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https://github.com/HigherOrderCO/Kind1.git
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get really really close to prove the node case
This commit is contained in:
Rígille S. B. Menezes
parent
4e4dcfdd2a
commit
29ab09c82c
@ -79,7 +79,7 @@ RLP.encode.many(trees: List<RLP>): Bytes
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RLP.encode(tree: RLP): Bytes
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case tree {
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data:
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if Bool.and(Nat.eql(List.length!(tree.value),1), U8.ltn(List.head_with_default!(0#8,tree.value), 128#8)) then
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if Bool.and(Nat.eql(List.length!(tree.value),1), Nat.ltn(U8.to_nat((List.head_with_default!(0#8,tree.value))), 128)) then
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tree.value
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else
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List.concat!(RLP.encode.length(128, List.length!(tree.value)), tree.value)
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@ -1,10 +1,14 @@
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because_i_said_so<A: Type>: A
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because_i_said_so<A>
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// These sub-theorems were not proven yet!
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// Most of them are simple, and should be finished over the next days
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//RLP.aux.split.0(
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// payload: Bytes
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// tail: Bytes
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// H: Equal<Bool>(Nat.lte(List.length!(payload), 55), true)
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//): RLP.split.length(128, RLP.encode.length(128, List.length<U8>(payload)) ++ payload ++ tail) == {payload, tail}
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RLP.aux.split.0(
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payload: Bytes
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tail: Bytes
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H: Equal<Bool>(Nat.lte(List.length!(payload), 55), true)
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): Pair.new(Bytes, Bytes, payload, tail) == RLP.split.length(128, Nat.to_u8(Nat.add(128, List.length!(payload))) & payload ++ tail)
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because_i_said_so!
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// let H = mirror(H)
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// case H {
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// refl:
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@ -19,6 +23,23 @@
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// }: RLP.split.length(128,List.concat(U8, H.b( () Bytes,List.cons(U8,Nat.to_u8(Nat.add(128,List.length(U8,payload))),List.nil(U8)),List.concat(U8,Bytes.from_nat(Nat.add(56,Nat.add(128,RLP.needed_bytes(List.length(U8,payload))))),Bytes.from_nat(List.length(U8,payload)))),List.concat(U8,payload,tail))) == Pair.new(Bytes,Bytes,payload,tail)
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RLP.aux.split.1(
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payload: Bytes
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tail: Bytes
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H: Equal<Bool>(Nat.lte(List.length!(payload), 55), true)
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): Pair.new(Bytes, Bytes, payload, tail) ==
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let b = Bytes.from_nat(List.length!(payload))
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let a = Nat.to_u8(Nat.add(56, Nat.add(128, List.length!(b))))
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RLP.split.length(192, a & (b ++ payload) ++ tail)
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because_i_said_so!
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RLP.aux.split.2(
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payload: Bytes
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tail: Bytes
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H: Equal<Bool>(Nat.lte(List.length!(payload), 55), true)
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): Pair.new(Bytes, Bytes, payload, tail) == RLP.split.length(192, Nat.to_u8(Nat.add(192, List.length!(payload))) & payload ++ tail)
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because_i_said_so!
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RLP.aux.split.3(
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payload: Bytes
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tail: Bytes
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H1: Equal<Bool>(Nat.lte(List.length!(payload), 55), false)
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@ -27,7 +48,7 @@ RLP.aux.split.1(
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let b = Bytes.from_nat(List.length!(payload))
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let a = Nat.to_u8(Nat.add(56, Nat.add(192, List.length!(b))))
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RLP.split.length(192, a & (b ++ payload) ++ tail)
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RLP.aux.split.1(payload, tail, H1, H0)
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because_i_said_so!
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// let H1 = mirror(H1)
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// case H1 {
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// refl:
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@ -1,6 +1,9 @@
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typeof<A: Type>(a: A): Type
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A
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because_i_said_so<A: Type>: A
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because_i_said_so<A>
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RLP.encode_identity(
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rlps: List<RLP>
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H: Equal<Bool>(Nat.lte(List.length(U8, RLP.encode.many(rlps)), RLP.max), true)
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@ -11,62 +14,83 @@ RLP.encode_identity(
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cons:
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case rlps.head {
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data:
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?data
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node:
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let ind = RLP.encode_identity(rlps.head.child, ?todo.0)
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case Nat.lte(List.length(U8,RLP.encode.many(rlps.head.child)), 55) {
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let split_conditions = Bool.and.split(Nat.eql(List.length!(rlps.head.value),1), Nat.ltn(U8.to_nat((List.head_with_default!(0#8,rlps.head.value))), 128))
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case Bool.and(Nat.eql(List.length!(rlps.head.value),1), Nat.ltn(U8.to_nat((List.head_with_default!(0#8,rlps.head.value))), 128)) with split_conditions {
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true:
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?true-1110-
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use conditions = split_conditions(refl)
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?true
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false:
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let recover_prefix = ?todo.1 :: Nat.add(248, List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))) == U8.to_nat(Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))))
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case recover_prefix {
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refl:
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let lemma = RLP.aux.split.1(RLP.encode.many(rlps.head.child), RLP.encode.many(rlps.tail), ?todo.2, ?todo.3)
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case lemma {
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refl:
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let ind_right = RLP.encode_identity(rlps.tail, ?todo.4)
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let ind_left = RLP.encode_identity(rlps.head.child, ?todo.5)
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?test-258
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}: lemma.b( () List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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}: Nat.lte( recover_prefix.b, 127,() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),List.nil(U8))),RLP.decode.many(List.concat(U8,List.concat(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail)))),Nat.lte( recover_prefix.b ,191,() List(RLP),RLP.split.length(128,List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),List.concat(U8,List.concat(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),List.concat(U8,List.concat(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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//?false-1110-278-70-10
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}: RLP.decode.many(List.concat(U8,List.concat(U8, self( () Bytes,List.cons(U8,Nat.to_u8(Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child)))),List.nil(U8)),List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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?false
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}!
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//?data-22-86-
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// let remember = Equal.refl(Bool, Bool.and(Nat.eql(List.length!(rlp.value),1), U8.ltn(List.head_with_default!(0#8,rlp.value), 128#8)))
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// case Bool.and(Nat.eql(List.length!(rlp.value),1), U8.ltn(List.head_with_default!(0#8,rlp.value), 128#8)) as X
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// with remember : Equal(Bool, Bool.and(Nat.eql(List.length!(rlp.value),1), U8.ltn(List.head_with_default!(0#8,rlp.value), 128#8)), X)
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// {
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// true :
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// let break_and1 = RLP.aux.10!!(remember)
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// let break_and2 = RLP.aux.11!!(remember)
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// let ensure_non_empty = RLP.aux.12(rlp.value, break_and1)
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// replace X with mirror(ensure_non_empty) in Maybe.default(RLP,List.head(RLP,X((bytes) List(RLP),List.nil(RLP),(bytes.head) (bytes.tail) U8.ltn(bytes.head,Nat.to_u8(128),() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,bytes.head,List.nil(U8))),RLP.decode.many(bytes.tail)),U8.ltn(bytes.head,Nat.to_u8(192),() List(RLP),RLP.split.length(128,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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// replace X with mirror(break_and2) in Maybe.default(RLP,List.head(RLP,X(() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,List.head_with_default(U8,Nat.to_u8(0),rlp.value),List.nil(U8))),RLP.decode.many(List.nil(U8))),U8.ltn(List.head_with_default(U8,Nat.to_u8(0),rlp.value),Nat.to_u8(192),() List(RLP),RLP.split.length(128,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail)))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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// let list_length_1 = RlP.new_aux.list_length_1_identity(U8, rlp.value, Nat.to_u8(0), break_and1)
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// replace X with mirror(list_length_1) in RLP.data(X) == RLP.data(rlp.value)
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// refl
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// false :
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// let list_u8 = Equal.refl<Bytes, RLP.encode.length(128,List.length(U8,rlp.value))>
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// case RLP.encode.length(128,List.length(U8,rlp.value)) as X with list_u8 : Equal(Bytes, RLP.encode.length(128,List.length(U8,rlp.value)), X) {
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// nil :
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// let absurd_rlp_length = RLP.aux.17(List.length(U8,rlp.value))
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// Empty.absurd!(absurd_rlp_length(list_u8))
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// cons :
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// let u8_le_128 = RLP.aux.19(List.length(U8,rlp.value), X.head, X.tail, list_u8)
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// replace X with mirror(u8_le_128) in Maybe.default(RLP,List.head(RLP, X(() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,X.head,List.nil(U8))),RLP.decode.many(List.concat(U8,X.tail,rlp.value))),U8.ltn(X.head,Nat.to_u8(192),() List(RLP),RLP.split.length(128,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail)))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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// let u8_le_192 = RLP.aux.20(List.length(U8,rlp.value) X.head, X.tail, list_u8)
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// replace X with mirror(u8_le_192) in Maybe.default(RLP,List.head(RLP, X(() List(RLP),RLP.split.length(128,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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// let e3 = RLP.aux.15.sym(X.head, X.tail)
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//
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// ?a-282-
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// } : RLP.decode(List.concat(U8,X,rlp.value)) == RLP.data(rlp.value)
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//
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// } : RLP.decode(X(() List(U8),rlp.value,List.concat(U8,RLP.encode.length(128,List.length(U8,rlp.value)),rlp.value))) == RLP.data(rlp.value)
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//?data
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node:
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because_i_said_so!
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// let ind = RLP.encode_identity(rlps.head.child, ?todo.0)
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// case Nat.lte(List.length(U8,RLP.encode.many(rlps.head.child)), 55) {
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// true:
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// let recover_prefix = ?todo.5 :: Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child))) == U8.to_nat(Nat.to_u8(Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child)))))
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// case recover_prefix {
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// refl:
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// let lemma = RLP.aux.split.2(RLP.encode.many(rlps.head.child), RLP.encode.many(rlps.tail), ?todo.2)
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// case lemma {
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// refl:
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// let ind_right = RLP.encode_identity(rlps.tail, ?todo.7)
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// let ind_left = apply(RLP.node, RLP.encode_identity(rlps.head.child, ?todo.8))
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// Equal.vapply(2)!!!!(ind_right)!!!(ind_left, List.cons(RLP))
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// }: lemma.b(() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))) == _
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//
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// }: Nat.lte( recover_prefix.b ,127,() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,Nat.to_u8(Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child)))),List.nil(U8))),RLP.decode.many(List.concat(U8,List.concat(U8,List.nil(U8),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail)))),Nat.lte( recover_prefix.b ,191,() List(RLP),RLP.split.length(128,List.cons(U8,Nat.to_u8(Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child)))),List.concat(U8,List.concat(U8,List.nil(U8),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,Nat.to_u8(Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child)))),List.concat(U8,List.concat(U8,List.nil(U8),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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//
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// false:
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// let recover_prefix = ?todo.1 :: Nat.add(248, List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))) == U8.to_nat(Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))))
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// case recover_prefix {
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// refl:
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// let lemma = RLP.aux.split.3(RLP.encode.many(rlps.head.child), RLP.encode.many(rlps.tail), ?todo.2, ?todo.3)
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// case lemma {
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// refl:
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// let ind_right = RLP.encode_identity(rlps.tail, ?todo.4)
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// let ind_left = apply(RLP.node, RLP.encode_identity(rlps.head.child, ?todo.5))
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// Equal.vapply(2)!!!!(ind_right)!!!(ind_left, List.cons(RLP))
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//
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// }: lemma.b( () List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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//
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// }: Nat.lte( recover_prefix.b, 127,() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),List.nil(U8))),RLP.decode.many(List.concat(U8,List.concat(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail)))),Nat.lte( recover_prefix.b ,191,() List(RLP),RLP.split.length(128,List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),List.concat(U8,List.concat(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),List.concat(U8,List.concat(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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//
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// }: RLP.decode.many(List.concat(U8,List.concat(U8, self( () Bytes,List.cons(U8,Nat.to_u8(Nat.add(192,List.length(U8,RLP.encode.many(rlps.head.child)))),List.nil(U8)),List.cons(U8,Nat.to_u8(Nat.add(56,Nat.add(192,List.length(U8,Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))))),Bytes.from_nat(List.length(U8,RLP.encode.many(rlps.head.child))))),RLP.encode.many(rlps.head.child)),RLP.encode.many(rlps.tail))) == List.cons(RLP,RLP.node(rlps.head.child),rlps.tail)
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}!
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}!
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// let remember = Equal.refl(Bool, Bool.and(Nat.eql(List.length!(rlp.value),1), U8.ltn(List.head_with_default!(0#8,rlp.value), 128#8)))
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// case Bool.and(Nat.eql(List.length!(rlp.value),1), U8.ltn(List.head_with_default!(0#8,rlp.value), 128#8)) as X
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// with remember : Equal(Bool, Bool.and(Nat.eql(List.length!(rlp.value),1), U8.ltn(List.head_with_default!(0#8,rlp.value), 128#8)), X)
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// {
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// true :
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// let break_and1 = RLP.aux.10!!(remember)
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// let break_and2 = RLP.aux.11!!(remember)
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// let ensure_non_empty = RLP.aux.12(rlp.value, break_and1)
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// replace X with mirror(ensure_non_empty) in Maybe.default(RLP,List.head(RLP,X((bytes) List(RLP),List.nil(RLP),(bytes.head) (bytes.tail) U8.ltn(bytes.head,Nat.to_u8(128),() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,bytes.head,List.nil(U8))),RLP.decode.many(bytes.tail)),U8.ltn(bytes.head,Nat.to_u8(192),() List(RLP),RLP.split.length(128,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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// replace X with mirror(break_and2) in Maybe.default(RLP,List.head(RLP,X(() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,List.head_with_default(U8,Nat.to_u8(0),rlp.value),List.nil(U8))),RLP.decode.many(List.nil(U8))),U8.ltn(List.head_with_default(U8,Nat.to_u8(0),rlp.value),Nat.to_u8(192),() List(RLP),RLP.split.length(128,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,rlp.value,() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail)))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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// let list_length_1 = RlP.new_aux.list_length_1_identity(U8, rlp.value, Nat.to_u8(0), break_and1)
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// replace X with mirror(list_length_1) in RLP.data(X) == RLP.data(rlp.value)
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// refl
|
||||
// false :
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||||
// let list_u8 = Equal.refl<Bytes, RLP.encode.length(128,List.length(U8,rlp.value))>
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// case RLP.encode.length(128,List.length(U8,rlp.value)) as X with list_u8 : Equal(Bytes, RLP.encode.length(128,List.length(U8,rlp.value)), X) {
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// nil :
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||||
// let absurd_rlp_length = RLP.aux.17(List.length(U8,rlp.value))
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||||
// Empty.absurd!(absurd_rlp_length(list_u8))
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||||
// cons :
|
||||
// let u8_le_128 = RLP.aux.19(List.length(U8,rlp.value), X.head, X.tail, list_u8)
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||||
// replace X with mirror(u8_le_128) in Maybe.default(RLP,List.head(RLP, X(() List(RLP),List.cons(RLP,RLP.data(List.cons(U8,X.head,List.nil(U8))),RLP.decode.many(List.concat(U8,X.tail,rlp.value))),U8.ltn(X.head,Nat.to_u8(192),() List(RLP),RLP.split.length(128,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail)))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
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||||
// let u8_le_192 = RLP.aux.20(List.length(U8,rlp.value) X.head, X.tail, list_u8)
|
||||
// replace X with mirror(u8_le_192) in Maybe.default(RLP,List.head(RLP, X(() List(RLP),RLP.split.length(128,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.data(head),RLP.decode.many(tail))),RLP.split.length(192,List.cons(U8,X.head,List.concat(U8,X.tail,rlp.value)),() List(RLP),(head) (tail) List.cons(RLP,RLP.node(RLP.decode.many(head)),RLP.decode.many(tail))))),RLP.data(List.nil(U8))) == RLP.data(rlp.value)
|
||||
// let e3 = RLP.aux.15.sym(X.head, X.tail)
|
||||
//
|
||||
// ?a-282-
|
||||
// } : RLP.decode(List.concat(U8,X,rlp.value)) == RLP.data(rlp.value)
|
||||
//
|
||||
// } : RLP.decode(X(() List(U8),rlp.value,List.concat(U8,RLP.encode.length(128,List.length(U8,rlp.value)),rlp.value))) == RLP.data(rlp.value)
|
||||
|
||||
// let pf = RLP.encode_identity.go(rlp, [])
|
||||
// let e0 = RLP.aux.16(RLP.encode(rlp))
|
||||
|
||||
Loading…
Reference in New Issue
Block a user