case in point: Krivine s machine and CEK machine. Well, the same holds for normalization functions. 33 Thank you. 34

BRICS. From Interpreter to Compiler and Virtual Machine: A Functional Derivation

BRICS. From Interpreter to Compiler and Virtual Machine: A Functional Derivation BRICS Basic Research in Computer Science BRICS RS-03-14 Ager et al.: From Interpreter to Compiler and Virtual Machine: A Functional Derivation From Interpreter to Compiler and Virtual Machine: A Functional