Mercurial > hg > Members > atton > agda-proofs

annotate cbc/subtype.agda @ 77:a2e6f61d5f2b default tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add modus-ponens
author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Thu, 09 Feb 2017 06:32:03 +0000
parents f1ab418bc37f
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
52
4880184e4ab5 Define push/pop using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 51
diff changeset
1 open import Level
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
2 open import Relation.Binary.PropositionalEquality
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
3
54
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
4 module subtype {l : Level} (Context : Set l) where
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
5
52
4880184e4ab5 Define push/pop using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 51
diff changeset
6
54
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
7 record DataSegment {ll : Level} (A : Set ll) : Set (l ⊔ ll) where
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
8 field
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
9 get : Context -> A
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
10 set : Context -> A -> Context
51
16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
diff changeset
11 open DataSegment
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
12
54
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
13 data CodeSegment {l1 l2 : Level} (A : Set l1) (B : Set l2) : Set (l ⊔ l1 ⊔ l2) where
51
16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
diff changeset
14 cs : {{_ : DataSegment A}} {{_ : DataSegment B}} -> (A -> B) -> CodeSegment A B
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
15
74
f1ab418bc37f Cleanup sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 71
diff changeset
16 goto : {l1 l2 : Level} {I : Set l1} {O : Set l2} -> CodeSegment I O -> I -> O
71
614997a2e21c Define goto
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 60
diff changeset
17 goto (cs b) i = b i
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
18
55
81c6779583b6 Add push-sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 54
diff changeset
19 exec : {l1 l2 : Level} {I : Set l1} {O : Set l2} {{_ : DataSegment I}} {{_ : DataSegment O}}
81c6779583b6 Add push-sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 54
diff changeset
20 -> CodeSegment I O -> Context -> Context
52
4880184e4ab5 Define push/pop using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 51
diff changeset
21 exec {l} {{i}} {{o}} (cs b) c = set o c (b (get i c))
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
22
40
e6b965df2137 Trying define type composition using subtype through DS
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 39
diff changeset
23
54
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
24 comp : {con : Context} -> {l1 l2 l3 l4 : Level}
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
25 {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
diff changeset
26 {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
46
af1fe3bd9f1e Define code segment compose operator using type -> ds cast
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 45
diff changeset
27 -> (C -> D) -> (A -> B) -> A -> D
47
49de29c12c7b Define code segment compose operator using type -> ds cast!
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 46
diff changeset
28 comp {con} {{i}} {{io}} {{oi}} {{o}} g f x = g (get oi (set io con (f x)))
46
af1fe3bd9f1e Define code segment compose operator using type -> ds cast
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 45
diff changeset
29
54
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
30 csComp : {con : Context} -> {l1 l2 l3 l4 : Level}
60
bd428bd6b394 Trying define n-push/n-pop
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 55
diff changeset
31 {A : Set l1} {B : Set l2} {C : Set l3} {D : Set l4}
51
16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
diff changeset
32 {{_ : DataSegment A}} {{_ : DataSegment B}} {{_ : DataSegment C}} {{_ : DataSegment D}}
49
8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 48
diff changeset
33 -> 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>
parents: 48
diff changeset
34 csComp {con} {A} {B} {C} {D} {{da}} {{db}} {{dc}} {{dd}} (cs g) (cs f)
48
fe5755744071 Trying prove associativity of composition of code segments
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 47
diff changeset
35 = cs {{da}} {{dd}} (comp {con} {{da}} {{db}} {{dc}} {{dd}} g f)
42
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
36
48
fe5755744071 Trying prove associativity of composition of code segments
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 47
diff changeset
37
47
49de29c12c7b Define code segment compose operator using type -> ds cast!
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 46
diff changeset
38
54
fa95e3070138 Define SingleLinkedStack using subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 53
diff changeset
39 comp-associative : {A B C D E F : Set l} {con : Context}
51
16e27df74ec5 Split subtype definitions for reuse context
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 50
diff changeset
40 {{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
diff changeset
41 {{dd : DataSegment D}} {{de : DataSegment E}} {{df : DataSegment F}}
49
8031568638d0 Define composition of codesegment using subtype without constraint list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 48
diff changeset
42 -> (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
diff changeset
43 -> 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
diff changeset
44 comp-associative (cs _) (cs _) (cs _) = refl