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/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/Relations.v')
-rw-r--r-- | src/Reflection/Relations.v | 147 |
1 files changed, 147 insertions, 0 deletions
diff --git a/src/Reflection/Relations.v b/src/Reflection/Relations.v new file mode 100644 index 000000000..bc8b58f35 --- /dev/null +++ b/src/Reflection/Relations.v @@ -0,0 +1,147 @@ +Require Import Coq.Classes.RelationClasses Coq.Classes.Morphisms. +Require Import Crypto.Reflection.Syntax. +Require Import Crypto.Util.Tactics. + +Local Open Scope ctype_scope. +Section language. + Context {base_type_code : Type}. + + Let Tbase := (@Tbase base_type_code). + Local Coercion Tbase : base_type_code >-> flat_type. + Local Notation flat_type := (flat_type base_type_code). + Local Notation type := (type base_type_code). + + Section type. + Context (interp_flat_type : flat_type -> Type) + (R : forall t, interp_flat_type t -> interp_flat_type t -> Prop). + Local Notation interp_type_gen := (interp_type_gen interp_flat_type). + Fixpoint interp_type_gen_rel_pointwise (t : type) + : interp_type_gen t -> interp_type_gen t -> Prop := + match t with + | Tflat t => R t + | Arrow _ y => fun f g => forall x, interp_type_gen_rel_pointwise y (f x) (g x) + end. + Global Instance interp_type_gen_rel_pointwise_Reflexive {H : forall t, Reflexive (R t)} + : forall t, Reflexive (interp_type_gen_rel_pointwise t). + Proof. induction t; repeat intro; reflexivity. Qed. + Global Instance interp_type_gen_rel_pointwise_Symmetric {H : forall t, Symmetric (R t)} + : forall t, Symmetric (interp_type_gen_rel_pointwise t). + Proof. induction t; simpl; repeat intro; symmetry; eauto. Qed. + Global Instance interp_type_gen_rel_pointwise_Transitive {H : forall t, Transitive (R t)} + : forall t, Transitive (interp_type_gen_rel_pointwise t). + Proof. induction t; simpl; repeat intro; etransitivity; eauto. Qed. + End type. + + Section flat_type. + Context {interp_base_type : base_type_code -> Type} + (R : forall t, interp_base_type t -> interp_base_type t -> Prop). + Local Notation interp_flat_type := (interp_flat_type interp_base_type). + Fixpoint interp_flat_type_rel_pointwise (t : flat_type) + : interp_flat_type t -> interp_flat_type t -> Prop := + match t with + | Syntax.Tbase t => R t + | Unit => fun _ _ => True + | Prod _ _ => fun x y => interp_flat_type_rel_pointwise _ (fst x) (fst y) + /\ interp_flat_type_rel_pointwise _ (snd x) (snd y) + end. + Definition interp_type_rel_pointwise + := interp_type_gen_rel_pointwise _ interp_flat_type_rel_pointwise. + End flat_type. + + Section rel_pointwise2. + Section type. + Section hetero. + Context (interp_src1 interp_src2 : base_type_code -> Type) + (interp_dst1 interp_dst2 : flat_type -> Type) + (Rsrc : forall t, interp_src1 t -> interp_src2 t -> Prop) + (Rdst : forall t, interp_dst1 t -> interp_dst2 t -> Prop). + + Fixpoint interp_type_gen_rel_pointwise2_hetero (t : type) + : interp_type_gen_hetero interp_src1 interp_dst1 t + -> interp_type_gen_hetero interp_src2 interp_dst2 t + -> Prop + := match t with + | Tflat t => Rdst t + | Arrow src dst => @respectful_hetero _ _ _ _ (Rsrc src) (fun _ _ => interp_type_gen_rel_pointwise2_hetero dst) + end. + End hetero. + Section homogenous. + Context (interp_flat_type1 interp_flat_type2 : flat_type -> Type) + (R : forall t, interp_flat_type1 t -> interp_flat_type2 t -> Prop). + + Definition interp_type_gen_rel_pointwise2 + : forall t, + interp_type_gen interp_flat_type1 t + -> interp_type_gen interp_flat_type2 t + -> Prop + := interp_type_gen_rel_pointwise2_hetero interp_flat_type1 interp_flat_type2 + interp_flat_type1 interp_flat_type2 + R R. + End homogenous. + End type. + Section flat_type. + Context (interp_base_type1 interp_base_type2 : base_type_code -> Type). + Section gen_prop. + Context (P : Type) + (and : P -> P -> P) + (True : P) + (R : forall t, interp_base_type1 t -> interp_base_type2 t -> P). + + Fixpoint interp_flat_type_rel_pointwise2_gen_Prop (t : flat_type) + : interp_flat_type interp_base_type1 t -> interp_flat_type interp_base_type2 t -> P + := match t with + | Syntax.Tbase t => R t + | Unit => fun _ _ => True + | Prod x y => fun a b => and (interp_flat_type_rel_pointwise2_gen_Prop x (fst a) (fst b)) + (interp_flat_type_rel_pointwise2_gen_Prop y (snd a) (snd b)) + end. + End gen_prop. + + Definition interp_flat_type_rel_pointwise2 + := @interp_flat_type_rel_pointwise2_gen_Prop Prop and True. + + Definition interp_type_rel_pointwise2 R + : forall t, interp_type interp_base_type1 t + -> interp_type interp_base_type2 t + -> Prop + := interp_type_gen_rel_pointwise2 _ _ (interp_flat_type_rel_pointwise2 R). + End flat_type. + End rel_pointwise2. + + Section lifting. + Section flat_type. + Context {interp_base_type : base_type_code -> Type}. + Local Notation interp_flat_type := (interp_flat_type interp_base_type). + Context (R : forall t, interp_flat_type t -> interp_flat_type t -> Prop) + (RUnit : R Unit tt tt). + Section RProd. + Context (RProd : forall A B x y, R A (fst x) (fst y) /\ R B (snd x) (snd y) -> R (Prod A B) x y) + (RProd' : forall A B x y, R (Prod A B) x y -> R A (fst x) (fst y) /\ R B (snd x) (snd y)). + Lemma lift_interp_flat_type_rel_pointwise1 t (x y : interp_flat_type t) + : interp_flat_type_rel_pointwise R t x y -> R t x y. + Proof. clear RProd'; induction t; simpl; destruct_head_hnf' unit; intuition. Qed. + Lemma lift_interp_flat_type_rel_pointwise2 t (x y : interp_flat_type t) + : R t x y -> interp_flat_type_rel_pointwise R t x y. + Proof. clear RProd; induction t; simpl; destruct_head_hnf' unit; split_and; intuition. Qed. + End RProd. + Section RProd_iff. + Context (RProd : forall A B x y, R A (fst x) (fst y) /\ R B (snd x) (snd y) <-> R (Prod A B) x y). + Lemma lift_interp_flat_type_rel_pointwise t (x y : interp_flat_type t) + : interp_flat_type_rel_pointwise R t x y <-> R t x y. + Proof. + split_iff; split; auto using lift_interp_flat_type_rel_pointwise1, lift_interp_flat_type_rel_pointwise2. + Qed. + End RProd_iff. + End flat_type. + End lifting. +End language. + +Global Arguments interp_type_rel_pointwise2 {_ _ _} R {t} _ _. +Global Arguments interp_type_gen_rel_pointwise2_hetero {_ _ _ _ _} Rsrc Rdst {t} _ _. +Global Arguments interp_type_gen_rel_pointwise2 {_ _ _} R {t} _ _. +Global Arguments interp_flat_type_rel_pointwise2_gen_Prop {_ _ _ P} and True R {t} _ _. +Global Arguments interp_flat_type_rel_pointwise2 {_ _ _} R {t} _ _. +Global Arguments interp_flat_type_rel_pointwise {_} _ _ {_} _ _. +Global Arguments interp_type_rel_pointwise {_} _ _ {_} _ _. +Global Arguments interp_type_gen_rel_pointwise {_ _} _ {_} _ _. +Global Arguments interp_flat_type_rel_pointwise {_} _ _ {_} _ _. |