The essence and origins of FRP

Transcription

1 The essence and origins of FRP Conal Elliott June 13, 2015 Conal Elliott The essence and origins of FRP June 13, / 31

2 What is FRP? Conal Elliott The essence and origins of FRP June 13, / 31

3 FRP s two fundamental properties Continuous time. (Natural & composable.) Precise, simple denotation. (Elegant & rigorous.) Conal Elliott The essence and origins of FRP June 13, / 31

4 FRP s two fundamental properties Continuous time. (Natural & composable.) Precise, simple denotation. (Elegant & rigorous.) Deterministic, continuous concurrency. Warning: most modern FRP systems have neither property. Conal Elliott The essence and origins of FRP June 13, / 31

5 Why continuous & infinite (vs discrete/finite) time? Conal Elliott The essence and origins of FRP June 13, / 31

6 Why continuous & infinite (vs discrete/finite) time? Transformation flexibility with simple & precise semantics Quality/accuracy Efficiency (adapative) Modularity/composability: Fewer assumptions, more uses (resolution-independence). More info available for extraction. Same benefits as pure, non-strict functional programming. See Why Functional Programming Matters. Integration and differentiation: natural, accurate, efficient. Reconcile differing input sampling rates. Conal Elliott The essence and origins of FRP June 13, / 31

7 Why continuous & infinite (vs discrete/finite) time? Transformation flexibility with simple & precise semantics Quality/accuracy Efficiency (adapative) Modularity/composability: Fewer assumptions, more uses (resolution-independence). More info available for extraction. Same benefits as pure, non-strict functional programming. See Why Functional Programming Matters. Integration and differentiation: natural, accurate, efficient. Reconcile differing input sampling rates. Same issues as for space, hence vector graphics. Conal Elliott The essence and origins of FRP June 13, / 31

8 Why continuous & infinite (vs discrete/finite) time? Transformation flexibility with simple & precise semantics Quality/accuracy Efficiency (adapative) Modularity/composability: Fewer assumptions, more uses (resolution-independence). More info available for extraction. Same benefits as pure, non-strict functional programming. See Why Functional Programming Matters. Integration and differentiation: natural, accurate, efficient. Reconcile differing input sampling rates. Same issues as for space, hence vector graphics. Principle: Approximations/prunings compose badly, so postpone. Conal Elliott The essence and origins of FRP June 13, / 31

9 Semantics Central abstract type: Behavior a a flow of values. Conal Elliott The essence and origins of FRP June 13, / 31

10 Semantics Central abstract type: Behavior a a flow of values. Precise & simple semantics: µ :: Behavior a Ñ pt Ñ aq where T R (reals). Conal Elliott The essence and origins of FRP June 13, / 31

11 Semantics Central abstract type: Behavior a a flow of values. Precise & simple semantics: µ :: Behavior a Ñ pt Ñ aq where T R (reals). Much of API and its specification follows from this one choice. Conal Elliott The essence and origins of FRP June 13, / 31

12 Original formulation Conal Elliott The essence and origins of FRP June 13, / 31

13 API time :: Behavior T lift 0 :: a Ñ Behavior a lift 1 :: pa Ñ bq Ñ Behavior a Ñ Behavior b lift 2 :: pa Ñ b Ñ cq Ñ Behavior a Ñ Behavior b Ñ Behavior c timetrans :: Behavior a Ñ Behavior T Ñ Behavior a integral :: VS a ñ Behavior a Ñ T Ñ Behavior a... instance Num a ñ Num pbehavior aq where Reactivity later. Conal Elliott The essence and origins of FRP June 13, / 31

14 Semantics µ time λt Ñ t µ plift 0 aq λt Ñ a µ plift 1 f xsq λt Ñ f pµ xs tq µ plift 2 f xs ysq λt Ñ f pµ xs tq pµ ys tq µ ptimetrans xs ttq λt Ñ µ xs pµ tt tq instance Num a ñ Num pbehavior aq where frominteger lift 0 frominteger p`q lift 2 p`q... Conal Elliott The essence and origins of FRP June 13, / 31

15 Semantics µ time id µ plift 0 aq const a µ plift 1 f xsq f µ xs µ plift 2 f xs ysq lifta 2 f pµ xsq pµ ysq µ ptimetrans xs ttq µ xs µ tt instance Num a ñ Num pbehavior aq where frominteger lift 0 frominteger p`q lift 2 p`q... Conal Elliott The essence and origins of FRP June 13, / 31

16 Events Secondary type: µ :: Event a Ñ rpt, aqs -- non-decreasing times never :: Event a once :: T Ñ a Ñ Event a p..q :: Event a Ñ Event a Ñ Event a pùñq :: Event a Ñ pa Ñ bq Ñ Event b predicate :: Behavior Bool Ñ T Ñ Event pq snapshot :: Event a Ñ Behavior b Ñ Event pa, bq Conal Elliott The essence and origins of FRP June 13, / 31

17 Reactivity Reactive behaviors are defined piecewise, via events. Conal Elliott The essence and origins of FRP June 13, / 31

18 Reactivity Reactive behaviors are defined piecewise, via events.: switcher :: Behavior a Ñ Event pbehavior aq Ñ Behavior a Conal Elliott The essence and origins of FRP June 13, / 31

19 Reactivity Reactive behaviors are defined piecewise, via events.: switcher :: Behavior a Ñ Event pbehavior aq Ñ Behavior a Semantics: µ pb 0 switcher eq t µ plast pb 0 : before pµ eq tqq t before :: rpt, aqs Ñ T Ñ ra s before os t ra pt a, aq Ð os, t a ă t s Conal Elliott The essence and origins of FRP June 13, / 31

20 Reactivity Reactive behaviors are defined piecewise, via events.: switcher :: Behavior a Ñ Event pbehavior aq Ñ Behavior a Semantics: µ pb 0 switcher eq t µ plast pb 0 : before pµ eq tqq t before :: rpt, aqs Ñ T Ñ ra s before os t ra pt a, aq Ð os, t a ă t s Question: Can occurrences be extracted ( changes )? Conal Elliott The essence and origins of FRP June 13, / 31

21 Modernized formulation Conal Elliott The essence and origins of FRP June 13, / 31

22 API Replace several operations with standard abstractions: instance Functor Behavior where... instance Applicative Behavior where... instance Monoid a ñ Monoid pbehavior aq where... instance Functor Event where... instance Monoid a ñ Monoid pevent aq where... Less learning, more leverage. Conal Elliott The essence and origins of FRP June 13, / 31

23 Semantic instances instance Functor ppñq z q where... instance Applicative ppñq z q where... instance Monoid a ñ Monoid pz Ñ aq where... instance Num a ñ Num pz Ñ aq where The Behavior instances follow in precise analogy. Conal Elliott The essence and origins of FRP June 13, / 31

24 Homomorphisms A homomorphism h is a function that preserves (distributes over) an algebraic structure. For instance, for Monoid: h ε ε h pas bsq h as h bs Conal Elliott The essence and origins of FRP June 13, / 31

25 Homomorphisms A homomorphism h is a function that preserves (distributes over) an algebraic structure. For instance, for Monoid: h ε ε h pas bsq h as h bs Some monoid homomorphisms: length 1 :: ra s Ñ Sum Int length 1 Sum length log 1 :: Product R Ñ Sum R log 1 Sum log getproduct Conal Elliott The essence and origins of FRP June 13, / 31

26 More homomorphism properties Functor: h pfmap f xsq fmap f ph xsq Applicative: h ppure aq pure a h pfs ă ą xsq h fs ă ą h xs Monad: h pm ą kq h m ą h k Conal Elliott The essence and origins of FRP June 13, / 31

27 Specification by semantic homomorphism Specification: µ as homomorphism. For instance, µ pfmap f asq fmap f pµ asq µ ppure aq pure a µ pfs ă ą xsq µ fs ă ą µ xs Conal Elliott The essence and origins of FRP June 13, / 31

28 Semantic instances instance Monoid a ñ Monoid pz Ñ aq where ε λz Ñ ε f g λz Ñ f z g z instance Functor ppñq z q where fmap g f g f instance Applicative ppñq z q where pure a λz Ñ a ff ă ą fx λz Ñ pff zq pfx zq Conal Elliott The essence and origins of FRP June 13, / 31

29 Semantic homomorphisms Put the pieces together: µ ppure aq pure a µ pfs ă ą xsq µ fs ă ą µ xs λt Ñ a λt Ñ pµ fs tq pµ xs tq Likewise for Functor, Monoid, Num, etc. Conal Elliott The essence and origins of FRP June 13, / 31

30 Semantic homomorphisms Put the pieces together: µ ppure aq pure a µ pfs ă ą xsq µ fs ă ą µ xs λt Ñ a λt Ñ pµ fs tq pµ xs tq Likewise for Functor, Monoid, Num, etc. Notes: Corresponds exactly to the original FRP denotation. Follows inevitably from semantic homomorphism principle. Laws hold for free (already paid for). Conal Elliott The essence and origins of FRP June 13, / 31

31 Laws for free µ ε ε µ pa bq µ a µ b ñ a ε a ε b b a pb cq pa bq c where equality is semantic. Conal Elliott The essence and origins of FRP June 13, / 31

32 Laws for free µ ε ε µ pa bq µ a µ b ñ a ε a ε b b a pb cq pa bq c where equality is semantic. Proofs: µ pa εq µ a µ ε µ a ε µ a µ pε bq µ ε µ b ε µ b µ b µ pa pb cqq µ a pµ b µ cq pµ a µ bq µ c µ ppa bq cq Works for other classes as well. Conal Elliott The essence and origins of FRP June 13, / 31

33 Events newtype Event a Event pbehavior ra sq deriving pmonoid, Functor q -- discretely non-empty Conal Elliott The essence and origins of FRP June 13, / 31

34 Events newtype Event a Event pbehavior ra sq deriving pmonoid, Functor q -- discretely non-empty Derived instances: instance Monoid a ñ Monoid pevent aq where ε Event ppure εq Event u Event v Event plifta 2 p q u vq instance Functor Event where fmap f pevent bq Event pfmap pfmap f q bq Conal Elliott The essence and origins of FRP June 13, / 31

35 Events newtype Event a Event pbehavior ra sq deriving pmonoid, Functor q -- discretely non-empty Derived instances: instance Monoid a ñ Monoid pevent aq where ε Event ppure εq Event u Event v Event plifta 2 p q u vq instance Functor Event where fmap f pevent bq Event pfmap pfmap f q bq Alternatively, type Event Behavior r s Conal Elliott The essence and origins of FRP June 13, / 31

36 Conclusion Two fundamental properties: Continuous time. (Natural & composable.) Precise, simple denotation. (Elegant & rigorous.) Warning: most recent FRP systems lack both. Conal Elliott The essence and origins of FRP June 13, / 31

37 Conclusion Two fundamental properties: Continuous time. (Natural & composable.) Precise, simple denotation. (Elegant & rigorous.) Warning: most recent FRP systems lack both. Semantic homomorphisms: Mine semantic model for API. Inevitable API semantics (minimize invention). Laws hold for free (already paid for). No abstraction leaks. Matches original FRP semantics. Generally useful principle for library design. Conal Elliott The essence and origins of FRP June 13, / 31

38 History Conal Elliott The essence and origins of FRP June 13, / 31

39 at CMU I went for graphics. Did program transformation, FP, type theory. Class in denotational semantics. Conal Elliott The essence and origins of FRP June 13, / 31

40 1989 at CMU Kavi Arya s visit Functional animation Streams of pictures Mostly elegant John Reynolds insight: continuous time. Roughly, You can think of sequences as functions from the natural numbers. Have you thought about functions from the reals instead? Doing so might help with the awkwardness of interpolation. Finished my dissertation anyway. Conal Elliott The essence and origins of FRP June 13, / 31

41 at Sun: TBAG 3D geometry etc as first-class immutable values. Optimizing compiler via partial evaluation. For animation & interaction, immutable functions of time. Multi-way constraints on time-functions. Differentiation, integration and ODEs specified via derivative. Adaptive Runge-Kutta-5 solver (fast & accurate). Efficient multi-user distributed execution for free. Reactivity via assert/retract (high-level but imperative). In Common Lisp, C++, Scheme. Conal Elliott The essence and origins of FRP June 13, / 31

42 at MSR: RBML/ActiveVRML Programming model & fast implementation for new 3D hardware. TBAG + denotative/functional reactivity. Add event algebra to behavior algebra. Reactivity via behavior-valued events. Drop multi-way constraints at first. Started in ML as RBML. Rebranded to ActiveVRML, then DirectAnimation. Conal Elliott The essence and origins of FRP June 13, / 31

43 at MSR: RBMH/Fran Found Haskell: reborn as RBMH (research vehicle). Very fast implementation via sprite engine. John Hughes suggested using Arrow. Conal Elliott The essence and origins of FRP June 13, / 31

44 2000 at MSR: first try at push-based implementation Algebra of imperative event listeners. Challenges: Garbage collection & dependency reversal. Determinacy of timing & simultaneity. I doubt anyone has gotten correct. Conal Elliott The essence and origins of FRP June 13, / 31

45 2009: Push-pull FRP Minimal computation, low latency, provably correct. Push for reactivity and pull for continuous phases. Push is really blocked pull. Modernized API: Standard abstractions. Semantics as homomorphisms. Laws for free. Reactive normal form, via equational properties (denotation!). Uses lub (basis of PL semantics). Implementation subtleties & GHC RTS bugs. Didn t quite work. Conal Elliott The essence and origins of FRP June 13, / 31

46 : Paul Hudak / Yale Paul Hudak visited MSR in 1996 or so and saw RBMH. Encouraged me to publish and suggested collaboration. Proposed names Fran & FRP. Many FRP-based papers and theses, drawing much attention. July 15, 1952 April 29, 2015 Conal Elliott The essence and origins of FRP June 13, / 31