annotate a02/agda/lambda.agda @ 139:3be1afb87f82

add utm
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Sat, 14 Mar 2020 17:34:54 +0900
parents 7a0634a7c25a
children b3f05cd08d24
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
138
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
1 module lambda ( T : Set) ( t : T ) where
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
2
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
3
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
4 A→A : (A : Set ) → ( A → A )
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
5 A→A = λ A → λ ( a : A ) → a
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
6
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
7 lemma2 : (A : Set ) → A → A
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
8 lemma2 A a = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
9
139
3be1afb87f82 add utm
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 138
diff changeset
10 →intro : {A B : Set } → A → B → ( A → B )
3be1afb87f82 add utm
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 138
diff changeset
11 →intro _ b = λ x → b
3be1afb87f82 add utm
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 138
diff changeset
12
3be1afb87f82 add utm
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 138
diff changeset
13 →elim : {A B : Set } → A → ( A → B ) → B
3be1afb87f82 add utm
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents: 138
diff changeset
14 →elim a f = f a
138
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
15
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
16 ex1 : {A B : Set} → Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
17 ex1 {A} {B} = ( A → B ) → A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
18
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
19 ex1' : {A B : Set} → Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
20 ex1' {A} {B} = A → B → A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
21
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
22 ex2 : {A : Set} → Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
23 ex2 {A} = A → ( A → A )
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
24
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
25 ex3 : {A B : Set} → Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
26 ex3 {A}{B} = A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
27
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
28 ex4 : {A B : Set} → Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
29 ex4 {A}{B} = A → B → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
30
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
31 ex5 : {A B : Set} → Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
32 ex5 {A}{B} = A → B → A
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
33
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
34 proof5 : {A B : Set } → ex5 {A} {B}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
35 proof5 = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
36
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
37
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
38 postulate S : Set
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
39 postulate s : S
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
40
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
41 ex6 : {A : Set} → A → S
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
42 ex6 a = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
43
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
44 ex7 : {A : Set} → A → T
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
45 ex7 a = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
46
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
47 ex11 : (A B : Set) → ( A → B ) → A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
48 ex11 = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
49
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
50 ex12 : (A B : Set) → ( A → B ) → A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
51 ex12 = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
52
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
53 ex13 : {A B : Set} → ( A → B ) → A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
54 ex13 {A} {B} = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
55
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
56 ex14 : {A B : Set} → ( A → B ) → A → B
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
57 ex14 x = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
58
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
59 proof5' : {A B : Set} → ex5 {A} {B}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
60 proof5' = {!!}
Shinji KONO <kono@ie.u-ryukyu.ac.jp>
parents:
diff changeset
61