diff options
author | Jason Gross <jgross@mit.edu> | 2017-01-19 19:35:24 -0500 |
---|---|---|
committer | Jason Gross <jgross@mit.edu> | 2017-01-19 19:35:24 -0500 |
commit | fa027c4a37ed455a26a5bb12c6f3d54ae4bd8774 (patch) | |
tree | 4e6d08d6d36595a068f3facf2c70f540bae0e8b1 /src/Reflection/Z/Interpretations128/Relations.v | |
parent | 320c013f0c5550aed168dd7fd25274dbb9756590 (diff) |
Remove the Const constructor of exprf
We instead use the [Op] constructor for constants. This allows [exprf]
to not depend on the interpretation function; this means we don't need
to map over it to change the interpretation function. This saves us
about 300 lines of code and about 30s of build time, total.
After | File Name | Before || Change
-----------------------------------------------------------------------------------------------------------
18m11.34s | Total | 18m46.86s || -0m35.52s
-----------------------------------------------------------------------------------------------------------
0m19.99s | Specific/GF25519ReflectiveAddCoordinates | 0m31.78s || -0m11.79s
1m53.69s | Specific/GF25519Reflective/Reified/LadderStep | 2m01.32s || -0m07.62s
1m27.74s | Specific/GF25519Reflective/Reified/AddCoordinates | 1m34.03s || -0m06.29s
0m01.45s | Specific/GF25519Reflective | 0m06.31s || -0m04.85s
0m04.62s | Reflection/InlineInterp | 0m01.52s || +0m03.10s
1m19.68s | CompleteEdwardsCurve/ExtendedCoordinates | 1m21.19s || -0m01.50s
0m02.90s | Reflection/InlineWf | 0m01.80s || +0m01.09s
N/A | Reflection/MapWithInterpInfo | 0m01.70s || -0m01.70s
1m32.32s | Test/Curve25519SpecTestVectors | 1m32.25s || +0m00.06s
1m12.79s | Experiments/Ed25519 | 1m13.17s || -0m00.38s
0m40.52s | ModularArithmetic/Conversion | 0m40.44s || +0m00.08s
0m34.57s | Spec/Ed25519 | 0m34.53s || +0m00.03s
0m30.82s | ModularArithmetic/ModularBaseSystemProofs | 0m30.89s || -0m00.07s
0m30.11s | Specific/GF25519Bounded | 0m30.21s || -0m00.10s
0m23.20s | Experiments/MontgomeryCurve | 0m23.26s || -0m00.06s
0m22.16s | Reflection/Z/Interpretations128/Relations | 0m21.72s || +0m00.44s
0m21.69s | ModularArithmetic/Pow2BaseProofs | 0m21.58s || +0m00.11s
0m20.25s | Algebra | 0m20.27s || -0m00.01s
0m19.81s | Specific/GF25519 | 0m19.83s || -0m00.01s
0m18.82s | Reflection/Z/Interpretations64/Relations | 0m18.50s || +0m00.32s
0m18.19s | EdDSARepChange | 0m18.26s || -0m00.07s
0m17.08s | CompleteEdwardsCurve/CompleteEdwardsCurveTheorems | 0m17.16s || -0m00.08s
0m14.10s | Util/ZUtil | 0m14.03s || +0m00.07s
0m10.05s | Testbit | 0m10.02s || +0m00.03s
0m08.95s | Specific/GF25519BoundedCommon | 0m08.90s || +0m00.04s
0m08.87s | BoundedArithmetic/ArchitectureToZLikeProofs | 0m08.81s || +0m00.05s
0m08.80s | Assembly/GF25519 | 0m08.82s || -0m00.01s
0m08.80s | ModularArithmetic/Montgomery/ZProofs | 0m08.87s || -0m00.06s
0m08.51s | Encoding/PointEncoding | 0m08.53s || -0m00.01s
0m08.37s | BoundedArithmetic/Double/Proofs/Multiply | 0m08.39s || -0m00.02s
0m08.34s | Specific/GF1305 | 0m08.31s || +0m00.02s
0m07.85s | BoundedArithmetic/Double/Proofs/ShiftRightDoubleWordImmediate | 0m07.86s || -0m00.01s
0m07.60s | Specific/GF25519Reflective/Reified/Mul | 0m07.52s || +0m00.08s
0m07.13s | MxDHRepChange | 0m07.08s || +0m00.04s
0m06.85s | BoundedArithmetic/Double/Proofs/SpreadLeftImmediate | 0m06.77s || +0m00.08s
0m06.62s | Reflection/Z/InterpretationsGen | 0m06.62s || +0m00.00s
0m05.69s | Reflection/Z/Interpretations64/RelationsCombinations | 0m05.60s || +0m00.09s
0m05.68s | Reflection/Z/Interpretations128/RelationsCombinations | 0m05.67s || +0m00.00s
0m05.48s | Specific/SC25519 | 0m05.38s || +0m00.10s
0m05.40s | BoundedArithmetic/Double/Proofs/RippleCarryAddSub | 0m05.36s || +0m00.04s
0m04.93s | ModularArithmetic/ModularBaseSystemListProofs | 0m04.96s || -0m00.03s
0m04.87s | WeierstrassCurve/Pre | 0m04.83s || +0m00.04s
0m04.45s | Specific/GF25519Reflective/Reified/PreFreeze | 0m04.56s || -0m00.10s
0m04.33s | Specific/GF25519Reflective/CommonBinOp | 0m04.55s || -0m00.21s
0m03.95s | ModularArithmetic/BarrettReduction/ZHandbook | 0m03.98s || -0m00.02s
0m03.87s | Specific/GF25519Reflective/CommonUnOp | 0m04.08s || -0m00.20s
0m03.86s | Encoding/PointEncodingPre | 0m03.88s || -0m00.02s
0m03.84s | BaseSystemProofs | 0m03.88s || -0m00.04s
0m03.75s | Specific/GF25519Reflective/CommonUnOpWireToFE | 0m03.96s || -0m00.20s
0m03.64s | CompleteEdwardsCurve/Pre | 0m03.60s || +0m00.04s
0m03.51s | BoundedArithmetic/InterfaceProofs | 0m03.42s || +0m00.08s
0m03.41s | ModularArithmetic/Tutorial | 0m03.38s || +0m00.03s
0m03.30s | Reflection/LinearizeWf | 0m04.24s || -0m00.94s
0m03.20s | Specific/GF25519Reflective/Reified/CarrySub | 0m03.28s || -0m00.07s
0m03.14s | ModularArithmetic/ZBoundedZ | 0m03.14s || +0m00.00s
0m03.14s | ModularArithmetic/BarrettReduction/ZGeneralized | 0m03.14s || +0m00.00s
0m02.95s | Specific/GF25519Reflective/Reified/CarryAdd | 0m02.93s || +0m00.02s
0m02.92s | Specific/GF25519Reflective/Common9_4Op | 0m02.89s || +0m00.02s
0m02.82s | Specific/GF25519Reflective/Reified/CarryOpp | 0m02.95s || -0m00.13s
0m02.82s | BoundedArithmetic/Double/Proofs/Decode | 0m02.90s || -0m00.08s
0m02.69s | BoundedArithmetic/Double/Proofs/ShiftRight | 0m02.69s || +0m00.00s
0m02.66s | ModularArithmetic/ModularArithmeticTheorems | 0m02.67s || -0m00.00s
0m02.63s | Specific/FancyMachine256/Montgomery | 0m02.24s || +0m00.38s
0m02.61s | Specific/GF25519Reflective/CommonUnOpFEToWire | 0m02.76s || -0m00.14s
0m02.58s | BoundedArithmetic/Double/Proofs/ShiftLeft | 0m02.58s || +0m00.00s
0m02.56s | Specific/GF25519Reflective/Common | 0m02.60s || -0m00.04s
0m02.52s | Specific/FancyMachine256/Barrett | 0m02.20s || +0m00.31s
0m02.50s | Specific/GF25519BoundedAddCoordinates | 0m02.60s || -0m00.10s
0m02.39s | ModularArithmetic/BarrettReduction/ZBounded | 0m02.31s || +0m00.08s
0m02.34s | ModularArithmetic/ModularBaseSystemOpt | 0m02.31s || +0m00.02s
0m02.02s | Specific/GF25519Reflective/Reified/Sub | 0m02.01s || +0m00.01s
0m01.98s | Reflection/WfReflective | 0m02.54s || -0m00.56s
0m01.94s | Specific/GF25519Reflective/Reified/Pack | 0m02.07s || -0m00.12s
0m01.93s | Assembly/Evaluables | 0m01.93s || +0m00.00s
0m01.92s | Specific/GF25519Reflective/Reified/Unpack | 0m02.04s || -0m00.12s
0m01.90s | Specific/FancyMachine256/Core | 0m01.79s || +0m00.10s
0m01.79s | ModularArithmetic/Montgomery/ZBounded | 0m01.86s || -0m00.07s
0m01.77s | Specific/GF25519ExtendedAddCoordinates | 0m01.76s || +0m00.01s
0m01.68s | Specific/GF25519Reflective/Reified/Add | 0m01.69s || -0m00.01s
0m01.67s | Specific/GF25519BoundedExtendedAddCoordinates | 0m01.79s || -0m00.12s
0m01.63s | Experiments/Ed25519Extraction | 0m01.66s || -0m00.03s
0m01.62s | Specific/GF25519Reflective/Reified/Opp | 0m01.72s || -0m00.09s
0m01.54s | Specific/GF25519Reflective/Reified/GeModulus | 0m01.59s || -0m00.05s
0m01.50s | Reflection/TestCase | 0m01.42s || +0m00.08s
0m01.47s | ModularArithmetic/BarrettReduction/Z | 0m01.47s || +0m00.00s
0m01.43s | Assembly/Compile | 0m01.46s || -0m00.03s
0m01.33s | Reflection/WfProofs | 0m01.95s || -0m00.61s
0m01.26s | ModularArithmetic/PrimeFieldTheorems | 0m01.28s || -0m00.02s
0m01.20s | Assembly/Conversions | 0m01.19s || +0m00.01s
0m01.16s | ModularArithmetic/ExtendedBaseVector | 0m01.22s || -0m00.06s
0m01.16s | BaseSystem | 0m01.15s || +0m00.01s
0m01.09s | BoundedArithmetic/Double/Repeated/Proofs/Decode | 0m01.11s || -0m00.02s
0m00.99s | Util/NumTheoryUtil | 0m00.96s || +0m00.03s
0m00.96s | Assembly/HL | 0m00.96s || +0m00.00s
0m00.94s | Assembly/LL | 0m00.99s || -0m00.05s
0m00.94s | Assembly/Pipeline | 0m00.92s || +0m00.01s
0m00.88s | Reflection/WfInversion | 0m01.21s || -0m00.32s
0m00.86s | Assembly/PhoasCommon | 0m00.91s || -0m00.05s
0m00.86s | Specific/GF25519Reflective/CommonUnOpFEToZ | 0m01.02s || -0m00.16s
0m00.85s | BoundedArithmetic/Double/Proofs/LoadImmediate | 0m00.86s || -0m00.01s
0m00.84s | BoundedArithmetic/Double/Proofs/BitwiseOr | 0m00.91s || -0m00.07s
0m00.82s | BoundedArithmetic/X86ToZLikeProofs | 0m00.85s || -0m00.03s
0m00.79s | Util/IterAssocOp | 0m00.82s || -0m00.02s
0m00.75s | Reflection/Z/Syntax | 0m00.67s || +0m00.07s
0m00.73s | Util/PartiallyReifiedProp | 0m00.73s || +0m00.00s
0m00.70s | Encoding/ModularWordEncodingTheorems | 0m00.76s || -0m00.06s
0m00.70s | Specific/GF25519Reflective/Reified | 0m00.72s || -0m00.02s
0m00.66s | BoundedArithmetic/Double/Repeated/Proofs/Multiply | 0m00.62s || +0m00.04s
0m00.66s | ModularArithmetic/PseudoMersenneBaseParamProofs | 0m00.66s || +0m00.00s
0m00.64s | Encoding/ModularWordEncodingPre | 0m00.63s || +0m00.01s
0m00.61s | ModularArithmetic/ModularBaseSystem | 0m00.66s || -0m00.05s
0m00.61s | Util/AdditionChainExponentiation | 0m00.64s || -0m00.03s
0m00.60s | ModularArithmetic/ExtPow2BaseMulProofs | 0m00.64s || -0m00.04s
0m00.60s | Reflection/MultiSizeTest2 | 0m00.71s || -0m00.10s
0m00.60s | Spec/EdDSA | 0m00.65s || -0m00.05s
0m00.59s | BoundedArithmetic/Double/Repeated/Proofs/RippleCarryAddSub | 0m00.51s || +0m00.07s
0m00.58s | BoundedArithmetic/Interface | 0m00.60s || -0m00.02s
0m00.58s | ModularArithmetic/ModularBaseSystemList | 0m00.61s || -0m00.03s
0m00.55s | Spec/ModularWordEncoding | 0m00.63s || -0m00.07s
0m00.55s | BoundedArithmetic/Double/Repeated/Proofs/ShiftLeftRight | 0m00.50s || +0m00.05s
0m00.55s | Reflection/InterpWfRel | 0m00.58s || -0m00.02s
0m00.54s | BoundedArithmetic/X86ToZLike | 0m00.55s || -0m00.01s
0m00.54s | BoundedArithmetic/Double/Repeated/Proofs/SelectConditional | 0m00.53s || +0m00.01s
0m00.54s | BoundedArithmetic/Double/Proofs/SelectConditional | 0m00.62s || -0m00.07s
0m00.54s | Reflection/WfReflectiveGen | 0m00.58s || -0m00.03s
0m00.52s | BoundedArithmetic/ArchitectureToZLike | 0m00.41s || +0m00.11s
0m00.51s | BoundedArithmetic/Double/Core | 0m00.48s || +0m00.03s
0m00.50s | BoundedArithmetic/Double/Repeated/Proofs/BitwiseOr | 0m00.51s || -0m00.01s
0m00.49s | Spec/WeierstrassCurve | 0m00.42s || +0m00.07s
0m00.48s | BoundedArithmetic/Double/Repeated/Proofs/LoadImmediate | 0m00.54s || -0m00.06s
0m00.47s | BoundedArithmetic/Double/Repeated/Proofs/ShiftRightDoubleWordImmediate | 0m00.58s || -0m00.10s
0m00.47s | Reflection/InterpWf | 0m00.50s || -0m00.03s
0m00.47s | ModularArithmetic/Pre | 0m00.48s || -0m00.01s
0m00.47s | BoundedArithmetic/Double/Repeated/Core | 0m00.46s || +0m00.00s
0m00.46s | Reflection/Z/Interpretations64 | 0m00.49s || -0m00.02s
0m00.45s | Reflection/InputSyntax | 0m00.42s || +0m00.03s
N/A | Reflection/MapInterpWf | 0m00.44s || -0m00.44s
0m00.44s | Spec/CompleteEdwardsCurve | 0m00.39s || +0m00.04s
0m00.44s | BoundedArithmetic/Double/Proofs/ShiftLeftRightTactic | 0m00.42s || +0m00.02s
0m00.44s | Reflection/Z/Interpretations128 | 0m00.52s || -0m00.08s
0m00.44s | ModularArithmetic/ZBounded | 0m00.45s || -0m00.01s
0m00.42s | BoundedArithmetic/StripCF | 0m00.42s || +0m00.00s
0m00.42s | Reflection/Z/Reify | 0m00.43s || -0m00.01s
0m00.42s | ModularArithmetic/ModularBaseSystemListZOperationsProofs | 0m00.47s || -0m00.04s
0m00.41s | Reflection/Named/DeadCodeElimination | 0m00.43s || -0m00.02s
0m00.41s | ModularArithmetic/PseudoMersenneBaseParams | 0m00.38s || +0m00.02s
0m00.41s | Spec/ModularArithmetic | 0m00.34s || +0m00.06s
0m00.41s | Reflection/Named/RegisterAssign | 0m00.37s || +0m00.03s
0m00.41s | Reflection/Reify | 0m00.39s || +0m00.01s
0m00.40s | ModularArithmetic/Pow2Base | 0m00.42s || -0m00.01s
0m00.40s | Reflection/Named/EstablishLiveness | 0m00.33s || +0m00.07s
0m00.40s | Reflection/ExprInversion | 0m00.57s || -0m00.16s
0m00.40s | Reflection/Named/Syntax | 0m00.40s || +0m00.00s
0m00.38s | Reflection/Named/Compile | 0m00.34s || +0m00.03s
N/A | Reflection/MapInterp | 0m00.38s || -0m00.38s
0m00.38s | ModularArithmetic/Montgomery/Z | 0m00.39s || -0m00.01s
0m00.38s | ModularArithmetic/ModularBaseSystemWord | 0m00.36s || +0m00.02s
N/A | Reflection/WfRel | 0m00.38s || -0m00.38s
0m00.38s | Reflection/Tuple | N/A || +0m00.38s
0m00.37s | Spec/MxDH | 0m00.39s || -0m00.02s
0m00.37s | BoundedArithmetic/Eta | 0m00.36s || +0m00.01s
0m00.36s | Reflection/Named/ContextOn | 0m00.37s || -0m00.01s
0m00.34s | Reflection/FilterLive | 0m00.34s || +0m00.00s
0m00.34s | Reflection/LinearizeInterp | 0m00.53s || -0m00.19s
0m00.33s | Reflection/Relations | N/A || +0m00.33s
0m00.32s | Reflection/Equality | 0m00.41s || -0m00.08s
0m00.30s | Reflection/Syntax | 0m00.52s || -0m00.22s
0m00.30s | Reflection/InterpProofs | 0m00.47s || -0m00.17s
0m00.30s | Reflection/ApplicationLemmas | 0m00.43s || -0m00.13s
0m00.30s | Reflection/CommonSubexpressionElimination | 0m00.50s || -0m00.20s
0m00.28s | Reflection/Inline | 0m00.37s || -0m00.08s
0m00.28s | Reflection/Conversion | 0m00.44s || -0m00.15s
0m00.27s | Reflection/MapCastWithCastOp | 0m00.38s || -0m00.10s
0m00.26s | Reflection/MapCast | 0m00.40s || -0m00.14s
0m00.26s | Reflection/ApplicationRelations | 0m00.35s || -0m00.08s
0m00.24s | Reflection/Application | 0m00.38s || -0m00.14s
0m00.23s | Reflection/Linearize | 0m00.35s || -0m00.11s
0m00.20s | Reflection/CountLets | 0m00.33s || -0m00.13s
0m00.20s | Reflection/Named/NameUtil | 0m00.36s || -0m00.15s
0m00.09s | Util/PointedProp | 0m00.08s || +0m00.00s
0m00.05s | Util/LetIn | 0m00.06s || -0m00.00s
0m00.03s | Util/Notations | 0m00.03s || +0m00.00s
0m00.03s | Util/AutoRewrite | 0m00.03s || +0m00.00s
Diffstat (limited to 'src/Reflection/Z/Interpretations128/Relations.v')
-rw-r--r-- | src/Reflection/Z/Interpretations128/Relations.v | 81 |
1 files changed, 54 insertions, 27 deletions
diff --git a/src/Reflection/Z/Interpretations128/Relations.v b/src/Reflection/Z/Interpretations128/Relations.v index 5ce0df08e..fcd7bf2d8 100644 --- a/src/Reflection/Z/Interpretations128/Relations.v +++ b/src/Reflection/Z/Interpretations128/Relations.v @@ -2,7 +2,8 @@ Require Import Coq.ZArith.ZArith. Require Import Coq.micromega.Psatz. Require Import Crypto.Reflection.Z.Syntax. Require Import Crypto.Reflection.Syntax. -Require Import Crypto.Reflection.Application. +Require Import Crypto.Reflection.Relations. +Require Import Crypto.Reflection.Tuple. Require Import Crypto.Reflection.Z.InterpretationsGen. Require Import Crypto.Reflection.Z.Interpretations128. Require Import Crypto.ModularArithmetic.ModularBaseSystemListZOperationsProofs. @@ -152,7 +153,7 @@ Lemma related_tuples_None_left (v : interp_flat_type interp_base_type' (tuple (Tbase TZ) (S n))) : interp_flat_type_rel_pointwise2 R - (flat_interp_untuple' (T:=Tbase TZ) (Tuple.push_option (n:=S n) None)) + (flat_interp_untuple (T:=Tbase TZ) (Tuple.push_option None)) v. Proof. induction n; simpl; intuition. @@ -162,16 +163,17 @@ Lemma related_tuples_Some_left n T interp_base_type' (R : forall t, T -> interp_base_type' t -> Prop) u - (v : interp_flat_type interp_base_type' (tuple (Tbase TZ) (S n))) + (v : interp_flat_type interp_base_type' (tuple (Tbase TZ) n)) : interp_flat_type_rel_pointwise2 R - (flat_interp_untuple' (T:=Tbase TZ) u) + (flat_interp_untuple (T:=Tbase TZ) u) v <-> interp_flat_type_rel_pointwise2 (LiftOption.lift_relation R) - (flat_interp_untuple' (T:=Tbase TZ) (Tuple.push_option (n:=S n) (Some u))) + (flat_interp_untuple (T:=Tbase TZ) (Tuple.push_option (Some u))) v. Proof. + destruct n as [|n]; [ reflexivity | ]. induction n; [ reflexivity | ]. simpl in *; rewrite <- IHn; clear IHn. reflexivity. @@ -181,14 +183,15 @@ Lemma related_tuples_Some_left_ext {n T interp_base_type'} {R : forall t, T -> interp_base_type' t -> Prop} {u v u'} - (H : Tuple.lift_option (flat_interp_tuple (T:=Tbase TZ) (n:=S n) u) = Some u') + (H : Tuple.lift_option (flat_interp_tuple (T:=Tbase TZ) (n:=n) u) = Some u') : interp_flat_type_rel_pointwise2 R - (flat_interp_untuple' (T:=Tbase TZ) u') v + (flat_interp_untuple (T:=Tbase TZ) u') v <-> interp_flat_type_rel_pointwise2 (LiftOption.lift_relation R) u v. Proof. + destruct n as [|n]; [ reflexivity | ]. induction n. { simpl in *; subst; reflexivity. } { destruct_head_hnf' prod. @@ -200,13 +203,14 @@ Qed. Lemma related_tuples_proj_eq_rel_untuple {n T interp_base_type'} {proj : forall t, T -> interp_base_type' t} - {u : Tuple.tuple _ (S n)} {v : Tuple.tuple _ (S n)} + {u : Tuple.tuple _ n} {v : Tuple.tuple _ n} : interp_flat_type_rel_pointwise2 (fun t => proj_eq_rel (proj t)) - (flat_interp_untuple' (T:=Tbase TZ) u) - (flat_interp_untuple' (T:=Tbase TZ) v) + (flat_interp_untuple (T:=Tbase TZ) u) + (flat_interp_untuple (T:=Tbase TZ) v) <-> (Tuple.map (proj _) u = v). Proof. + destruct n as [|n]; [ destruct_head_hnf' unit; simpl; tauto | ]. induction n; [ reflexivity | ]. destruct_head_hnf' prod. simpl @Tuple.tuple. @@ -222,27 +226,27 @@ Lemma related_tuples_proj_eq_rel_tuple : interp_flat_type_rel_pointwise2 (fun t => proj_eq_rel (proj t)) u v - <-> (Tuple.map (proj _) (flat_interp_tuple (n:=S n) (T:=Tbase TZ) u) + <-> (Tuple.map (proj _) (flat_interp_tuple (n:=n) (T:=Tbase TZ) u) = flat_interp_tuple (T:=Tbase TZ) v). Proof. - rewrite <- related_tuples_proj_eq_rel_untuple, !flat_interp_untuple'_tuple; reflexivity. + rewrite <- related_tuples_proj_eq_rel_untuple, !flat_interp_untuple_tuple; reflexivity. Qed. Local Arguments LiftOption.lift_relation2 _ _ _ _ !_ !_ / . -Lemma related_tuples_lift_relation2_untuple' +Lemma related_tuples_lift_relation2_untuple n T U (R : T -> U -> Prop) (t : option (Tuple.tuple T (S n))) (u : option (Tuple.tuple U (S n))) : interp_flat_type_rel_pointwise2 (LiftOption.lift_relation2 R) - (flat_interp_untuple' (T:=Tbase TZ) (Tuple.push_option t)) - (flat_interp_untuple' (T:=Tbase TZ) (Tuple.push_option u)) + (flat_interp_untuple (T:=Tbase TZ) (Tuple.push_option t)) + (flat_interp_untuple (T:=Tbase TZ) (Tuple.push_option u)) <-> LiftOption.lift_relation2 (interp_flat_type_rel_pointwise2 (fun _ => R)) TZ - (option_map (flat_interp_untuple' (interp_base_type:=fun _ => T) (T:=Tbase TZ)) t) - (option_map (flat_interp_untuple' (interp_base_type:=fun _ => U) (T:=Tbase TZ)) u). + (option_map (flat_interp_untuple (interp_base_type:=fun _ => T) (T:=Tbase TZ)) t) + (option_map (flat_interp_untuple (interp_base_type:=fun _ => U) (T:=Tbase TZ)) u). Proof. induction n. { destruct_head' option; reflexivity. } @@ -255,7 +259,7 @@ Proof. try (simpl @interp_flat_type_rel_pointwise2; tauto). } Qed. -Lemma related_tuples_lift_relation2_untuple'_ext +Lemma related_tuples_lift_relation2_untuple_ext {n T U} {R : T -> U -> Prop} {t u} @@ -267,8 +271,8 @@ Lemma related_tuples_lift_relation2_untuple'_ext <-> LiftOption.lift_relation2 (interp_flat_type_rel_pointwise2 (fun _ => R)) TZ - (option_map (flat_interp_untuple' (interp_base_type:=fun _ => T) (T:=Tbase TZ)) (Tuple.lift_option (flat_interp_tuple (T:=Tbase TZ) t))) - (option_map (flat_interp_untuple' (interp_base_type:=fun _ => U) (T:=Tbase TZ)) (Tuple.lift_option (flat_interp_tuple (T:=Tbase TZ) u))). + (option_map (flat_interp_untuple (interp_base_type:=fun _ => T) (T:=Tbase TZ)) (Tuple.lift_option (flat_interp_tuple (T:=Tbase TZ) t))) + (option_map (flat_interp_untuple (interp_base_type:=fun _ => U) (T:=Tbase TZ)) (Tuple.lift_option (flat_interp_tuple (T:=Tbase TZ) u))). Proof. induction n. { destruct_head_hnf' option; reflexivity. } @@ -293,22 +297,22 @@ Proof. | progress break_match ] ]. } Qed. -Lemma lift_option_flat_interp_tuple' +Lemma lift_option_flat_interp_tuple {n T x y} - : (Tuple.lift_option (n:=S n) (A:=T) (flat_interp_tuple' (interp_base_type:=LiftOption.interp_base_type' _) (T:=Tbase TZ) x) = Some y) - <-> (x = flat_interp_untuple' (T:=Tbase TZ) (n:=n) (Tuple.push_option (n:=S n) (Some y))). + : (Tuple.lift_option (n:=S n) (A:=T) (flat_interp_tuple (interp_base_type:=LiftOption.interp_base_type' _) (T:=Tbase TZ) x) = Some y) + <-> (x = flat_interp_untuple (T:=Tbase TZ) (n:=S n) (Tuple.push_option (n:=S n) (Some y))). Proof. rewrite Tuple.push_lift_option; generalize (Tuple.push_option (Some y)); intro. split; intro; subst; - rewrite ?flat_interp_tuple'_untuple', ?flat_interp_untuple'_tuple'; + rewrite ?flat_interp_tuple_untuple, ?flat_interp_untuple_tuple; reflexivity. Qed. Lemma lift_option_None_interp_flat_type_rel_pointwise2_1 T U n R x y (H : interp_flat_type_rel_pointwise2 (LiftOption.lift_relation2 R) x y) - (HNone : Tuple.lift_option (A:=T) (n:=S n) (flat_interp_tuple' (T:=Tbase TZ) (n:=n) x) = None) - : Tuple.lift_option (A:=U) (n:=S n) (flat_interp_tuple' (T:=Tbase TZ) (n:=n) y) = None. + (HNone : Tuple.lift_option (A:=T) (n:=S n) (flat_interp_tuple (T:=Tbase TZ) (n:=S n) x) = None) + : Tuple.lift_option (A:=U) (n:=S n) (flat_interp_tuple (T:=Tbase TZ) (n:=S n) y) = None. Proof. induction n; [ | specialize (IHn (fst x) (fst y) (proj1 H)) ]; repeat first [ progress destruct_head_hnf' False @@ -328,12 +332,18 @@ Local Arguments LiftOption.lift_relation _ _ _ _ !_ _ / . Local Arguments LiftOption.of' _ _ !_ / . Local Arguments BoundedWordW.BoundedWordToBounds !_ / . +Local Ltac unfold_related_const := + intros; hnf; simpl; + unfold related_wordW, LiftOption.lift_relation, LiftOption.of', BoundedWordW.wordWToBoundedWord, BoundedWordW.SmartBuildBoundedWord, BoundedWordW.of_Z, BoundedWordW.of_wordW, BoundedWordW.wordWToBoundedWord; + simpl. + Lemma related_wordW_op : related_op related_wordW (@BoundedWordW.interp_op) (@WordW.interp_op). Proof. (let op := fresh in intros ?? op; destruct op; simpl); try first [ apply related_wordW_t_map1 | apply related_wordW_t_map2 - | apply related_wordW_t_map4 ]. + | apply related_wordW_t_map4 + | unfold_related_const; break_innermost_match; reflexivity ]. Qed. Lemma related_bounds_t_map1 opW opB pf @@ -383,9 +393,25 @@ Local Arguments Tuple.map : simpl never. Local Arguments Tuple.map2 : simpl never. Local Arguments ZBounds.SmartBuildBounds _ _ / . + +Local Ltac related_const_op_t := + unfold_related_const; break_innermost_match; try reflexivity; hnf; simpl; + repeat match goal with + | [ H : andb _ _ = true |- _ ] => apply andb_prop in H + | _ => progress destruct_head' and + | _ => progress Z.ltb_to_lt + | _ => rewrite WordW.wordWToZ_ZToWordW by (simpl @Z.of_nat; omega) + | [ H : _ |- _ ] => rewrite WordW.wordWToZ_ZToWordW in H by (simpl @Z.of_nat; omega) + | [ H : (Z.log2 ?x < ?y)%Z |- _ ] + => unique assert (x < 2^y)%Z by (apply WordW.log2_lt_pow2_alt_proj_r2l; omega) + | _ => reflexivity + | _ => omega + end. + Lemma related_bounds_op : related_op related_bounds (@BoundedWordW.interp_op) (@ZBounds.interp_op). Proof. let op := fresh in intros ?? op; destruct op; simpl. + { related_const_op_t. } { apply related_bounds_t_map2; intros; destruct_head' option; reflexivity. } { apply related_bounds_t_map2; intros; destruct_head' option; reflexivity. } { apply related_bounds_t_map2; intros; destruct_head' option; reflexivity. } @@ -515,6 +541,7 @@ Local Arguments ZBounds.neg _ !_ / . Lemma related_Z_op : related_op related_Z (@BoundedWordW.interp_op) (@Z.interp_op). Proof. let op := fresh in intros ?? op; destruct op; simpl. + { related_const_op_t. } { apply related_Z_t_map2; related_Z_op_fin_t. } { apply related_Z_t_map2; related_Z_op_fin_t. } { apply related_Z_t_map2; related_Z_op_fin_t. } |