Fix RHole, add test files, papers, piforall examples

newt/Fix.newt

@@ -0,0 +1,50 @@
+module Fix
+
+-- from piforall Fix.pi
+Type: U
+Type = U
+
+-- TODO piforall makes the A in scope for the constructors
+-- and has it on the let of the :
+-- I think we want that for parameters?
+data D : (A : Type) -> Type where
+  F : {A : Type} -> (D A -> D A) -> D A
+  V : {A : Type} -> A -> D A
+
+
+-- Here we have two A in play, so y is type of the
+-- A in V and the expected return value is the other.
+-- We do need to sort this out
+
+unV : { A : U} -> D A -> A
+unV = \ v => case v of
+  V y => ?  -- y
+ --  F f => TRUSTME
+
+-- And here we have D A:4 and D A:1
+unF : {A : Type} -> D A -> D A -> D A
+unF = \ {A} v x =>
+  case v of
+    F {A} f => ? -- f x
+    -- V y => TRUSTME
+
+-- fix : {A : U} -> (A -> A) -> A
+-- fix = \ {A} g =>
+--   -- RLet is not yet implemented...
+--   let omega = -- : D A -> D A =
+--         (\ x => V (g (unv {A} (unF {A} x x))))
+--   in unV {A} (omega (F omega))
+
+-- data Nat : Type where
+--    Zero : Nat
+--    Succ : Nat -> Nat
+
+-- fix_add : Nat -> Nat -> Nat
+-- fix_add = fix [Nat -> Nat -> Nat]
+--         \radd. \x. \y.
+--             case x of
+--               Zero   -> y
+--               Succ n -> Succ (radd n y)
+
+-- test : fix_add 5 2 = 7
+-- test = Refl

newt/testcase.newt

@@ -1,5 +1,10 @@
 module Scratch
 
+-- I'm testing cases here, but using examples carefully design to be
+-- simple case trees. Patterns are a var or a constructor applied to vars.
+
+-- There are indexes below, but we're got pulling constraints out of them yet.
+
 data Nat : U where
   Z : Nat
   S : Nat -> Nat

newt/testprim.newt

@@ -0,0 +1,43 @@
+module TestPrim
+
+
+-- we need to be able to declare a primitive type
+-- distinct from inductive type. there are no constructors per-se but it is inhabited
+
+ptype String
+ptype Int
+
+pfunc strlen : String -> Int := "(x) => x.length()"
+
+-- why is there an eta in here?
+foo : String -> Int
+foo = \ x => strlen x
+
+bar : String -> String -> Int
+bar = \ x y => strlen x
+
+pfunc append : String -> String -> String := "(a,b) => a + b"
+
+blah : String
+blah = append "hello" "world"
+
+pfunc plus : Int -> Int -> Int := "(a,b) => a + b"
+
+answer : Int
+answer = plus 40 2
+
+-- I'd like to define prim operators too
+
+-- codegen test cases
+-- works, but two looks like () => (eta1) => (eta0) => one(eta1, eta0)
+pfunc one : Int -> Int -> Int := "(x,y) => x + y"
+
+two : Int -> Int -> Int
+two = one
+
+three : Int -> Int -> Int
+three = \ x => two x
+
+four : Int -> Int -> Int
+four = \x y => three x y
+