fact stringlengths 6 1.53k | type stringclasses 16
values | library stringclasses 5
values | imports listlengths 1 79 | filename stringclasses 205
values | symbolic_name stringlengths 1 55 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
subst_map_binder_insertb v vs e :
subst_map (binder_insert b v vs) e =
subst' b v (subst_map (binder_delete b vs) e).
Proof. destruct b; rewrite ?subst_map_insert //. Qed. | Lemma | iris_heap_lang | [
"From stdpp Require Import gmap stringmap",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/metatheory.v | subst_map_binder_insert | |
subst_map_binder_insert_emptyb v e :
subst_map (binder_insert b v ∅) e = subst' b v e.
Proof. by rewrite subst_map_binder_insert binder_delete_empty subst_map_empty. Qed. | Lemma | iris_heap_lang | [
"From stdpp Require Import gmap stringmap",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/metatheory.v | subst_map_binder_insert_empty | |
subst_map_binder_insert_2b1 v1 b2 v2 vs e :
subst_map (binder_insert b1 v1 (binder_insert b2 v2 vs)) e =
subst' b2 v2 (subst' b1 v1 (subst_map (binder_delete b2 (binder_delete b1 vs)) e)).
Proof.
destruct b1 as [|s1], b2 as [|s2]=> /=; auto using subst_map_insert.
rewrite subst_map_insert. destruct (decide (s1 ... | Lemma | iris_heap_lang | [
"From stdpp Require Import gmap stringmap",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/metatheory.v | subst_map_binder_insert_2 | |
subst_map_binder_insert_2_emptyb1 v1 b2 v2 e :
subst_map (binder_insert b1 v1 (binder_insert b2 v2 ∅)) e =
subst' b2 v2 (subst' b1 v1 e).
Proof.
by rewrite subst_map_binder_insert_2 !binder_delete_empty subst_map_empty.
Qed. | Lemma | iris_heap_lang | [
"From stdpp Require Import gmap stringmap",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/metatheory.v | subst_map_binder_insert_2_empty | |
subst_map_is_closedX e vs :
is_closed_expr X e →
(∀ x, x ∈ X → vs !! x = None) →
subst_map vs e = e.
Proof.
revert X vs. assert (∀ x x1 x2 X (vs : gmap string val),
(∀ x, x ∈ X → vs !! x = None) →
x ∈ set_binder_insert x2 (set_binder_insert x1 X) →
binder_delete x1 (binder_delete x2 vs) !! x = None)... | Lemma | iris_heap_lang | [
"From stdpp Require Import gmap stringmap",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/metatheory.v | subst_map_is_closed | |
subst_map_is_closed_emptye vs : is_closed_expr ∅ e → subst_map vs e = e.
Proof. intros. apply subst_map_is_closed with (∅ : stringset); set_solver. Qed. | Lemma | iris_heap_lang | [
"From stdpp Require Import gmap stringmap",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/metatheory.v | subst_map_is_closed_empty | |
LitInt: Z >-> base_lit. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | LitInt | |
LitBool: bool >-> base_lit. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | LitBool | |
LitLoc: loc >-> base_lit. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | LitLoc | |
LitProphecy: proph_id >-> base_lit. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | LitProphecy | |
App: expr >-> Funclass. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | App | |
Val: val >-> expr. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Val | |
Var: string >-> expr. | Coercion | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Var | |
Lamx e := (Rec BAnon x e) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Lam | |
Letx e1 e2 := (App (Lam x e2) e1) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Let | |
Seqe1 e2 := (Let BAnon e1 e2) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Seq | |
LamVx e := (RecV BAnon x e) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | LamV | |
LetCtxx e2 := (AppRCtx (LamV x e2)) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | LetCtx | |
SeqCtxe2 := (LetCtx BAnon e2) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | SeqCtx | |
Matche0 x1 e1 x2 e2 := (Case e0 (Lam x1 e1) (Lam x2 e2)) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Match | |
Alloce := (AllocN (Val $ LitV $ LitInt 1) e) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Alloc | |
CASl e1 e2 := (Snd (CmpXchg l e1 e2)) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | CAS | |
Skip:= (App (Val $ LamV BAnon (Val $ LitV LitUnit)) (Val $ LitV LitUnit)). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | Skip | |
NONE:= (InjL (LitV LitUnit)) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | NONE | |
NONEV:= (InjLV (LitV LitUnit)) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | NONEV | |
SOMEx := (InjR x) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | SOME | |
SOMEVx := (InjRV x) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | SOMEV | |
ResolveProphe1 e2 := (Resolve Skip e1 e2) (only parsing). | Notation | iris_heap_lang | [
"From iris.program_logic Require Import language",
"From iris.heap_lang Require Export lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/notation.v | ResolveProph | |
Instancepretty_loc : Pretty loc :=
λ l, pretty l.(loc_car). | Global | iris_heap_lang | [
"From stdpp Require Export pretty",
"From iris.heap_lang Require Import lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/pretty.v | Instance | |
Instancepretty_base_lit : Pretty base_lit :=
λ l, match l with
| LitInt z => pretty z
| LitBool b => if b then "true" else "false"
| LitUnit => "()"
| LitPoison => "<poison>"
| LitLoc l => "(loc " +:+ pretty l +:+ ")"
| LitProphecy i => "(prophecy " +:+ pretty i +:+ ")"
... | Global | iris_heap_lang | [
"From stdpp Require Export pretty",
"From iris.heap_lang Require Import lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/pretty.v | Instance | |
Instancepretty_binder : Pretty binder :=
λ b, match b with
| BNamed x => x
| BAnon => "<>"
end. | Global | iris_heap_lang | [
"From stdpp Require Export pretty",
"From iris.heap_lang Require Import lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/pretty.v | Instance | |
Instancepretty_val : Pretty val :=
fix go v :=
match v with
| LitV l => "#" +:+ pretty l
| RecV f x e =>
match f with
| BNamed f => "rec: " +:+ f +:+ " " +:+ pretty x +:+ " := <body>"
| BAnon => "λ: " +:+ pretty x +:+ ", <body>"
end
| PairV v1 v2 => "(" +:+ go v1 +:+ ", " +:+ g... | Global | iris_heap_lang | [
"From stdpp Require Export pretty",
"From iris.heap_lang Require Import lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/pretty.v | Instance | |
Instancepretty_un_op : Pretty un_op :=
λ op, match op with
| NegOp => "~"
| MinusUnOp => "-"
end. | Global | iris_heap_lang | [
"From stdpp Require Export pretty",
"From iris.heap_lang Require Import lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/pretty.v | Instance | |
Instancepretty_bin_op : Pretty bin_op :=
λ op, match op with
| PlusOp => "+"
| MinusOp => "-"
| MultOp => "*"
| QuotOp => "`quot`"
| RemOp => "`rem`"
| AndOp => "&"
| OrOp => "|"
| XorOp => "`xor`"
| ShiftLOp => "<<"
| ShiftROp => ">>"
... | Global | iris_heap_lang | [
"From stdpp Require Export pretty",
"From iris.heap_lang Require Import lang",
"From iris.prelude Require Import options"
] | iris_heap_lang/pretty.v | Instance | |
heapGS_genhlc Σ := HeapGS {
heapGS_invGS : invGS_gen hlc Σ;
#[global] heapGS_gen_heapGS :: gen_heapGS loc (option val) Σ;
#[global] heapGS_inv_heapGS :: inv_heapGS loc (option val) Σ;
#[global] heapGS_proph_mapGS :: proph_mapGS proph_id (val * val) Σ;
heapGS_step_name : gname;
heapGS_step_cnt : mono_natG Σ;... | Class | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | heapGS_gen | |
ExistingInstance heapGS_step_cnt. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Existing | |
heapGS:= (heapGS_gen HasLc). | Notation | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | heapGS | |
Definitionsteps_auth (n : nat) : iProp Σ :=
mono_nat_auth_own heapGS_step_name 1 n. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Definition | |
steps_lb(n : nat) : iProp Σ :=
mono_nat_lb_own heapGS_step_name n. | Definition | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | steps_lb | |
steps_lb_0:
⊢ |==> steps_lb 0.
Proof. by apply mono_nat_lb_own_0. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | steps_lb_0 | |
Lemmasteps_lb_valid n m :
steps_auth n -∗ steps_lb m -∗ ⌜m ≤ n⌝.
Proof.
iIntros "Hauth Hlb".
by iDestruct (mono_nat_lb_own_valid with "Hauth Hlb") as %[_ Hle].
Qed. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Lemma | |
Lemmasteps_lb_get n :
steps_auth n -∗ steps_lb n.
Proof. apply mono_nat_lb_own_get. Qed. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Lemma | |
Lemmasteps_auth_update n n' :
n ≤ n' → steps_auth n ==∗ steps_auth n' ∗ steps_lb n'.
Proof. intros Hle. by apply mono_nat_own_update. Qed. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Lemma | |
Lemmasteps_auth_update_S n :
steps_auth n ==∗ steps_auth (S n).
Proof.
iIntros "Hauth".
iMod (mono_nat_own_update with "Hauth") as "[$ _]"; [lia|done].
Qed. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Lemma | |
steps_lb_len n' :
n' ≤ n → steps_lb n -∗ steps_lb n'.
Proof. intros Hle. by iApply mono_nat_lb_own_le. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | steps_lb_le | |
ProgramInstance heapGS_irisGS `{!heapGS_gen hlc Σ} : irisGS_gen hlc heap_lang Σ := {
iris_invGS := heapGS_invGS;
state_interp σ step_cnt κs _ :=
(gen_heap_interp σ.(heap) ∗ proph_map_interp κs σ.(used_proph_id) ∗
steps_auth step_cnt)%I;
fork_post _ := True%I;
num_laters_per_step n := n;
}.
Next Obligat... | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Program | |
Definitionpointsto_def `{heapGS_gen hlc Σ}
(l : loc) (dq : dfrac) (v : val) : iProp Σ :=
pointsto l dq (Some v). | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Definition | |
Definitionpointsto_aux : seal (@pointsto_def). Proof. by eexists. Qed. | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Definition | |
pointsto:= pointsto_aux.(unseal). | Definition | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto | |
Definitionpointsto_unseal :
@pointsto = @pointsto_def := pointsto_aux.(seal_eq). | Local | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Definition | |
Argumentspointsto {hlc Σ _}. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Arguments | |
inv_pointsto_own(l : loc) (v : val) (I : val → Prop) : iProp Σ :=
inv_pointsto_own l (Some v) (from_option I False). | Definition | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_pointsto_own | |
inv_pointsto(l : loc) (I : val → Prop) : iProp Σ :=
inv_pointsto l (from_option I False). | Definition | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_pointsto | |
Instance: Params (@inv_pointsto_own) 4 := {}. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instance: Params (@inv_pointsto) 3 := {}. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
inv_heap_inv:= (inv_heap_inv loc (option val)). | Notation | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_heap_inv | |
wp_lb_updates n E e Φ :
TCEq (to_val e) None →
steps_lb n -∗
WP e @ s; E {{ v, steps_lb (S n) -∗ Φ v }} -∗
WP e @ s; E {{ Φ }}.
Proof. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_lb_update | |
twp_wp_step_lcs n E e P Φ :
TCEq (to_val e) None →
steps_lb n -∗
▷^(S n) P -∗
WP e @ s; E [{ v, P -∗ £ (S n) ={E}=∗ Φ v }] -∗
WP e @ s; E {{ Φ }}.
Proof.
iIntros (?) "#Hlb HP Hwp".
iApply (twp_wp_fupdN_strong (S n) _ _ _ _ (P ∗ £ (S n))); [done|]. iSplit.
- iIntros (σ ns κ m) "(Hσ & Hκ & Hsteps)".
i... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_wp_step_lc | |
twp_wp_step_lc_texans n E e P Φ :
TCEq (to_val e) None →
steps_lb n -∗
▷ P -∗
WP e @ s; E [{ v, P -∗ £ (S n) ={E}=∗ Φ v }] -∗
WP e @ s; E {{ Φ }}.
Proof.
iIntros (?) "#Hlb HP Hwp".
iApply (twp_wp_step_lc with "[$] [HP] Hwp"); auto.
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_wp_step_lc_texan | |
wp_step_fupdN_lbs n E1 E2 e P Φ :
TCEq (to_val e) None →
E2 ⊆ E1 →
steps_lb n -∗
(|={E1∖E2,∅}=> |={∅}▷=>^(S n) |={∅,E1∖E2}=> P) -∗
WP e @ s; E2 {{ v, P ={E1}=∗ Φ v }} -∗
WP e @ s; E1 {{ Φ }}.
Proof.
iIntros (He HE) "Hlb HP Hwp".
iApply wp_step_fupdN; [done|].
iSplit; [|by iFrame].
iIntros (σ ns κs n... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_step_fupdN_lb | |
wp_rec_löbs E f x e Φ Ψ :
□ ( □ (∀ v, Ψ v -∗ WP (rec: f x := e)%V v @ s; E {{ Φ }}) -∗
∀ v, Ψ v -∗ WP (subst' x v (subst' f (rec: f x := e) e)) @ s; E {{ Φ }}) -∗
∀ v, Ψ v -∗ WP (rec: f x := e)%V v @ s; E {{ Φ }}.
Proof.
iIntros "#Hrec". iLöb as "IH". iIntros (v) "HΨ".
iApply lifting.wp_pure_step_later; fi... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_rec_löb | |
wp_forks E e Φ :
▷ WP e @ s; ⊤ {{ _, True }} -∗ ▷ Φ (LitV LitUnit) -∗ WP Fork e @ s; E {{ Φ }}.
Proof.
iIntros "He HΦ". iApply wp_lift_atomic_base_step; [done|].
iIntros (σ1 ns κ κs nt) "(?&?&Hsteps) !>"; iSplit; first by eauto with base_step.
iIntros "!>" (v2 σ2 efs Hstep) "_"; inv_base_step.
iMod (steps_aut... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_fork | |
twp_forks E e Φ :
WP e @ s; ⊤ [{ _, True }] -∗ Φ (LitV LitUnit) -∗ WP Fork e @ s; E [{ Φ }].
Proof.
iIntros "He HΦ". iApply twp_lift_atomic_base_step; [done|].
iIntros (σ1 ns κs nt) "(?&?&Hsteps) !>"; iSplit; first by eauto with base_step.
iIntros (κ v2 σ2 efs Hstep); inv_base_step.
iMod (steps_auth_update_S ... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_fork | |
Instancepointsto_timeless l dq v : Timeless (l ↦{dq} v).
Proof. rewrite pointsto_unseal. apply _. Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instancepointsto_fractional l v : Fractional (λ q, l ↦{#q} v)%I.
Proof. rewrite pointsto_unseal. apply _. Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instancepointsto_as_fractional l q v :
AsFractional (l ↦{#q} v) (λ q, l ↦{#q} v)%I q.
Proof. rewrite pointsto_unseal. apply _. Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instancepointsto_persistent l v : Persistent (l ↦□ v).
Proof. rewrite pointsto_unseal. apply _. Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instancepointsto_combine_sep_gives l dq1 dq2 v1 v2 :
CombineSepGives (l ↦{dq1} v1) (l ↦{dq2} v2) ⌜✓ (dq1 ⋅ dq2) ∧ v1 = v2⌝.
Proof.
rewrite pointsto_unseal /CombineSepGives. iIntros "[H1 H2]".
iCombine "H1 H2" gives %[? [=->]]. eauto.
Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
pointsto_combinel dq1 dq2 v1 v2 :
l ↦{dq1} v1 -∗ l ↦{dq2} v2 -∗ l ↦{dq1 ⋅ dq2} v1 ∗ ⌜v1 = v2⌝.
Proof.
rewrite pointsto_unseal.
iIntros "Hl1 Hl2". by iCombine "Hl1 Hl2" as "$" gives %[_ [= ->]].
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_combine | |
Instancepointsto_combine_as l dq1 dq2 v1 v2 :
CombineSepAs (l ↦{dq1} v1) (l ↦{dq2} v2) (l ↦{dq1 ⋅ dq2} v1) | 60. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
pointsto_validl dq v : l ↦{dq} v -∗ ⌜✓ dq⌝.
Proof. rewrite pointsto_unseal. apply pointsto_valid. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_valid | |
pointsto_valid_2l dq1 dq2 v1 v2 :
l ↦{dq1} v1 -∗ l ↦{dq2} v2 -∗ ⌜✓ (dq1 ⋅ dq2) ∧ v1 = v2⌝.
Proof. iIntros "H1 H2". iCombine "H1 H2" gives %[? [= ?]]. done. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_valid_2 | |
pointsto_agreel dq1 dq2 v1 v2 : l ↦{dq1} v1 -∗ l ↦{dq2} v2 -∗ ⌜v1 = v2⌝.
Proof. iIntros "H1 H2". iCombine "H1 H2" gives %[_ [= ?]]. done. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_agree | |
pointsto_frac_nel1 l2 dq1 dq2 v1 v2 :
¬ ✓(dq1 ⋅ dq2) → l1 ↦{dq1} v1 -∗ l2 ↦{dq2} v2 -∗ ⌜l1 ≠ l2⌝.
Proof. rewrite pointsto_unseal. apply pointsto_frac_ne. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_frac_ne | |
pointsto_nel1 l2 dq2 v1 v2 : l1 ↦ v1 -∗ l2 ↦{dq2} v2 -∗ ⌜l1 ≠ l2⌝.
Proof. rewrite pointsto_unseal. apply pointsto_ne. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_ne | |
pointsto_persistl dq v : l ↦{dq} v ==∗ l ↦□ v.
Proof. rewrite pointsto_unseal. apply pointsto_persist. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_persist | |
pointsto_unpersistl v : l ↦□ v ==∗ ∃ q, l ↦{#q} v.
Proof. rewrite pointsto_unseal. apply pointsto_unpersist. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | pointsto_unpersist | |
Instanceframe_pointsto p l v q1 q2 q :
FrameFractionalQp q1 q2 q →
Frame p (l ↦{#q1} v) (l ↦{#q2} v) (l ↦{#q} v) | 5.
Proof. apply: frame_fractional. Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instanceinv_pointsto_own_proper l v :
Proper (pointwise_relation _ iff ==> (≡)) (inv_pointsto_own l v).
Proof.
intros I1 I2 HI. rewrite /inv_pointsto_own. f_equiv=>-[w|]; last done.
simpl. apply HI.
Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
Instanceinv_pointsto_proper l :
Proper (pointwise_relation _ iff ==> (≡)) (inv_pointsto l).
Proof.
intros I1 I2 HI. rewrite /inv_pointsto. f_equiv=>-[w|]; last done.
simpl. apply HI.
Qed. | Global | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | Instance | |
make_inv_pointstol v (I : val → Prop) E :
↑inv_heapN ⊆ E →
I v →
inv_heap_inv -∗ l ↦ v ={E}=∗ l ↦_I v.
Proof.
iIntros (??) "#HI Hl". rewrite pointsto_unseal.
iApply make_inv_pointsto; done.
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | make_inv_pointsto | |
inv_pointsto_own_invl v I : l ↦_I v -∗ l ↦_I □.
Proof. apply inv_pointsto_own_inv. Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_pointsto_own_inv | |
inv_pointsto_own_acc_strongE :
↑inv_heapN ⊆ E →
inv_heap_inv ={E, E ∖ ↑inv_heapN}=∗ ∀ l v I, l ↦_I v -∗
(⌜I v⌝ ∗ l ↦ v ∗ (∀ w, ⌜I w ⌝ -∗ l ↦ w ==∗
inv_pointsto_own l w I ∗ |={E ∖ ↑inv_heapN, E}=> True)).
Proof.
iIntros (?) "#Hinv". rewrite pointsto_unseal.
iMod (inv_pointsto_own_acc_strong with "Hinv"... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_pointsto_own_acc_strong | |
inv_pointsto_own_accE l v I:
↑inv_heapN ⊆ E →
inv_heap_inv -∗ l ↦_I v ={E, E ∖ ↑inv_heapN}=∗
(⌜I v⌝ ∗ l ↦ v ∗ (∀ w, ⌜I w ⌝ -∗ l ↦ w ={E ∖ ↑inv_heapN, E}=∗ l ↦_I w)).
Proof.
iIntros (?) "#Hinv Hl". rewrite pointsto_unseal.
iMod (inv_pointsto_own_acc with "Hinv Hl") as "(% & Hl & Hclose)"; first done.
iFram... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_pointsto_own_acc | |
inv_pointsto_accl I E :
↑inv_heapN ⊆ E →
inv_heap_inv -∗ l ↦_I □ ={E, E ∖ ↑inv_heapN}=∗
∃ v, ⌜I v⌝ ∗ l ↦ v ∗ (l ↦ v ={E ∖ ↑inv_heapN, E}=∗ True).
Proof.
iIntros (?) "#Hinv Hl". rewrite pointsto_unseal.
iMod (inv_pointsto_acc with "Hinv Hl") as ([v|]) "(% & Hl & Hclose)"; [done| |done].
iIntros "!>". iExis... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | inv_pointsto_acc | |
heap_array_to_seq_metal vs (n : nat) :
length vs = n →
([∗ map] l' ↦ _ ∈ heap_array l vs, meta_token l' ⊤) -∗
[∗ list] i ∈ seq 0 n, meta_token (l +ₗ (i : nat)) ⊤.
Proof.
iIntros (<-) "Hvs". iInduction vs as [|v vs IH] forall (l)=> //=.
rewrite big_opM_union; last first.
{ apply map_disjoint_spec=> l' v1 v2 ... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | heap_array_to_seq_meta | |
heap_array_to_seq_pointstol v (n : nat) :
([∗ map] l' ↦ ov ∈ heap_array l (replicate n v), gen_heap.pointsto l' (DfracOwn 1) ov) -∗
[∗ list] i ∈ seq 0 n, (l +ₗ (i : nat)) ↦ v.
Proof.
iIntros "Hvs". iInduction n as [|n IH] forall (l); simpl.
{ done. }
rewrite big_opM_union; last first.
{ apply map_disjoint_s... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | heap_array_to_seq_pointsto | |
twp_allocN_seqs E v n :
(0 < n)%Z →
[[{ True }]] AllocN (Val $ LitV $ LitInt $ n) (Val v) @ s; E
[[{ l, RET LitV (LitLoc l); [∗ list] i ∈ seq 0 (Z.to_nat n),
(l +ₗ (i : nat)) ↦ v ∗ meta_token (l +ₗ (i : nat)) ⊤ }]].
Proof.
iIntros (Hn Φ) "_ HΦ". iApply twp_lift_atomic_base_step_no_fork; first done.
iInt... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_allocN_seq | |
wp_allocN_seqs E v n :
(0 < n)%Z →
{{{ True }}} AllocN (Val $ LitV $ LitInt $ n) (Val v) @ s; E
{{{ l, RET LitV (LitLoc l); [∗ list] i ∈ seq 0 (Z.to_nat n),
(l +ₗ (i : nat)) ↦ v ∗ meta_token (l +ₗ (i : nat)) ⊤ }}}.
Proof.
iIntros (Hn Φ) "_ HΦ". iApply (twp_wp_step with "HΦ").
iApply twp_allocN_seq; [by ... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_allocN_seq | |
wp_allocN_seq_lcs E v n n' :
(0 < n)%Z →
{{{ steps_lb n' }}} AllocN (Val $ LitV $ LitInt $ n) (Val v) @ s; E
{{{ l, RET LitV (LitLoc l); ([∗ list] i ∈ seq 0 (Z.to_nat n),
(l +ₗ (i : nat)) ↦ v ∗ meta_token (l +ₗ (i : nat)) ⊤) ∗ £ (S n') }}}.
Proof.
iIntros (Hn Φ) "#? HΦ". iApply (twp_wp_step_lc_texan with ... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_allocN_seq_lc | |
twp_allocs E v :
[[{ True }]]
Alloc (Val v) @ s; E
[[{ l, RET LitV (LitLoc l); l ↦ v ∗ meta_token l ⊤ }]].
Proof.
iIntros (Φ) "_ HΦ". iApply twp_allocN_seq; [auto with lia..|].
iIntros (l) "/= (? & _)". rewrite Loc.add_0. iApply "HΦ"; iFrame.
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_alloc | |
wp_allocs E v :
{{{ True }}}
Alloc (Val v) @ s; E
{{{ l, RET LitV (LitLoc l); l ↦ v ∗ meta_token l ⊤ }}}.
Proof.
iIntros (Φ) "_ HΦ". iApply (twp_wp_step with "HΦ").
iApply twp_alloc; [by auto..|]; iIntros (l) "H HΦ". by iApply "HΦ".
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_alloc | |
wp_alloc_lcs E v n :
{{{ steps_lb n }}}
Alloc (Val v) @ s; E
{{{ l, RET LitV (LitLoc l); l ↦ v ∗ meta_token l ⊤ ∗ £ (S n) }}}.
Proof.
iIntros (Φ) "#? HΦ". iApply (twp_wp_step_lc_texan with "[$] HΦ").
iApply twp_alloc; [by auto..|]; iIntros (l) "[??] HΦ ? !>".
iApply "HΦ"; iFrame.
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_alloc_lc | |
twp_frees E l v :
[[{ l ↦ v }]] Free (Val $ LitV $ LitLoc l) @ s; E
[[{ RET LitV LitUnit; True }]].
Proof.
iIntros (Φ) "Hl HΦ". iApply twp_lift_atomic_base_step_no_fork; first done.
iIntros (σ1 ns κs nt) "(Hσ & Hκs & Hsteps) !>".
rewrite pointsto_unseal. iDestruct (gen_heap_valid with "Hσ Hl") as %?.
iSplit... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_free | |
wp_frees E l v :
{{{ ▷ l ↦ v }}} Free (Val $ LitV (LitLoc l)) @ s; E
{{{ RET LitV LitUnit; True }}}.
Proof.
iIntros (Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_free with "H"); [by auto..|]; iIntros "H HΦ". by iApply "HΦ".
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_free | |
wp_free_lcs E l v n :
{{{ steps_lb n ∗ ▷ l ↦ v }}} Free (Val $ LitV (LitLoc l)) @ s; E
{{{ RET LitV LitUnit; £ (S n) }}}.
Proof.
iIntros (Φ) "[#? >H] HΦ". iApply (twp_wp_step_lc_texan with "[$] HΦ").
iApply (twp_free with "H"); [by auto..|]; iIntros "H HΦ ? !>". by iApply "HΦ".
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_free_lc | |
twp_loads E l dq v :
[[{ l ↦{dq} v }]] Load (Val $ LitV $ LitLoc l) @ s; E [[{ RET v; l ↦{dq} v }]].
Proof.
iIntros (Φ) "Hl HΦ". iApply twp_lift_atomic_base_step_no_fork; first done.
iIntros (σ1 ns κs nt) "(Hσ & Hκs & Hsteps) !>".
rewrite pointsto_unseal. iDestruct (gen_heap_valid with "Hσ Hl") as %?.
iSplit;... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_load | |
wp_loads E l dq v :
{{{ ▷ l ↦{dq} v }}} Load (Val $ LitV $ LitLoc l) @ s; E {{{ RET v; l ↦{dq} v }}}.
Proof.
iIntros (Φ) ">H HΦ". iApply (twp_wp_step with "HΦ").
iApply (twp_load with "H"). iIntros "H HΦ". by iApply "HΦ".
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_load | |
wp_load_lcs E l dq v n :
{{{ steps_lb n ∗ ▷ l ↦{dq} v }}}
Load (Val $ LitV $ LitLoc l) @ s; E
{{{ RET v; l ↦{dq} v ∗ £ (S n) }}}.
Proof.
iIntros (Φ) "[#? >H] HΦ". iApply (twp_wp_step_lc_texan with "[$] HΦ").
iApply (twp_load with "H"). iIntros "H HΦ ? !>". iApply "HΦ"; iFrame.
Qed. | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | wp_load_lc | |
twp_stores E l v' v :
[[{ l ↦ v' }]] Store (Val $ LitV $ LitLoc l) (Val v) @ s; E
[[{ RET LitV LitUnit; l ↦ v }]].
Proof.
iIntros (Φ) "Hl HΦ". iApply twp_lift_atomic_base_step_no_fork; first done.
iIntros (σ1 ns κs nt) "(Hσ & Hκs & Hsteps) !>".
rewrite pointsto_unseal. iDestruct (gen_heap_valid with "Hσ Hl") ... | Lemma | iris_heap_lang | [
"From iris.proofmode Require Import proofmode",
"From iris.bi.lib Require Import fractional",
"From iris.base_logic.lib Require Import mono_nat",
"From iris.base_logic.lib Require Export gen_heap proph_map gen_inv_heap",
"From iris.program_logic Require Export weakestpre total_weakestpre",
"From iris.prog... | iris_heap_lang/primitive_laws.v | twp_store |
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