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module Encoded.Container
import Encoded.Arith
import Encoded.Bool
import Encoded.Fin
import Encoded.Pair
import Encoded.Sum
import Encoded.Vect
import Term.Syntax
%ambiguity_depth 4
%prefix_record_projections off
public export
Case : Type
Case = (Maybe Ty, Nat)
public export
record Container where
constructor Cases
constructors : SnocList Case
{auto 0 ok : NonEmpty constructors}
%name Container c
public export
semCase : Case -> Ty -> Ty
semCase (Just tag, k) ty = tag * Vect k ty
semCase (Nothing, k) ty = Vect k ty
public export
sem : Container -> Ty -> Ty
sem c ty = Sum (map (flip semCase ty) c.constructors) @{mapNonEmpty c.ok}
unitCase : Case -> Ty
unitCase (Just tag, k) = tag
unitCase (Nothing, k) = N
unitSem : Container -> Ty
unitSem c = Sum (map unitCase c.constructors) @{mapNonEmpty c.ok}
dmapCase :
{c : Case} ->
{ty, ty' : Ty} ->
Term ((Fin (snd c) ~> ty ~> ty') ~> semCase c ty ~> semCase c ty') ctx
dmapCase {c = (Just tag, k)} = Abs' (\f => App (mapSnd . dmap) [<f])
dmapCase {c = (Nothing, k)} = dmap
forgetCase : {c : Case} -> {ty : Ty} -> Term (semCase c ty ~> unitCase c) ctx
forgetCase {c = (Just tag, k)} = fst
forgetCase {c = (Nothing, k)} = Arb
recurse : {c : Case} -> {ty : Ty} -> Term (semCase c ty ~> Vect (snd c) ty) ctx
recurse {c = (Just tag, k)} = snd
recurse {c = (Nothing, k)} = Id
export
W : Container -> Ty
W c = N * (N ~> N * N) * (N ~> unitSem c)
-- ^ ^ ^- data
-- | + index mapping function: each index has a different base and stride
-- +- pred(fuel) for induction
fuel : {c : Container} -> Term (W c ~> N) ctx
fuel = fst . fst
offset : {c : Container} -> Term (W c ~> N ~> N * N) ctx
offset = snd . fst
vals : {c : Container} -> Term (W c ~> N ~> unitSem c) ctx
vals = snd
-- Adds a value to the start of a stream
cons : {ty : Ty} -> Term (ty ~> (N ~> ty) ~> (N ~> ty)) ctx
cons = Abs $ Abs $ Abs $
let x = Var (There $ There Here) in
let xs = Var (There Here) in
let n = Var Here in
App rec [<n, x, xs . fst]
-- Calculates total fuel for a new W value.
getFuel :
{cont : Container} ->
{c : Case} ->
Term (semCase c (W cont) ~> N) ctx
getFuel {c = (tag, k)} = App foldr [<Zero, plus] . App map [<Abs' Suc . fuel] . recurse
-- Updates the base and stride for a single recursive position.
-- These are multiplexed later.
stepOffset : {k : Nat} -> Term (Fin k ~> (N ~> N * N) ~> (N ~> N * N)) ctx
stepOffset = Abs $ Abs $ Abs $
let i = Var (There $ There Here) in
let f = Var (There Here) in
let x = Var Here in
App bimap
-- Suc is for the initial tag
[<App (plus . forget . suc) [<i] . App mult [<Lit k]
, App mult [<Lit k]
, App f [<x]
]
-- Calculates all offsets for a new W value.
getOffset :
{cont : Container} ->
{c : Case} ->
Term (semCase c (W cont) ~> N ~> N * N) ctx
getOffset {c = (tag, 0)} = Const $ Const $ App pair [<Lit 1, Zero]
getOffset {c = (tag, k@(S _))} = Abs' (\x =>
App cons
[<App pair [<Lit 1, Zero]
, Abs' (\n =>
let dm = App (divmod' k) [<n] in
let div = App fst [<dm] in
let mod = App snd [<dm] in
App stepOffset [<mod, App offset [<App (index . recurse) [<shift x, mod]], div])
])
-- Calculates data map for a new W value.
getVals :
{cont : Container} ->
{c : Case} ->
(i : Elem c cont.constructors) ->
Term (semCase c (W cont) ~> N ~> unitSem cont) ctx
getVals i {c = (tag', 0)} =
Abs' (\x => Const $ App (tag @{mapNonEmpty cont.ok} (elemMap unitCase i) . forgetCase) [<x])
getVals i {c = (tag', k@(S _))} = Abs' (\x =>
App Container.cons
[<App (tag @{mapNonEmpty cont.ok} (elemMap unitCase i) . forgetCase) [<x]
, Abs' (\n =>
let dm = App (divmod' k) [<n] in
let div = App fst [<dm] in
let mod = App snd [<dm] in
App vals [<App (index . recurse) [<shift x, mod], div])
])
-- Constructs a value for a specific constructor
introCase :
{cont : Container} ->
{c : Case} ->
(i : Elem c cont.constructors) ->
Term (semCase c (W cont) ~> W cont) ctx
introCase i = Abs' (\x =>
App pair [<App pair [<App getFuel [<x], App getOffset [<x]], App (getVals i) [<x]])
gtabulate : {sx : SnocList a} -> ({x : a} -> Elem x sx -> p (f x)) -> All p (map f sx)
gtabulate {sx = [<]} g = [<]
gtabulate {sx = sx :< x} g = gtabulate (g . There) :< g Here
export
intro : {c : Container} -> Term (sem c (W c) ~> W c) ctx
intro =
App (any @{mapNonEmpty c.ok}) {sty = map (~> W c) $ map (flip semCase (W c)) c.constructors} $
rewrite mapFusion (~> W c) (flip semCase (W c)) c.constructors in
gtabulate introCase
calcIndex : Term (N * N ~> N ~> N) ctx
calcIndex = Abs' (\bs => App (plus . fst) [<bs] . App (mult . snd) [<bs])
fillCase :
{c : Case} ->
{ty : Ty} ->
Term ((Fin (snd c) ~> ty) ~> (semCase c ty ~> ty) ~> unitCase c ~> ty) ctx
fillCase {c = (Just tag, k)} = Abs $ Abs $ Abs $
let f = Var (There $ There Here) in
let sem = Var (There Here) in
let val = Var Here in
App sem [<App pair [<val, App tabulate [<f]]]
fillCase {c = (Nothing, k)} =
Abs $ Abs $ Const $
let f = Var (There Here) in
let sem = Var Here in
App (sem . tabulate) [<f]
elimStep :
{c : Container} ->
{ty : Ty} ->
Term
(map (\c => semCase c ty ~> ty) c.constructors ~>*
(N ~> N * N) ~>
(N ~> unitSem c) ~>
(N ~> ty) ~>
(N ~> ty))
ctx
elimStep = AbsAll (_ :< _ :< _ :< _ :< _)
(\(fs :< offsets :< vals :< rec :< n) =>
let val = App vals [<n] in
let offset = App offsets [<n] in
App (any @{mapNonEmpty c.ok}) {sty = map (~> ty) (map unitCase c.constructors) :< unitSem c} $
rewrite mapFusion (~> ty) unitCase c.constructors in
gtabulate (\i =>
Syntax.App fillCase
[<rec . App calcIndex [<offset] . forget
, indexAll (elemMap (\c => semCase c ty ~> ty) i) fs
]) :<
val)
export
elim :
{c : Container} ->
{ty : Ty} ->
Term (map (\c => semCase c ty ~> ty) c.constructors ~>* W c ~> ty) ctx
elim = AbsAll (_ :< _)
(\(fs :< x) =>
App
(Rec (App fuel [<x])
Arb
(App elimStep (fs :< App offset [<x] :< App vals [<x])))
[<Zero])
|
