From b2d0b395695b65c284dc042f77253f2827ab4009 Mon Sep 17 00:00:00 2001
From: Chloe Brown <chloe.brown.00@outlook.com>
Date: Mon, 22 Jan 2024 12:13:39 +0000
Subject: Add test driver.

---
 src/Encoded/Term.idr | 342 +++++++++++++++++++++++++++++++++++++++++++++++++++
 src/Encoded/Test.idr | 116 +++++++++++++++++
 2 files changed, 458 insertions(+)
 create mode 100644 src/Encoded/Term.idr
 create mode 100644 src/Encoded/Test.idr

(limited to 'src')

diff --git a/src/Encoded/Term.idr b/src/Encoded/Term.idr
new file mode 100644
index 0000000..4f69c84
--- /dev/null
+++ b/src/Encoded/Term.idr
@@ -0,0 +1,342 @@
+module Encoded.Term
+
+import Data.Vect
+
+import Encoded.Bool
+import Encoded.Container
+import Encoded.Pair
+import Encoded.Sum
+import Encoded.Vect
+
+import Term.Syntax
+
+%ambiguity_depth 6
+%prefix_record_projections off
+
+-- Utilities ----------------------
+
+rec : Nat -> a -> (a -> a) -> a
+rec 0 z s = z
+rec (S k) z s = s (rec k z s)
+
+AppVect :
+  forall ctx.
+  {ty, ty' : Ty} ->
+  Term (rec k ty' (ty ~>)) ctx ->
+  Vect k (Term ty ctx) ->
+  Term ty' ctx
+AppVect f [] = f
+AppVect f (t :: ts) = AppVect (App f t) ts
+
+-- Definition ------------------------------------------------------------------
+
+TermC : Container
+TermC = Cases
+  [<(Just N, 0)  -- Var
+  , (Nothing, 0) -- Zero
+  , (Nothing, 1) -- Suc
+  , (Nothing, 3) -- Rec
+  , (Nothing, 1) -- Abs
+  , (Nothing, 2) -- App
+  ]
+
+export
+Term : Ty
+Term = W TermC
+
+-- Smart Constructors ----------------------------------------------------------
+
+export
+Var : Term (N ~> Term) ctx
+Var =
+  let i = There $ There $ There $ There $ There Here in
+  Abs' (\n => App (intro {c = TermC} . tag i) [<App pair [<n, nil]])
+
+export
+Zero : Term Term ctx
+Zero =
+  let i = There $ There $ There $ There Here in
+  App (intro {c = TermC} . tag i) [<nil]
+
+export
+Suc : Term (Term ~> Term) ctx
+Suc =
+  let i = There $ There $ There Here in
+  Abs' (\t => App (intro {c = TermC} . tag i) [<fromVect [t]])
+
+export
+Rec : Term (Term ~> Term ~> Term ~> Term) ctx
+Rec =
+  let i = There $ There Here in
+  AbsAll [<_,_,_] (\[<t, u, v] => App (intro {c = TermC} . tag i) [<fromVect [t, u, v]])
+
+export
+Abs : Term (Term ~> Term) ctx
+Abs =
+  let i = There Here in
+  Abs' (\t => App (intro {c = TermC} . tag i) [<fromVect [t]])
+
+export
+App : Term (Term ~> Term ~> Term) ctx
+App =
+  let i = Here in
+  AbsAll [<_,_] (\[<t, u] => App (intro {c = TermC} . tag i) [<fromVect [t, u]])
+
+-- Initiality ------------------------------------------------------------------
+
+public export
+EliminatorTy : Ty -> Ty
+EliminatorTy ty =
+  (N ~> ty) *
+  (ty) *
+  (ty ~> ty) *
+  (ty ~> ty ~> ty ~> ty) *
+  (ty ~> ty) *
+  (ty ~> ty ~> ty)
+
+public export
+record Eliminator (ty : Ty) (ctx : SnocList Ty) where
+  constructor MkElim
+  var : Term (N ~> ty) ctx
+  zero : Term ty ctx
+  suc : Term (ty ~> ty) ctx
+  rec : Term (ty ~> ty ~> ty ~> ty) ctx
+  abs : Term (ty ~> ty) ctx
+  app : Term (ty ~> ty ~> ty) ctx
+
+%name Eliminator elim
+
+export
+unpack : {ty : Ty} -> Term (EliminatorTy ty) ctx -> Eliminator ty ctx
+unpack t =
+  MkElim
+    { var = App (fst . fst . fst . fst . fst) [<t]
+    , zero = App (snd . fst . fst . fst . fst) [<t]
+    , suc = App (snd . fst . fst . fst) [<t]
+    , rec = App (snd . fst . fst) [<t]
+    , abs = App (snd . fst) [<t]
+    , app = App snd [<t]
+    }
+
+export
+pack : {ty : Ty} -> Eliminator ty ctx -> Term (EliminatorTy ty) ctx
+pack elim =
+  App pair
+  [<App pair
+  [<App pair
+  [<App pair
+  [<App pair
+  [<elim.var
+  , elim.zero]
+  , elim.suc]
+  , elim.rec]
+  , elim.abs]
+  , elim.app]
+
+export
+Elim : {ty : Ty} -> Term (EliminatorTy ty ~> Term ~> ty) ctx
+Elim = Abs' (\e =>
+  let el = unpack e in
+  App (elim {c = TermC})
+    [<el.var . fst
+    , Const el.zero
+    , Abs' (\v => AppVect (shift el.suc) (toVect v))
+    , Abs' (\v => AppVect (shift el.rec) (toVect v))
+    , Abs' (\v => AppVect (shift el.abs) (toVect v))
+    , Abs' (\v => AppVect (shift el.app) (toVect v))
+    ])
+  where
+
+public export
+DiscriminatorTy : Ty -> Ty
+DiscriminatorTy ty =
+  (N ~> ty) *
+  (ty) *
+  (Term ~> ty) *
+  (Term ~> Term ~> Term ~> ty) *
+  (Term ~> ty) *
+  (Term ~> Term ~> ty)
+
+public export
+record Discriminator (ty : Ty) (ctx : SnocList Ty) where
+  constructor MkDiscrim
+  var : Term (N ~> ty) ctx
+  zero : Term ty ctx
+  suc : Term (Term ~> ty) ctx
+  rec : Term (Term ~> Term ~> Term ~> ty) ctx
+  abs : Term (Term ~> ty) ctx
+  app : Term (Term ~> Term ~> ty) ctx
+
+%name Eliminator elim
+
+export
+unpackDisc : {ty : Ty} -> Term (DiscriminatorTy ty) ctx -> Discriminator ty ctx
+unpackDisc t =
+  MkDiscrim
+    { var = App (fst . fst . fst . fst . fst) [<t]
+    , zero = App (snd . fst . fst . fst . fst) [<t]
+    , suc = App (snd . fst . fst . fst) [<t]
+    , rec = App (snd . fst . fst) [<t]
+    , abs = App (snd . fst) [<t]
+    , app = App snd [<t]
+    }
+
+export
+packDisc : {ty : Ty} -> Discriminator ty ctx -> Term (DiscriminatorTy ty) ctx
+packDisc elim =
+  App pair
+  [<App pair
+  [<App pair
+  [<App pair
+  [<App pair
+  [<elim.var
+  , elim.zero]
+  , elim.suc]
+  , elim.rec]
+  , elim.abs]
+  , elim.app]
+
+export
+Inspect : {ty : Ty} -> Term (DiscriminatorTy ty ~> Term ~> ty) ctx
+Inspect = Abs' (\e =>
+  let el = unpackDisc e in
+  App (inspect {c = TermC})
+    [<el.var . fst
+    , Const el.zero
+    , Abs' (\v => AppVect (shift el.suc) (toVect v))
+    , Abs' (\v => AppVect (shift el.rec) (toVect v))
+    , Abs' (\v => AppVect (shift el.abs) (toVect v))
+    , Abs' (\v => AppVect (shift el.app) (toVect v))
+    ])
+
+-- Weakening -------------------------------------------------------------------
+
+liftNat : Term ((N ~> N) ~> (N ~> N)) ctx
+liftNat = AbsAll [<_,_] (\[<f, n] => App if' [<App isZero [<n], 0, Suc (App f [<n])])
+
+WeakenElim : Eliminator ((N ~> N) ~> Term) ctx
+WeakenElim =
+  MkElim
+    { var = AbsAll [<_,_] (\[<i, f] => App (Var . f) [<i])
+    , zero = Const Zero
+    , suc = Abs' (\t => Suc . t)
+    , rec = AbsAll [<_,_,_,_] (\[<t, u, v, f] => App Rec [<App t [<f], App u [<f], App v [<f]])
+    , abs = Abs' (\t => Abs . t . liftNat)
+    , app = AbsAll [<_,_,_] (\[<t, u, f] => App App [<App t [<f], App u [<f]])
+    }
+
+export
+weaken : Term ((N ~> N) ~> Term ~> Term) ctx
+weaken = AbsAll [<_,_] (\[<f, t] => App Elim [<pack WeakenElim, t, f])
+
+liftTerm : Term ((N ~> Term) ~> (N ~> Term)) ctx
+liftTerm = AbsAll [<_,_] (\[<f, n] =>
+  App if'
+    [<App isZero [<n]
+    , App Var [<0]
+    , App weaken [<Op Suc, App f [<n]]])
+
+-- Substitution ----------------------------------------------------------------
+
+SubstElim : Eliminator ((N ~> Term) ~> Term) ctx
+SubstElim =
+  MkElim
+    { var = AbsAll [<_,_] (\[<i, f] => App f [<i])
+    , zero = Const Zero
+    , suc = Abs' (\t => Suc . t)
+    , rec = AbsAll [<_,_,_,_] (\[<t, u, v, f] => App Rec [<App t [<f], App u [<f], App v [<f]])
+    , abs = Abs' (\t => Abs . t . liftTerm)
+    , app = AbsAll [<_,_,_] (\[<t, u, f] => App App [<App t [<f], App u [<f]])
+    }
+
+export
+subst : Term ((N ~> Term) ~> Term ~> Term) ctx
+subst = AbsAll [<_,_] (\[<f, t] => App Elim [<pack SubstElim, t, f])
+
+-- Reduction -------------------------------------------------------------------
+
+-- Performs an application step.
+-- Arguments are whether inspected term stepped, and argument term
+AppDisc : Discriminator (Term ~> B ~> Term * B) ctx
+AppDisc =
+  MkDiscrim
+    { var = fallthrough . Var
+    , zero = App fallthrough [<Zero]
+    , suc = fallthrough . Suc
+    , rec = AbsAll [<_,_,_] (\[<t, u, v] => App fallthrough [<App Rec [<t, u, v]])
+    , abs = AbsAll [<_,_,_] (\[<t, u, b] =>
+      App pair
+        [<App subst
+          [<Abs' (\n => App if' [<App isZero [<n], shift t, App Var [<pred n]])
+          , u
+          ]
+        , True
+        ])
+    , app = AbsAll [<_,_] (\[<t, u] => App fallthrough [<App App [<t, u]])
+    }
+  where
+  fallthrough : forall ctx. Term (Term ~> Term ~> B ~> Term * B) ctx
+  fallthrough =
+    AbsAll [<_,_,_] (\[<t, u, b] =>
+      App pair
+        [<App App [<t, u]
+        , b
+        ])
+
+RecDisc : Discriminator (Term ~> Term ~> B ~> Term * B) ctx
+RecDisc =
+  MkDiscrim
+    { var = fallthrough . Var
+    , zero = AbsAll [<_,_,_] (\[<u, v, b] =>
+      App pair [<u, True])
+    , suc = AbsAll [<_,_,_,_] (\[<t, u, v, b] =>
+      App pair
+        [<App App [<v, App Rec [<t, u, v]]
+        , True
+        ])
+    , rec = AbsAll [<_,_,_] (\[<t, u, v] => App fallthrough [<App Rec [<t, u, v]])
+    , abs = fallthrough . Abs
+    , app = AbsAll [<_,_] (\[<t, u] => App fallthrough [<App App [<t, u]])
+    }
+  where
+  fallthrough : forall ctx. Term (Term ~> Term ~> Term ~> B ~> Term * B) ctx
+  fallthrough =
+    AbsAll [<_,_,_,_] (\[<t, u, v, b] =>
+      App pair
+        [<App Rec [<t, u, v]
+        , b
+        ])
+
+StepElim : Eliminator (Term * B) ctx
+StepElim =
+  MkElim
+    { var = Abs' (\i => App pair [<App Var [<i], False])
+    , zero = App pair [<Term.Zero, False]
+    , suc = App mapFst [<Suc]
+    , rec = AbsAll [<_,_,_] (\[<t, u, v] =>
+      App Inspect
+        [<packDisc RecDisc
+        , App fst [<t]
+        , App fst [<u]
+        , App fst [<v]
+        , App or [<App snd t, App or [<App snd u, App snd v]]
+        ])
+    , abs = App mapFst [<Abs]
+    , app = AbsAll [<_,_] (\[<t, u] =>
+      App Inspect
+        [<packDisc AppDisc
+        , App fst [<t]
+        , App fst [<u]
+        , App or [<App snd [<t], App snd [<u]]
+        ])
+    }
+
+export
+reduce : Term (N ~> Term ~> Term) ctx
+reduce = Abs' (\n =>
+  Rec n
+    Id
+    (Abs' (\rec =>
+      (Abs' {ty = Term * B} (\ub =>
+        App if' [<App snd [<ub], App (shift rec) [<App fst [<ub]], App fst [<ub]])) .
+      (App Elim [<pack StepElim]))))
diff --git a/src/Encoded/Test.idr b/src/Encoded/Test.idr
new file mode 100644
index 0000000..ad6e114
--- /dev/null
+++ b/src/Encoded/Test.idr
@@ -0,0 +1,116 @@
+module Encoded.Test
+
+import Data.Stream
+import Data.String
+
+import Encoded.Arith
+import Encoded.Container
+import Encoded.Fin
+import Encoded.Pair
+import Encoded.Sum
+import Encoded.Term
+import Encoded.Vect
+
+import System
+
+import Term.Compile
+import Term.Pretty
+import Term.Syntax
+import Term.Semantics
+
+%ambiguity_depth 4
+
+-- ListC : Ty -> Container
+-- ListC ty = Cases [<(Nothing, 0), (Just ty, 1)]
+
+-- List : Ty -> Ty
+-- List = W . ListC
+
+-- nil : {ty : Ty} -> Term (List ty) ctx
+-- nil = App (intro . tag (There Here)) [<Vect.nil {ty = List ty}]
+
+-- cons : {ty : Ty} -> Term (ty ~> List ty ~> List ty) ctx
+-- cons = AbsAll [<_, _] (\[<x, xs] =>
+--   App (intro . tag @{IsSnoc} Here) [<App pair [<x, App Vect.cons [<xs, Vect.nil]]])
+
+-- sum : Term (List N ~> N) ctx
+-- sum = App (elim {c = ListC N})
+--   [<Const 0
+--   , Abs' (\x => App fst x + App index [<App snd [<x], zero])
+--   ]
+
+-- fromList' : List Nat -> Term (List N) [<List N, N ~> List N ~> List N]
+-- fromList' [] = Var (There Here)
+-- fromList' (x :: xs) = App (Var Here) [<Op (Lit x), fromList' xs]
+
+-- fromList : List Nat -> Term (List N) [<]
+-- fromList xs = App (Abs $ Abs $ fromList' xs) [<Test.nil, Test.cons]
+
+%inline
+layoutOptions : LayoutOptions
+layoutOptions = MkLayoutOptions (AvailablePerLine 213 0.5)
+
+data Mode = Color | NoColor | FastCompile | Compile | Profile
+
+%inline
+render : Len ctx => Mode -> Term ty ctx -> IO ()
+render Color t =
+  renderIO $
+  layoutSmart layoutOptions $ prettyTerm t
+render NoColor t =
+  putStrLn $
+  renderShow (layoutSmart layoutOptions $ prettyTerm {ann = ()} t) ""
+render _ t = pure ()
+
+run : Show (TypeOf ty) => Len ctx => Mode -> Term ty ctx -> All TypeOf ctx -> IO ()
+run FastCompile t args =
+  putStrLn $
+  renderShow (layoutCompact $ compileTerm {ann = ()} Run t) ""
+run Compile t args =
+  putStrLn $
+  renderShow (layoutSmart layoutOptions $ compileTerm {ann = ()} Run t) ""
+run Profile t args =
+  putStrLn $
+  renderShow (layoutSmart layoutOptions $ compileTerm {ann = ()} Profile t) ""
+run _ t args = printLn (sem t args)
+
+parseArgs : List String -> IO (Mode, Bool, Nat, Nat)
+parseArgs [_, "--color", k, n] = pure (Color, True, stringToNatOrZ k, stringToNatOrZ n)
+parseArgs [_, "--no-color", k, n] = pure (NoColor, True, stringToNatOrZ k, stringToNatOrZ n)
+parseArgs [_, "--fast-compile", k, n] = pure (FastCompile, False, stringToNatOrZ k, stringToNatOrZ n)
+parseArgs [_, "--compile", k, n] = pure (Compile, False, stringToNatOrZ k, stringToNatOrZ n)
+parseArgs [_, "--profile", k, n] = pure (Profile, False, stringToNatOrZ k, stringToNatOrZ n)
+parseArgs [_, k, n] = pure (Color, False, stringToNatOrZ k, stringToNatOrZ n)
+parseArgs _ = do putStrLn "Bad arguments"; exitFailure
+
+lit : Term (N ~> Term) ctx
+lit = Abs' (\n => Rec n Zero Suc)
+
+add : Term (N ~> N ~> Term) ctx
+add = AbsAll [<_,_] (\[<k, n] =>
+  App Rec [<App lit [<k], App lit [<n], App (Abs . Suc . Var) [<0]])
+
+AssumeNat : Eliminator N ctx
+AssumeNat =
+  MkElim
+    { var = Arb
+    , zero = 0
+    , suc = Op Suc
+    , rec = Arb
+    , abs = Arb
+    , app = Arb
+    }
+
+main : IO ()
+main = do
+  args <- getArgs
+  (mode, print, k, n) <- parseArgs args
+  let t : Term Term [<] = App add [<Op (Lit k), Op (Lit n)]
+  let t : Term Term [<] = App reduce [<4096, t]
+  if print then render mode t else pure ()
+  let t : Term N [<] = App Elim [<pack AssumeNat, t]
+  run mode t [<]
+
+  -- let ns = take n nats
+  -- let t : Term (List N) [<] = fromList ns
+  -- let t : Term N [<] = App sum [<t]
-- 
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