Mercurial > hg > Members > kono > Proof > automaton
diff a02/agda/lambda.agda @ 138:7a0634a7c25a
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Wed, 18 Dec 2019 17:34:15 +0900 |
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children | 3be1afb87f82 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/a02/agda/lambda.agda Wed Dec 18 17:34:15 2019 +0900 @@ -0,0 +1,56 @@ +module lambda ( T : Set) ( t : T ) where + + +A→A : (A : Set ) → ( A → A ) +A→A = λ A → λ ( a : A ) → a + +lemma2 : (A : Set ) → A → A +lemma2 A a = {!!} + + +ex1 : {A B : Set} → Set +ex1 {A} {B} = ( A → B ) → A → B + +ex1' : {A B : Set} → Set +ex1' {A} {B} = A → B → A → B + +ex2 : {A : Set} → Set +ex2 {A} = A → ( A → A ) + +ex3 : {A B : Set} → Set +ex3 {A}{B} = A → B + +ex4 : {A B : Set} → Set +ex4 {A}{B} = A → B → B + +ex5 : {A B : Set} → Set +ex5 {A}{B} = A → B → A + +proof5 : {A B : Set } → ex5 {A} {B} +proof5 = {!!} + + +postulate S : Set +postulate s : S + +ex6 : {A : Set} → A → S +ex6 a = {!!} + +ex7 : {A : Set} → A → T +ex7 a = {!!} + +ex11 : (A B : Set) → ( A → B ) → A → B +ex11 = {!!} + +ex12 : (A B : Set) → ( A → B ) → A → B +ex12 = {!!} + +ex13 : {A B : Set} → ( A → B ) → A → B +ex13 {A} {B} = {!!} + +ex14 : {A B : Set} → ( A → B ) → A → B +ex14 x = {!!} + +proof5' : {A B : Set} → ex5 {A} {B} +proof5' = {!!} +