On the Expressive Power of Programming Languages 1 Historical - PowerPoint PPT Presentation

On the Expressive Power of Programming Languages 1

Historical Context Control Reduction delimiters DrScheme ( 1997) Parametricity (1983) Semantics ( 1992) ( 1990) This Progress and Revenge of the Son of R3R Scheme Preservation (1994) paper the LISP Machine ( 1999) ( 1986 ) (1991) 2

Historical Context 1991: Writes this 1994: Shriram pivots paper from CompBio after reading it 3

Historical Context 1991: Writes this 1994: Shriram pivots 2010: Essence of 2019: nothing of note. paper from CompBio after JavaScript reading it 4

Expressivity Language L’ 5

Expressivity Constructs F Language L’ Language L 6

Expressivity > Language L Language L’ 7

Expressivity Constructs F 𝜚 (compiler) Language L’ 8

Expressivity Let x = init in body Let x = ref 0 in x++ ( fun x -> body) init Let x = makeBox () in x.setRef(x.getRef + 1) 9

Eliminable Constructs 10

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Let x = init in body 𝜚 ( Let x = init in body) => ( fun x -> 𝜚 (body)) 𝜚 (init) ( fun x -> body) init Eliminable: Example 14

Contextual Equivalence Or Observational Equivalence 15

e1 e2 16

e1 e2 Context C Context C 17

e1 e2 Context C Context C Distinguishing 18 Context

x y C(a) = ( fun x, y -> a) 1 (throw 1) Contextual Equivalence: Example 19

( fun x, y -> x) ( fun x -> x) (throw 1) ( fun x, y -> y) ( fun x -> x) (throw 1) 1 (throw 1) ⊥ Contextual Equivalence: Example 20

Expressivity 21

is expressible in if Constructs F Language L 𝜚 satisfies E1, E2, E3 There is no distinguishing context for F and 𝜚 (F). F is eliminable 22

Macro-expressivity 23

For (init, test, update, body) While (test, body) Macro expressivity: Example 24

For (init, test, update, body) For (init, test, upd, body) => init in While ( 𝜚 (test), 𝜚 (body) ++ 𝜚 (update)) While (test, body) Macro expressivity: Example 25

Polymorphic let Call-by-value STLC Expressive but Macro-inexpressive 26

Polymorphic let Let (x, e, b) => ( fun x -> subst (x, 𝜚 (e), 𝜚 (b))) 𝜚 (e) Call-by-value STLC Expressive! Expressive but Macro-inexpressive 27

AST function, not a syntactic abstraction! Let (x, e, b) => ( fun x -> subst (x, 𝜚 (e), 𝜚 (b))) 𝜚 (e) Recursive macros are not a problem! Macro-based subst implementation will generate scoped macros. subst is truly performing a compile-time computation. Expressive but Macro-inexpressive 28

What do we get? Eliminability (Macro) expressivity 29

What do we get? Eliminability State Continuations Inexpressible (Macro) expressivity Lambda Calculus 30

What do we get? Eliminability State Continuations Bad? (Macro) expressivity Lambda Calculus 31

Case Study 32

Essence of JavaScript * let x = { with (x) { a: 10, a + b + 10 b: 20, } } > 30 > { a: 10, b: 20 } * The Essence of JavaScript (2010); Arjun Guha, Claudiu Saftoiu, and Shriram Krishnamurthi 33

Essence of JavaScript * let x = { with (x) { a: 10, a + b + 10 b: 20, } } > 30 > { a: 10, b: 20 } Lambda Calculus + objects * The Essence of JavaScript (2010); Arjun Guha, Claudiu Saftoiu, and Shriram Krishnamurthi 34

Essence of JavaScript * let x = { with (x) { a: 10, a + b + 10 b: 20, } } > 40 > { a: 10, b: 20 } Not macro expressible Lambda Calculus + objects * The Essence of JavaScript (2010); Arjun Guha, Claudiu Saftoiu, and Shriram Krishnamurthi 35

Thanks! (call/cc (lambda (return) (while (true) (return "Power Overwhelming!")))) 36

Discussion points ● ● Expressivity as a language design Programming languages: isolated principle vs type directed language mathematical formalisms or design. complete ecosystems? ● Why is this not the prevailing way of designing languages? 37