From fca3750d46832e2bf1d94ccb2997c0a86ef706a4 Mon Sep 17 00:00:00 2001
From: Robert Sloan <varomodt@gmail.com>
Date: Sun, 19 Jun 2016 00:08:11 -0400
Subject: Decent machinery for automatic pseudo-conversion

---
 src/Assembly/Pseudize.v | 101 ++++++++++++++++++++++++++++++++++++++----------
 src/Assembly/State.v    |   5 ++-
 2 files changed, 85 insertions(+), 21 deletions(-)

(limited to 'src/Assembly')

diff --git a/src/Assembly/Pseudize.v b/src/Assembly/Pseudize.v
index af234fdb3..d1f872eaf 100644
--- a/src/Assembly/Pseudize.v
+++ b/src/Assembly/Pseudize.v
@@ -1,13 +1,13 @@
 Require Export Bedrock.Word Bedrock.Nomega.
 Require Import NArith NPeano List Sumbool.
-Require Import QhasmCommon QhasmUtil Pseudo State Wordize.
+Require Import QhasmCommon QhasmEvalCommon QhasmUtil Pseudo State.
+Require Export Wordize Vectorize.
 
 Module Conversion.
-  Import Pseudo ListNotations StateCommon.
+  Import Pseudo ListNotations StateCommon EvalUtil ListState.
 
-  Hint Unfold ListState.setList ListState.getList ListState.getVar
-       ListState.setCarry ListState.setCarryOpt ListState.getCarry
-       ListState.getMem ListState.setMem overflows.
+  Hint Unfold setList getList getVar setCarry setCarryOpt getCarry
+       getMem setMem overflows.
 
   Lemma pseudo_var: forall {w s n} x k v b p m c,
       nth_error x k = Some v
@@ -22,7 +22,7 @@ Module Conversion.
     -> pseudoEval (@PMem w s n len (indexize _ p0 name) (indexize _ p1 index)) (x, m, c) = Some ([v], m, c).
   Proof.
     intros; autounfold; simpl.
-    unfold ListState.getMem; simpl.
+    unfold getMem; simpl.
     rewrite H; autounfold; simpl.
     rewrite NToWord_wordToN; intuition.
   Qed.
@@ -46,26 +46,37 @@ Module Conversion.
       try rewrite NToWord_wordToN; intuition.
   Qed.
 
-  Lemma pseudo_plus:
+  Lemma pseudo_bin:
     forall {w s n} (p: @Pseudo w s n 2) x out0 out1 m0 m1 c0 c1 op,
-      op ⋄ Add
-    → pseudoEval p (x, m0, c0) = Some ([out0; out1], m1, c1)
-    → pseudoEval (PBin n op p) (x, m0, c0) =
-        Some ([out0 ^+ out1], m1,
-          Some (proj1_sig (bool_of_sumbool (overflows out0 out1)))).
+      op <> Add
+    -> pseudoEval p (x, m0, c0) = Some ([out0; out1], m1, c1)
+    -> pseudoEval (PBin n op p) (x, m0, c0) =
+        Some ([fst (evalIntOp op out0 out1)], m1, c1).
   Proof.
-    intros; simpl; rewrite H; simpl.
+    intros; simpl; rewrite H0; simpl.
 
-    pose proof (wordize_plus out0 out1).
-    destruct (overflows out0 out1); autounfold; simpl; try rewrite H0;
-      try rewrite <- (@Npow2_ignore w (out0 ^+ out1));
-      try rewrite NToWord_wordToN; intuition.
+    induction op;
+      try (contradict H; reflexivity);
+      unfold evalIntOp; autounfold; simpl;
+      reflexivity.
+  Qed.
+
+  Lemma pseudo_and:
+    forall {w s n} (p: @Pseudo w s n 2) x out0 out1 m0 m1 c0 c1,
+      pseudoEval p (x, m0, c0) = Some ([out0; out1], m1, c1)
+    -> pseudoEval (PBin n And p) (x, m0, c0) =
+        Some ([out0 ^& out1], m1, c1).
+  Proof.
+    intros.
+    replace (out0 ^& out1) with (fst (evalIntOp And out0 out1)).
+    - apply pseudo_bin; intuition; inversion H0.
+    - unfold evalIntOp; simpl; intuition.
   Qed.
 
   Lemma pseudo_comb:
     forall {w s n a b} (p0: @Pseudo w s n a) (p1: @Pseudo w s n b)
       input out0 out1 m0 m1 m2 c0 c1 c2,
-       pseudoEval p0 (input, m0, c0) = Some (out0, m1, c1)
+      pseudoEval p0 (input, m0, c0) = Some (out0, m1, c1)
     -> pseudoEval p1 (input, m1, c1) = Some (out1, m2, c2)
     -> pseudoEval (@PComb w s n _ _ p0 p1) (input, m0, c0) =
         Some (out0 ++ out1, m2, c2).
@@ -75,9 +86,59 @@ Module Conversion.
     rewrite H0; autounfold; simpl; intuition.
   Qed.
 
-  Program Definition ex0: Program Unary32 := ($0 :-: $0)%p.
+  Lemma pseudo_cons:
+    forall {w s n b} (p0: @Pseudo w s n 1) (p1: @Pseudo w s n b)
+        (p2: @Pseudo w s n (S b)) input x xs m0 m1 m2 c0 c1 c2,
+      pseudoEval p0 (input, m0, c0) = Some ([x], m1, c1)
+    -> pseudoEval p1 (input, m1, c1) = Some (xs, m2, c2)
+    -> p2 = (@PComb w s n _ _ p0 p1)
+    -> pseudoEval p2 (input, m0, c0) = Some (x :: xs, m2, c2).
+  Proof.
+    intros.
+    replace (x :: xs) with ([x] ++ xs) by (simpl; intuition).
+    rewrite H1.
+    apply (pseudo_comb p0 p1 input _ _ m0 m1 m2 c0 c1 c2); intuition.
+  Qed.
+
+  Definition pseudeq {w s} (n m: nat) (f: list (word w) -> list (word w)) : Type := 
+    {p: @Pseudo w s n m | forall x: (list (word w)),
+      List.length x = n -> exists m' c',
+      pseudoEval p (x, TripleM.empty N, None) = Some (f x, m', c')}.
+
+  Definition example (v: list (word 32)) : list (word 32) :=
+      [(natToWord _ 1) ^& (nth 0 v (wzero _))].
+
+  Definition convert_example: @pseudeq 32 W32 1 1 example.
+    eexists; intro x; eexists; eexists.
+
+    destruct x as [v x|]; try destruct x; autounfold.
+
+    Focus 2.
+
+    - (* Unfold all of our boilerplate *)
+      unfold example; autounfold.
+
+      (* eapply the relevant lemmas *)
+
+      eapply pseudo_and.
+      eapply pseudo_cons.
+      eapply pseudo_const.
+      eapply pseudo_var.
+
+      (* leftovers *)
+
+      + instantiate (1 := 0); abstract (simpl; intuition).
+      + reflexivity.
+
+    - contradict H; abstract (simpl; intuition).
+
+    - contradict H; abstract (simpl; intuition).
 
-  Eval vm_compute in (run ex0 [natToWord _ 7]).
+    (* Deal with leftover existentials *)
+    Grab Existential Variables.
+    abstract (simpl; intuition).
+    refine None.
+  Defined.
 
 End Conversion.
 
diff --git a/src/Assembly/State.v b/src/Assembly/State.v
index ea7628bb7..20bb532ad 100644
--- a/src/Assembly/State.v
+++ b/src/Assembly/State.v
@@ -215,7 +215,10 @@ Module ListState.
     (fst st, Some v).
 
   Definition setCarryOpt {n: nat} (v: option bool) (st: ListState n): ListState n :=
-    (fst st, v).
+    match v with
+    | Some v' => (fst st, v)
+    | None => st
+    end.
 
 End ListState.
 
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