particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} {@(tactic checking monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC #-} (continues

monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC #-} {-# BUILTIN AGDATCMRETURN returnTC #-} {-# BUILTIN AGDATCMBIND bindTC #-} The TC monad provides an interface to the Agda type checker using the following primitive operations: postulate -- metavariables in the process. unify : Term → Term → TC ⊤ -- Throw a type error. Can be caught by catchTC. typeError : ∀ {a} {A : Set a} → List ErrorPart → TC A -- Block a type checking computation on a

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} {@(tactic checking monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC #-} {-# BUILTIN

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} {@(tactic checking monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC #-} {-# BUILTIN

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} {@(tactic checking monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC #-} {-# BUILTIN

particular implicit argument using the @(tactic t) attribute, where t : Term → TC ⊤. For instance: clever-search : Term → TC ⊤ clever-search hole = unify hole (lit (nat 17)) the-best-number : {@(tactic arguments to the function: default : {A : Set} → A → Term → TC ⊤ default x hole = bindTC (quoteTC x) (unify hole) search : (depth : Nat) → Term → TC ⊤ example : {@(tactic default 10) depth : Nat} {@(tactic checking monad TC: postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B {-# BUILTIN AGDATCM TC #-} {-# BUILTIN