unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. _∈_ : ∀ {i} {A} → List i A → Lang i i A → Bool [] ∈ a = ν a (x ∷ w) ∈ a = w ∈ δ a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. __ : {i} {A} → List i A → Lang i A A → Bool [] a = ? a (x w) a = w ? a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular, non-sized

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. __ : {i} {A} → List i A → Lang i A A → Bool [] a = ? a (x w) a = w ? a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular, non-sized

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. _∈_ : ∀ {i} {A} → List i A → Lang i i A → Bool [] ∈ a = ν a (x ∷ w) ∈ a = w ∈ δ a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. __ : {i} {A} → List i A → Lang i A A → Bool [] a = ? a (x w) a = w ? a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular, non-sized

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. _∈_ : ∀ {i} {A} → List i A → Lang i i A → Bool [] ∈ a = ν a (x ∷ w) ∈ a = w ∈ δ a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular

call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. _∈_ : ∀ {i} {A} → List i A → Lang i i A → Bool [] ∈ a = ν a (x ∷ w) ∈ a = w ∈ δ a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular, followed by “false”, and viceversa. bip-bop = (⟦ true ⟧ · ⟦ false ⟧)* We can now test words for membership in the language bip-bop test₁ : (true ∷ false ∷ true ∷ false ∷ true ∷ false ∷ []) ∈ bip-bop ≡

Types 73 Agda Documentation, Release 2.5.2 Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. __ : {i} {A} → List i A → Lang i A A → Bool [] a = ? a (x w) a = w ? a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular, non-sized is followed by “false”, and viceversa. bip-bop = ( true · false )* We can now test words for membership in the language bip-bop test1 : (true false true false true false []) bip-bop true test1 = refl

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. _∈_ : ∀ {i} {A} → List i A → Lang i i A → Bool [] ∈ a = ν a (x ∷ w) ∈ a = w ∈ δ a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular

unsquash x = proof x Example 3. We can define the subset of x : A satisfying P x with irrelevant membership certificates. record Subset (A : Set) (P : A -> Set) : Set where constructor _#_ field elem call to a * under a function call to _·_. Testing First, we want to give a precise notion of membership in a language. We consider a word as a List of characters. _∈_ : ∀ {i} {A} → List i A → Lang i i A → Bool [] ∈ a = ν a (x ∷ w) ∈ a = w ∈ δ a x Note how the size of the word we test for membership cannot be larger than the depth to which the language tree is defined. If we want to use regular