<commit_before>------------------------------------------------------------------------------
-- Logical constants
------------------------------------------------------------------------------

module Common.LogicalConstants where

-- This module just exported all the logical constants.

------------------------------------------------------------------------------
-- The logical connectives

-- The logical connectives are hard-coded in our translation,
-- i.e. the symbols ⊥, ⊤, ¬, ∧, ∨, →, and ↔ must be used.
-- For the implication we use the Agda function type.
open import Common.Data.Empty public using ( ⊥ ; ⊥-elim )
open import Common.Data.Product public using ( _∧_ ; _,_ ; ∧-proj₁ ; ∧-proj₂ )
open import Common.Data.Sum public using ( _∨_ ; [_,_] ; inj₁ ; inj₂ )
open import Common.Data.Unit public using ( ⊤ )
open import Common.Relation.Nullary public using ( ¬_ )

infixr 2 _↔_

_↔_ : Set → Set → Set
P ↔ Q = (P → Q) ∧ (Q → P)

------------------------------------------------------------------------------
-- The quantifiers

-- The existential quantifier
-- The existential quantifier is hard-coded in our translation,
-- i.e. the symbol ∃ must be used.

open import Common.Data.Product public using ( _,_ ; ∃ ; ∃-proj₁ ; ∃-proj₂ )

-- The universal quantifier
-- For the universal quantifier we use the Agda (dependent) function type.<commit_msg>Added doc.<commit_after>------------------------------------------------------------------------------
-- Logical constants
------------------------------------------------------------------------------

module Common.LogicalConstants where

-- This module just exported all the logical constants.

------------------------------------------------------------------------------
-- The propositional logical connectives

-- The logical connectives are hard-coded in our translation,
-- i.e. the symbols ⊥, ⊤, ¬, ∧, ∨, →, and ↔ must be used.
-- N.B. For the implication we use the Agda function type.
open import Common.Data.Empty public using ( ⊥ ; ⊥-elim )
open import Common.Data.Product public using ( _∧_ ; _,_ ; ∧-proj₁ ; ∧-proj₂ )
open import Common.Data.Sum public using ( _∨_ ; [_,_] ; inj₁ ; inj₂ )
open import Common.Data.Unit public using ( ⊤ )
open import Common.Relation.Nullary public using ( ¬_ )

infixr 2 _↔_

_↔_ : Set → Set → Set
P ↔ Q = (P → Q) ∧ (Q → P)

------------------------------------------------------------------------------
-- The quantifiers

-- The existential quantifier
-- The existential quantifier is hard-coded in our translation,
-- i.e. the symbol ∃ must be used.

open import Common.Data.Product public using ( _,_ ; ∃ ; ∃-proj₁ ; ∃-proj₂ )

-- The universal quantifier
-- N.B. For the universal quantifier we use the Agda (dependent)
-- function type.
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{'dir': 'git-commits-cleaned', 'id': '6591318', 'n_tokens_mistral': 797, 'n_tokens_neox': 738, 'n_words': 291}