allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. Dependent types Typing for programmers Type theory is concerned both with programming and logic function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. Dependent types Typing for programmers Type theory is concerned both with programming and logic function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. 2.1.1 Dependent types Typing for programmers Type theory is concerned both with programming function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. 2.1.1 Dependent types Typing for programmers Type theory is concerned both with programming function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. Dependent types Typing for programmers Type theory [https://ncatlab.org/nlab/show/type+theory] function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. Dependent types Typing for programmers Type theory [https://ncatlab.org/nlab/show/type+theory] function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. Dependent types Typing for programmers Type theory [https://ncatlab.org/nlab/show/type+theory] function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. Dependent types Typing for programmers Type theory [https://ncatlab.org/nlab/show/type+theory] function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. 2.1.1 Dependent types Typing for programmers Type theory is concerned both with programming function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract

allowing to prove mathematical theorems (in a constructive setting) and to run such proofs as algorithms. 2.1.1 Dependent types Typing for programmers Type theory is concerned both with programming function graph type as follows (see Anonymous modules to learn about the use of a module to bind the type arguments to Graph and inspect): module _ {a b} {A : Set a} {B : A → Set b} where data Graph (f : : ∀ x → B x) (x : A) (y : B x) : Set b where ingraph : f x ≡ y → Graph f x y inspect : (f : ∀ x → B x) (x : A) → Graph f x (f x) inspect _ _ = ingraph refl To use this on a term g v you with-abstract