Mercurial > hg > Members > atton > agda-proofs

annotate cbc/named-product.agda @ 45:08b695ca359c

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Cannot compose code segments has another type signature ...
author atton <atton@cr.ie.u-ryukyu.ac.jp>
date Wed, 04 Jan 2017 08:16:02 +0000
parents 72cf35fb82af
children af1fe3bd9f1e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
1 module named-product where
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
2
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
3 open import Function
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
4 open import Data.Bool
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
5 open import Data.Nat
45
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
6 open import Data.Nat.Show
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
7 open import Data.String hiding (_++_ ; show)
41
2abf1cd97f10 Trying define type composition using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 40
diff changeset
8 open import Data.List
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
9 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
10
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
11
40
e6b965df2137 Trying define type composition using subtype through DS
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 39
diff changeset
12
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
13
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
14 record Context : Set where
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
15 field
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
16 cycle : ℕ
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
17 led : String
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
18 signature : String
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
19
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
20 record Datum (A : Set) : Set where
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
21 field
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
22 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
23 set : Context -> A -> Context
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
24
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
25
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
26 record LoopCounter : Set where
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
27 field
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
28 count : ℕ
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
29 name : String
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
30
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
31 record SignatureWithNum : Set where
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
32 field
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
33 signature : String
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
34 num : ℕ
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
35
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
36 instance
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
37 contextHasLoopCounter : Datum LoopCounter
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
38 contextHasLoopCounter = record {get = (\c -> record {count = Context.cycle c ;
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
39 name = Context.led c });
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
40 set = (\c l -> record {cycle = LoopCounter.count l;
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
41 led = LoopCounter.name l;
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
42 signature = Context.signature c})}
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
43 contextHasSignatureWithNum : Datum SignatureWithNum
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
44 contextHasSignatureWithNum = record {get = (\c -> record { signature = Context.signature c
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
45 ; num = Context.cycle c})
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
46 ;set = (\c s -> record { cycle = SignatureWithNum.num s
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
47 ; led = Context.led c
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
48 ; signature = SignatureWithNum.signature s})
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
49 }
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
50
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
51
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
52 inc : LoopCounter -> LoopCounter
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
53 inc l = record l {count = suc (LoopCounter.count l)}
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
54
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
55 firstContext : Context
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
56 firstContext = record { cycle = 3 ; led = "q" ; signature = "aaa" }
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
57
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
58 incContextCycle : {{_ : Datum LoopCounter }} -> Context -> Context
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
59 incContextCycle {{l}} c = Datum.set l c (inc (Datum.get l c))
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
60
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
61
38
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
62 equiv : incContextCycle firstContext ≡ record { cycle = 4 ; led = "q" ; signature = "aaa" }
a0ca5e29a9dc Call subtype using user-defined cast operator
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 37
diff changeset
63 equiv = refl
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
64
40
e6b965df2137 Trying define type composition using subtype through DS
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 39
diff changeset
65
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
66
41
2abf1cd97f10 Trying define type composition using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 40
diff changeset
67 data CodeSegment (A B : Set) : (List Set) -> Set where
43
0a780145c5ff Define compose operator using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 42
diff changeset
68 cs : {l : List Set} {{_ : Datum A}} {{_ : Datum B}} -> (A -> B) -> CodeSegment A B (A ∷ B ∷ l)
0a780145c5ff Define compose operator using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 42
diff changeset
69
44
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
70 basicCS : Set -> Set -> Set
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
71 basicCS A B = CodeSegment A B (A ∷ B ∷ [])
43
0a780145c5ff Define compose operator using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 42
diff changeset
72
44
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
73 csInc : basicCS LoopCounter LoopCounter
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
74 csInc = cs inc
40
e6b965df2137 Trying define type composition using subtype through DS
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 39
diff changeset
75
e6b965df2137 Trying define type composition using subtype through DS
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 39
diff changeset
76
42
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
77 exec : {I O : Set} -> {l : List Set} {{_ : Datum I}} {{_ : Datum O}} -> CodeSegment I O l -> Context -> Context
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
78 exec {l} {{i}} {{o}} (cs b) c = Datum.set o c (b (Datum.get i c))
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
79
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
80
42
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
81 equiv-exec : {l : List Set} -> incContextCycle firstContext ≡ exec (cs {l = l} inc) firstContext
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
82 equiv-exec = refl
39
d8312361afdc Call subtype using user-defined cast operator with subtype list
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 38
diff changeset
83
37
60e604972f30 Trying define codesegment using named-product with subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
84
43
0a780145c5ff Define compose operator using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 42
diff changeset
85 _◎_ : {A B C : Set} {{_ : Datum A}} {{_ : Datum B}} {{_ : Datum C}} {l ll : List Set}
0a780145c5ff Define compose operator using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 42
diff changeset
86 -> CodeSegment B C (B ∷ C ∷ l) -> CodeSegment A B (A ∷ B ∷ ll) -> CodeSegment A C (A ∷ C ∷ B ∷ (l ++ ll))
0a780145c5ff Define compose operator using list of subtype
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 42
diff changeset
87 _◎_ {A} {B} {C} {{da}} {{_}} {{dc}} {l} {ll} (cs g) (cs f) = cs {l = (B ∷ (l ++ ll))} {{da}} {{dc}} (g ∘ f)
42
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
88
f7916d13e2b1 Trying define type composition using list of subtype...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 41
diff changeset
89
44
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
90 comp-sample : CodeSegment LoopCounter LoopCounter (LoopCounter ∷ LoopCounter ∷ LoopCounter ∷ [])
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
91 comp-sample = csInc ◎ csInc
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
92
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
93 apply-sample : Context
72cf35fb82af Add composition sample
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 43
diff changeset
94 apply-sample = exec comp-sample firstContext
45
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
95
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
96
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
97 updateSignature : SignatureWithNum -> SignatureWithNum
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
98 updateSignature record { signature = signature ; num = num } = record { signature = (Data.String._++_) signature (show num ) ; num = num}
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
99
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
100 csUpdateSignature : basicCS SignatureWithNum SignatureWithNum
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
101 csUpdateSignature = cs updateSignature
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
102
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
103 comp-sample-2 : CodeSegment LoopCounter SignatureWithNum ?
08b695ca359c Cannot compose code segments has another type signature ...
atton <atton@cr.ie.u-ryukyu.ac.jp>
parents: 44
diff changeset
104 comp-sample-2 = csUpdateSignature ◎ csInc