Mercurial > hg > Members > atton > agda-proofs
comparison cbc/subtype.agda @ 50:ccb34e3f1514
Rename named-product to subtype
author | atton <atton@cr.ie.u-ryukyu.ac.jp> |
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date | Tue, 10 Jan 2017 01:40:55 +0000 |
parents | cbc/named-product.agda@8031568638d0 |
children | 16e27df74ec5 |
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49:8031568638d0 | 50:ccb34e3f1514 |
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1 module subtype where | 1 module subtype where |
2 | 2 |
3 open import Level | |
4 open import Function | |
5 open import Data.Nat hiding (_⊔_) | |
6 open import Data.Bool | 3 open import Data.Bool |
4 open import Data.Nat | |
5 open import Data.Nat.Show | |
6 open import Data.String hiding (_++_ ; show ; toList ; fromList) | |
7 open import Data.List | |
8 open import Data.AVL.Sets | |
9 open import Relation.Binary.PropositionalEquality | |
7 | 10 |
8 data DataSegment (X : Set -> Set) : Set₁ where | |
9 ds : {x : Set} -> X x -> DataSegment X | |
10 | |
11 | |
12 record DS1 (A : Set) : Set where | |
13 field | |
14 counter : A -> ℕ | |
15 | |
16 record DS2 (A : Set) : Set where | |
17 field | |
18 useSum : A -> Bool | |
19 | 11 |
20 record Context : Set where | 12 record Context : Set where |
21 field | 13 field |
22 loopCounter : ℕ | 14 cycle : ℕ |
23 flag : Bool | 15 led : String |
16 signature : String | |
17 | |
18 record Datum (A : Set) : Set where | |
19 field | |
20 get : Context -> A | |
21 set : Context -> A -> Context | |
22 open Datum | |
23 | |
24 record LoopCounter : Set where | |
25 field | |
26 count : ℕ | |
27 name : String | |
28 | |
29 record SignatureWithNum : Set where | |
30 field | |
31 signature : String | |
32 num : ℕ | |
24 | 33 |
25 instance | 34 instance |
26 ds1 : DS1 Context | 35 contextHasLoopCounter : Datum LoopCounter |
27 ds1 = record {counter = Context.loopCounter} | 36 contextHasLoopCounter = record {get = (\c -> record {count = Context.cycle c ; |
37 name = Context.led c }); | |
38 set = (\c l -> record {cycle = LoopCounter.count l; | |
39 led = LoopCounter.name l; | |
40 signature = Context.signature c})} | |
41 contextHasSignatureWithNum : Datum SignatureWithNum | |
42 contextHasSignatureWithNum = record {get = (\c -> record { signature = Context.signature c | |
43 ; num = Context.cycle c}) | |
44 ;set = (\c s -> record { cycle = SignatureWithNum.num s | |
45 ; led = Context.led c | |
46 ; signature = SignatureWithNum.signature s}) | |
47 } | |
28 | 48 |
29 hoge : Context -> {{ins : DS1 Context}} -> DataSegment DS1 | 49 |
30 hoge _ {{i}} = ds i | 50 inc : LoopCounter -> LoopCounter |
51 inc l = record l {count = suc (LoopCounter.count l)} | |
52 | |
53 firstContext : Context | |
54 firstContext = record { cycle = 3 ; led = "q" ; signature = "aaa" } | |
55 | |
56 | |
57 incContextCycle : {{_ : Datum LoopCounter }} -> Context -> Context | |
58 incContextCycle {{l}} c = Datum.set l c (inc (Datum.get l c)) | |
59 | |
60 | |
61 equiv : incContextCycle firstContext ≡ record { cycle = 4 ; led = "q" ; signature = "aaa" } | |
62 equiv = refl | |
63 | |
64 | |
65 data CodeSegment (A B : Set) : Set where | |
66 cs : {{_ : Datum A}} {{_ : Datum B}} -> (A -> B) -> CodeSegment A B | |
67 | |
68 BasicCS : Set -> Set -> Set | |
69 BasicCS A B = CodeSegment A B | |
70 | |
71 | |
72 exec : {I O : Set} {{_ : Datum I}} {{_ : Datum O}} -> CodeSegment I O -> Context -> Context | |
73 exec {l} {{i}} {{o}} (cs b) c = Datum.set o c (b (get i c)) | |
74 | |
75 | |
76 comp : {con : Context} -> {A B C D : Set} {{_ : Datum A}} {{_ : Datum B}} {{_ : Datum C}} {{_ : Datum D}} | |
77 -> (C -> D) -> (A -> B) -> A -> D | |
78 comp {con} {{i}} {{io}} {{oi}} {{o}} g f x = g (get oi (set io con (f x))) | |
79 | |
80 | |
81 csInc : BasicCS LoopCounter LoopCounter | |
82 csInc = cs inc | |
83 | |
84 | |
85 | |
86 equiv-exec : {l : List Set} -> incContextCycle firstContext ≡ exec csInc firstContext | |
87 equiv-exec = refl | |
88 | |
89 | |
90 csComp : {con : Context} {A B C D : Set} {{_ : Datum A}} {{_ : Datum B}} {{_ : Datum C}} {{_ : Datum D}} | |
91 -> CodeSegment C D -> CodeSegment A B -> CodeSegment A D | |
92 csComp {con} {A} {B} {C} {D} {{da}} {{db}} {{dc}} {{dd}} (cs g) (cs f) | |
93 = cs {{da}} {{dd}} (comp {con} {{da}} {{db}} {{dc}} {{dd}} g f) | |
94 | |
95 comp-sample : {c : Context} -> CodeSegment LoopCounter LoopCounter | |
96 comp-sample {c} = (csComp {c} csInc csInc) | |
97 | |
98 | |
99 apply-sample : Context | |
100 apply-sample = exec (comp-sample {firstContext}) firstContext | |
31 | 101 |
32 | 102 |
33 | 103 |
34 data CodeSegment (I O : (Set -> Set)) : Set₁ where | 104 updateSignature : SignatureWithNum -> SignatureWithNum |
35 cs : (DataSegment I -> DataSegment O) -> CodeSegment I O | 105 updateSignature record { signature = signature ; num = num } = record { signature = (Data.String._++_) signature (show num ) ; num = num} |
106 | |
107 | |
108 csUpdateSignature : BasicCS SignatureWithNum SignatureWithNum | |
109 csUpdateSignature = cs updateSignature | |
110 | |
111 | |
112 | |
113 comp-sample-2 : {c : Context} -> CodeSegment LoopCounter SignatureWithNum | |
114 comp-sample-2 {c} = csComp {c} csUpdateSignature csInc | |
115 | |
116 apply-sample-2 : Context | |
117 apply-sample-2 = exec (comp-sample-2 {firstContext}) firstContext | |
118 | |
119 | |
120 | |
121 comp-associative : {A B C D E F : Set} {con : Context} | |
122 {{da : Datum A}} {{db : Datum B}} {{dc : Datum C}} {{dd : Datum D}} {{de : Datum E}} {{df : Datum F}} | |
123 -> (a : CodeSegment A B) (b : CodeSegment C D) (c : CodeSegment E F) | |
124 -> csComp {con} c (csComp {con} b a) ≡ csComp {con} (csComp {con} c b) a | |
125 comp-associative (cs _) (cs _) (cs _) = refl |