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annotate cbc/subtype.agda @ 54:fa95e3070138

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Define SingleLinkedStack using subtype
author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Wed, 11 Jan 2017 10:56:13 +0000
parents 6af88ee5c4ca
children 81c6779583b6
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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4880184e4ab5 Define push/pop using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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1 open import Level
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a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
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2 open import Relation.Binary.PropositionalEquality
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
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fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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4 module subtype {l : Level} (Context : Set l) where
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60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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4880184e4ab5 Define push/pop using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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7 record DataSegment {ll : Level} (A : Set ll) : Set (l ⊔ ll) where
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d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
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8 field
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
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9 get : Context -> A
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
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10 set : Context -> A -> Context
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16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
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11 open DataSegment
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a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
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fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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13 data CodeSegment {l1 l2 : Level} (A : Set l1) (B : Set l2) : Set (l ⊔ l1 ⊔ l2) where
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16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
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14 cs : {{_ : DataSegment A}} {{_ : DataSegment B}} -> (A -> B) -> CodeSegment A B
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60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
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6af88ee5c4ca Prune level
atton <atton@cr.ie.u-ryukyu.ac.jp>
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17 exec : {I O : Set} {{_ : DataSegment I}} {{_ : DataSegment O}} -> CodeSegment I O -> Context -> Context
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4880184e4ab5 Define push/pop using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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18 exec {l} {{i}} {{o}} (cs b) c = set o c (b (get i c))
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60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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e6b965df2137 Trying define type composition using subtype through DS
atton <atton@cr.ie.u-ryukyu.ac.jp>
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fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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21 comp : {con : Context} -> {l1 l2 l3 l4 : Level}
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
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22 {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
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23 {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
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af1fe3bd9f1e Define code segment compose operator using type -> ds cast
atton <atton@cr.ie.u-ryukyu.ac.jp>
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24 -> (C -> D) -> (A -> B) -> A -> D
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49de29c12c7b Define code segment compose operator using type -> ds cast!
atton <atton@cr.ie.u-ryukyu.ac.jp>
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25 comp {con} {{i}} {{io}} {{oi}} {{o}} g f x = g (get oi (set io con (f x)))
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af1fe3bd9f1e Define code segment compose operator using type -> ds cast
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 45
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fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
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27 csComp : {con : Context} -> {l1 l2 l3 l4 : Level}
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
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28 {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
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16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
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29 {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
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8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 48
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30 -> CodeSegment C D -> CodeSegment A B -> CodeSegment A D
8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
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31 csComp {con} {A} {B} {C} {D} {{da}} {{db}} {{dc}} {{dd}} (cs g) (cs f)
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fe5755744071 Trying prove associativity of composition of code segments
atton <atton@cr.ie.u-ryukyu.ac.jp>
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32 = cs {{da}} {{dd}} (comp {con} {{da}} {{db}} {{dc}} {{dd}} g f)
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f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
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fe5755744071 Trying prove associativity of composition of code segments
atton <atton@cr.ie.u-ryukyu.ac.jp>
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49de29c12c7b Define code segment compose operator using type -> ds cast!
atton <atton@cr.ie.u-ryukyu.ac.jp>
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fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
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36 comp-associative : {A B C D E F : Set l} {con : Context}
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16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
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37 {{da : DataSegment A}} {{db : DataSegment B}} {{dc : DataSegment C}}
16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
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38 {{dd : DataSegment D}} {{de : DataSegment E}} {{df : DataSegment F}}
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8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 48
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39 -> (a : CodeSegment A B) (b : CodeSegment C D) (c : CodeSegment E F)
8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 48
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40 -> csComp {con} c (csComp {con} b a) ≡ csComp {con} (csComp {con} c b) a
8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 48
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41 comp-associative (cs _) (cs _) (cs _) = refl