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From stdpp Require Export coPset.
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From iris.bi Require Import interface derived_connectives.
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From iris.prelude Require Import options.
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Declare Scope expr_scope.
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Delimit Scope expr_scope with E.
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Declare Scope val_scope.
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Delimit Scope val_scope with V.
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Inductive stuckness := NotStuck | MaybeStuck.
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Definition stuckness_leb (s1 s2 : stuckness) : bool :=
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match s1, s2 with
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| MaybeStuck, NotStuck => false
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| _, _ => true
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end.
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Global Instance stuckness_le : SqSubsetEq stuckness := stuckness_leb.
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Global Instance stuckness_le_po : PreOrder stuckness_le.
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Proof. split; by repeat intros []. Qed.
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Class Swp (PROP EXPR VAL A : Type) :=
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wp : A → coPset → coPset → EXPR → (VAL → PROP) → PROP.
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Global Arguments wp {_ _ _ _ _} _ _ _ _%E _%I.
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Global Instance: Params (@wp) 9 := {}.
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Notation "'WP' e @ s ; E1 ; E2 {{ Φ } }" := (wp s E1 E2 e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e @ E1 ; E2 {{ Φ } }" := (wp NotStuck E1 E2 e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e @ E1 ; E2 ? {{ Φ } }" := (wp MaybeStuck E1 E2 e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e @ s ; E1 {{ Φ } }" := (wp s E1 E1 e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e @ E1 {{ Φ } }" := (wp NotStuck E1 E1 e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e @ E1 ? {{ Φ } }" := (wp MaybeStuck E1 E1 e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e {{ Φ } }" := (wp NotStuck ⊤ ⊤ e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e ? {{ Φ } }" := (wp MaybeStuck ⊤ ⊤ e%E Φ)
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(at level 20, e, Φ at level 200, only parsing) : bi_scope.
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Notation "'WP' e @ s ; E1 ; E2 {{ v , Q } }" := (wp s E1 E2 e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' @ '[' s ; '/' E1 ; '/' E2 ']' '/' {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e @ E1 ; E2 {{ v , Q } }" := (wp NotStuck E1 E2 e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' @ '[' E1 ; '/' E2 ']' '/' {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e @ E1 ; E2 ? {{ v , Q } }" := (wp MaybeStuck E1 E2 e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' @ '[' E1 ; '/' E2 ']' '/' ? {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e @ s ; E {{ v , Q } }" := (wp s E E e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' @ '[' s ; '/' E ']' '/' {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e @ E {{ v , Q } }" := (wp NotStuck E E e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' @ E '/' {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e @ E ? {{ v , Q } }" := (wp MaybeStuck E E e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' @ E '/' ? {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e {{ v , Q } }" := (wp NotStuck ⊤ ⊤ e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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Notation "'WP' e ? {{ v , Q } }" := (wp MaybeStuck ⊤ ⊤ e%E (λ v, Q))
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(at level 20, e, Q at level 200,
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format "'[hv' 'WP' e '/' ? {{ '[' v , '/' Q ']' } } ']'") : bi_scope.
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