mirror of
https://github.com/achlipala/frap.git
synced 2024-11-10 00:07:51 +00:00
EvaluationContexts: factored step0 into step0 and step1
This commit is contained in:
Adam Chlipala
parent
415aa99b88
commit
544e7fa500
1 changed files with 90 additions and 58 deletions
|
|
@ -978,38 +978,45 @@ Module StlcMutable.
|
||||||
|
|
||||||
Definition valuation := fmap var exp.
|
Definition valuation := fmap var exp.
|
||||||
|
|
||||||
Inductive step0 : valuation * exp -> valuation * exp -> Prop :=
|
Inductive step0 : exp -> exp -> Prop :=
|
||||||
| Beta : forall env x e v,
|
| Beta : forall x e v,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, App (Abs x e) v) (env, subst v x e)
|
-> step0 (App (Abs x e) v) (subst v x e)
|
||||||
| Add : forall env n1 n2,
|
| Add : forall n1 n2,
|
||||||
step0 (env, Plus (Const n1) (Const n2)) (env, Const (n1 + n2))
|
step0 (Plus (Const n1) (Const n2)) (Const (n1 + n2))
|
||||||
| FstPair : forall env v1 v2,
|
| FstPair : forall v1 v2,
|
||||||
value v1
|
value v1
|
||||||
-> value v2
|
-> value v2
|
||||||
-> step0 (env, Fst (Pair v1 v2)) (env, v1)
|
-> step0 (Fst (Pair v1 v2)) v1
|
||||||
| SndPair : forall env v1 v2,
|
| SndPair : forall v1 v2,
|
||||||
value v1
|
value v1
|
||||||
-> value v2
|
-> value v2
|
||||||
-> step0 (env, Snd (Pair v1 v2)) (env, v2)
|
-> step0 (Snd (Pair v1 v2)) v2
|
||||||
| MatchInl : forall env v x1 e1 x2 e2,
|
| MatchInl : forall v x1 e1 x2 e2,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, Match (Inl v) x1 e1 x2 e2) (env, subst v x1 e1)
|
-> step0 (Match (Inl v) x1 e1 x2 e2) (subst v x1 e1)
|
||||||
| MatchInr : forall env v x1 e1 x2 e2,
|
| MatchInr : forall v x1 e1 x2 e2,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, Match (Inr v) x1 e1 x2 e2) (env, subst v x2 e2)
|
-> step0 (Match (Inr v) x1 e1 x2 e2) (subst v x2 e2).
|
||||||
|
|
||||||
|
(* We build an intermediate relation on top of [step0], allowing for
|
||||||
|
* consultation of the mutable-variable valuation. *)
|
||||||
|
Inductive step1 : valuation * exp -> valuation * exp -> Prop :=
|
||||||
|
| Lift : forall env e1 e2,
|
||||||
|
step0 e1 e2
|
||||||
|
-> step1 (env, e1) (env, e2)
|
||||||
| Read : forall env x v,
|
| Read : forall env x v,
|
||||||
env $? x = Some v
|
env $? x = Some v
|
||||||
-> step0 (env, GetVar x) (env, v)
|
-> step1 (env, GetVar x) (env, v)
|
||||||
| Overwrite : forall env x v,
|
| Overwrite : forall env x v,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, SetVar x v) (env $+ (x, v), v).
|
-> step1 (env, SetVar x v) (env $+ (x, v), v).
|
||||||
|
|
||||||
Inductive step : valuation * exp -> valuation * exp -> Prop :=
|
Inductive step : valuation * exp -> valuation * exp -> Prop :=
|
||||||
| StepRule : forall C env1 e1 env2 e2 e1' e2',
|
| StepRule : forall C env1 e1 env2 e2 e1' e2',
|
||||||
plug C e1 e1'
|
plug C e1 e1'
|
||||||
-> plug C e2 e2'
|
-> plug C e2 e2'
|
||||||
-> step0 (env1, e1) (env2, e2)
|
-> step1 (env1, e1) (env2, e2)
|
||||||
-> step (env1, e1') (env2, e2').
|
-> step (env1, e1') (env2, e2').
|
||||||
|
|
||||||
Definition trsys_of (env : valuation) (e : exp) := {|
|
Definition trsys_of (env : valuation) (e : exp) := {|
|
||||||
|
|
@ -1074,7 +1081,7 @@ Module StlcMutable.
|
||||||
-> hasty M G e t
|
-> hasty M G e t
|
||||||
-> hasty M G (SetVar x e) t.
|
-> hasty M G (SetVar x e) t.
|
||||||
|
|
||||||
Local Hint Constructors value plug step0 step hasty : core.
|
Local Hint Constructors value plug step0 step1 step hasty : core.
|
||||||
|
|
||||||
(* Let's characterize what makes a typing context and a variable valuation
|
(* Let's characterize what makes a typing context and a variable valuation
|
||||||
* compatible. *)
|
* compatible. *)
|
||||||
|
|
@ -1188,8 +1195,18 @@ Module StlcMutable.
|
||||||
|
|
||||||
Local Hint Immediate compatible_hasty : core.
|
Local Hint Immediate compatible_hasty : core.
|
||||||
|
|
||||||
Lemma preservation0_exp : forall M env1 e1 env2 e2,
|
Lemma preservation0 : forall M e1 e2,
|
||||||
step0 (env1, e1) (env2, e2)
|
step0 e1 e2
|
||||||
|
-> forall t, hasty M $0 e1 t
|
||||||
|
-> hasty M $0 e2 t.
|
||||||
|
Proof.
|
||||||
|
invert 1; t.
|
||||||
|
Qed.
|
||||||
|
|
||||||
|
Local Hint Resolve preservation0 : core.
|
||||||
|
|
||||||
|
Lemma preservation1_exp : forall M env1 e1 env2 e2,
|
||||||
|
step1 (env1, e1) (env2, e2)
|
||||||
-> forall t, hasty M $0 e1 t
|
-> forall t, hasty M $0 e1 t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> hasty M $0 e2 t.
|
-> hasty M $0 e2 t.
|
||||||
|
|
@ -1197,8 +1214,8 @@ Module StlcMutable.
|
||||||
invert 1; t.
|
invert 1; t.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Lemma preservation0_env : forall M env1 e1 env2 e2,
|
Lemma preservation1_env : forall M env1 e1 env2 e2,
|
||||||
step0 (env1, e1) (env2, e2)
|
step1 (env1, e1) (env2, e2)
|
||||||
-> forall t, hasty M $0 e1 t
|
-> forall t, hasty M $0 e1 t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> compatible M env2.
|
-> compatible M env2.
|
||||||
|
|
@ -1206,12 +1223,12 @@ Module StlcMutable.
|
||||||
invert 1; t.
|
invert 1; t.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Local Hint Resolve preservation0_exp preservation0_env : core.
|
Local Hint Resolve preservation1_exp preservation1_env : core.
|
||||||
|
|
||||||
Lemma preservation'_exp : forall M C e1 e1',
|
Lemma preservation'_exp : forall M C e1 e1',
|
||||||
plug C e1 e1'
|
plug C e1 e1'
|
||||||
-> forall e2 e2' t env1 env2, plug C e2 e2'
|
-> forall e2 e2' t env1 env2, plug C e2 e2'
|
||||||
-> step0 (env1, e1) (env2, e2)
|
-> step1 (env1, e1) (env2, e2)
|
||||||
-> hasty M $0 e1' t
|
-> hasty M $0 e1' t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> hasty M $0 e2' t.
|
-> hasty M $0 e2' t.
|
||||||
|
|
@ -1223,7 +1240,7 @@ Module StlcMutable.
|
||||||
|
|
||||||
Lemma preservation'_env' : forall M C e1 e1',
|
Lemma preservation'_env' : forall M C e1 e1',
|
||||||
plug C e1 e1'
|
plug C e1 e1'
|
||||||
-> forall t e2 env1 env2, step0 (env1, e1) (env2, e2)
|
-> forall t e2 env1 env2, step1 (env1, e1) (env2, e2)
|
||||||
-> hasty M $0 e1' t
|
-> hasty M $0 e1' t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> compatible M env2.
|
-> compatible M env2.
|
||||||
|
|
@ -1232,7 +1249,7 @@ Module StlcMutable.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Lemma preservation'_env : forall M C e1 e1' t e2 env1 env2,
|
Lemma preservation'_env : forall M C e1 e1' t e2 env1 env2,
|
||||||
step0 (env1, e1) (env2, e2)
|
step1 (env1, e1) (env2, e2)
|
||||||
-> plug C e1 e1'
|
-> plug C e1 e1'
|
||||||
-> hasty M $0 e1' t
|
-> hasty M $0 e1' t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
|
|
@ -1399,44 +1416,49 @@ Module StlcConcur.
|
||||||
|
|
||||||
Definition valuation := fmap var exp.
|
Definition valuation := fmap var exp.
|
||||||
|
|
||||||
Inductive step0 : valuation * exp -> valuation * exp -> Prop :=
|
Inductive step0 : exp -> exp -> Prop :=
|
||||||
| Beta : forall env x e v,
|
| Beta : forall x e v,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, App (Abs x e) v) (env, subst v x e)
|
-> step0 (App (Abs x e) v) (subst v x e)
|
||||||
| Add : forall env n1 n2,
|
| Add : forall n1 n2,
|
||||||
step0 (env, Plus (Const n1) (Const n2)) (env, Const (n1 + n2))
|
step0 (Plus (Const n1) (Const n2)) (Const (n1 + n2))
|
||||||
| FstPair : forall env v1 v2,
|
| FstPair : forall v1 v2,
|
||||||
value v1
|
value v1
|
||||||
-> value v2
|
-> value v2
|
||||||
-> step0 (env, Fst (Pair v1 v2)) (env, v1)
|
-> step0 (Fst (Pair v1 v2)) v1
|
||||||
| SndPair : forall env v1 v2,
|
| SndPair : forall v1 v2,
|
||||||
value v1
|
value v1
|
||||||
-> value v2
|
-> value v2
|
||||||
-> step0 (env, Snd (Pair v1 v2)) (env, v2)
|
-> step0 (Snd (Pair v1 v2)) v2
|
||||||
| MatchInl : forall env v x1 e1 x2 e2,
|
| MatchInl : forall v x1 e1 x2 e2,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, Match (Inl v) x1 e1 x2 e2) (env, subst v x1 e1)
|
-> step0 (Match (Inl v) x1 e1 x2 e2) (subst v x1 e1)
|
||||||
| MatchInr : forall env v x1 e1 x2 e2,
|
| MatchInr : forall v x1 e1 x2 e2,
|
||||||
value v
|
value v
|
||||||
-> step0 (env, Match (Inr v) x1 e1 x2 e2) (env, subst v x2 e2)
|
-> step0 (Match (Inr v) x1 e1 x2 e2) (subst v x2 e2)
|
||||||
| Read : forall env x v,
|
|
||||||
env $? x = Some v
|
|
||||||
-> step0 (env, GetVar x) (env, v)
|
|
||||||
| Overwrite : forall env x v,
|
|
||||||
value v
|
|
||||||
-> step0 (env, SetVar x v) (env $+ (x, v), v)
|
|
||||||
|
|
||||||
(* New case: *)
|
(* New case: *)
|
||||||
| ParDone : forall env v1 v2,
|
| ParDone : forall v1 v2,
|
||||||
value v1
|
value v1
|
||||||
-> value v2
|
-> value v2
|
||||||
-> step0 (env, Par v1 v2) (env, Pair v1 v2).
|
-> step0 (Par v1 v2) (Pair v1 v2).
|
||||||
|
|
||||||
|
Inductive step1 : valuation * exp -> valuation * exp -> Prop :=
|
||||||
|
| Lift : forall env e1 e2,
|
||||||
|
step0 e1 e2
|
||||||
|
-> step1 (env, e1) (env, e2)
|
||||||
|
| Read : forall env x v,
|
||||||
|
env $? x = Some v
|
||||||
|
-> step1 (env, GetVar x) (env, v)
|
||||||
|
| Overwrite : forall env x v,
|
||||||
|
value v
|
||||||
|
-> step1 (env, SetVar x v) (env $+ (x, v), v).
|
||||||
|
|
||||||
Inductive step : valuation * exp -> valuation * exp -> Prop :=
|
Inductive step : valuation * exp -> valuation * exp -> Prop :=
|
||||||
| StepRule : forall C env1 e1 env2 e2 e1' e2',
|
| StepRule : forall C env1 e1 env2 e2 e1' e2',
|
||||||
plug C e1 e1'
|
plug C e1 e1'
|
||||||
-> plug C e2 e2'
|
-> plug C e2 e2'
|
||||||
-> step0 (env1, e1) (env2, e2)
|
-> step1 (env1, e1) (env2, e2)
|
||||||
-> step (env1, e1') (env2, e2').
|
-> step (env1, e1') (env2, e2').
|
||||||
|
|
||||||
Definition trsys_of (env : valuation) (e : exp) := {|
|
Definition trsys_of (env : valuation) (e : exp) := {|
|
||||||
|
|
@ -1503,7 +1525,7 @@ Module StlcConcur.
|
||||||
-> hasty M G e2 t2
|
-> hasty M G e2 t2
|
||||||
-> hasty M G (Par e1 e2) (Prod t1 t2).
|
-> hasty M G (Par e1 e2) (Prod t1 t2).
|
||||||
|
|
||||||
Local Hint Constructors value plug step0 step hasty : core.
|
Local Hint Constructors value plug step0 step1 step hasty : core.
|
||||||
|
|
||||||
Definition compatible (M : fmap var type) (env : valuation) :=
|
Definition compatible (M : fmap var type) (env : valuation) :=
|
||||||
forall x t, M $? x = Some t
|
forall x t, M $? x = Some t
|
||||||
|
|
@ -1613,8 +1635,18 @@ Module StlcConcur.
|
||||||
|
|
||||||
Local Hint Immediate compatible_hasty : core.
|
Local Hint Immediate compatible_hasty : core.
|
||||||
|
|
||||||
Lemma preservation0_exp : forall M env1 e1 env2 e2,
|
Lemma preservation0 : forall M e1 e2,
|
||||||
step0 (env1, e1) (env2, e2)
|
step0 e1 e2
|
||||||
|
-> forall t, hasty M $0 e1 t
|
||||||
|
-> hasty M $0 e2 t.
|
||||||
|
Proof.
|
||||||
|
invert 1; t.
|
||||||
|
Qed.
|
||||||
|
|
||||||
|
Local Hint Resolve preservation0 : core.
|
||||||
|
|
||||||
|
Lemma preservation1_exp : forall M env1 e1 env2 e2,
|
||||||
|
step1 (env1, e1) (env2, e2)
|
||||||
-> forall t, hasty M $0 e1 t
|
-> forall t, hasty M $0 e1 t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> hasty M $0 e2 t.
|
-> hasty M $0 e2 t.
|
||||||
|
|
@ -1622,8 +1654,8 @@ Module StlcConcur.
|
||||||
invert 1; t.
|
invert 1; t.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Lemma preservation0_env : forall M env1 e1 env2 e2,
|
Lemma preservation1_env : forall M env1 e1 env2 e2,
|
||||||
step0 (env1, e1) (env2, e2)
|
step1 (env1, e1) (env2, e2)
|
||||||
-> forall t, hasty M $0 e1 t
|
-> forall t, hasty M $0 e1 t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> compatible M env2.
|
-> compatible M env2.
|
||||||
|
|
@ -1631,12 +1663,12 @@ Module StlcConcur.
|
||||||
invert 1; t.
|
invert 1; t.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Local Hint Resolve preservation0_exp preservation0_env : core.
|
Local Hint Resolve preservation1_exp preservation1_env : core.
|
||||||
|
|
||||||
Lemma preservation'_exp : forall M C e1 e1',
|
Lemma preservation'_exp : forall M C e1 e1',
|
||||||
plug C e1 e1'
|
plug C e1 e1'
|
||||||
-> forall e2 e2' t env1 env2, plug C e2 e2'
|
-> forall e2 e2' t env1 env2, plug C e2 e2'
|
||||||
-> step0 (env1, e1) (env2, e2)
|
-> step1 (env1, e1) (env2, e2)
|
||||||
-> hasty M $0 e1' t
|
-> hasty M $0 e1' t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> hasty M $0 e2' t.
|
-> hasty M $0 e2' t.
|
||||||
|
|
@ -1648,7 +1680,7 @@ Module StlcConcur.
|
||||||
|
|
||||||
Lemma preservation'_env' : forall M C e1 e1',
|
Lemma preservation'_env' : forall M C e1 e1',
|
||||||
plug C e1 e1'
|
plug C e1 e1'
|
||||||
-> forall t e2 env1 env2, step0 (env1, e1) (env2, e2)
|
-> forall t e2 env1 env2, step1 (env1, e1) (env2, e2)
|
||||||
-> hasty M $0 e1' t
|
-> hasty M $0 e1' t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
-> compatible M env2.
|
-> compatible M env2.
|
||||||
|
|
@ -1657,7 +1689,7 @@ Module StlcConcur.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Lemma preservation'_env : forall M C e1 e1' t e2 env1 env2,
|
Lemma preservation'_env : forall M C e1 e1' t e2 env1 env2,
|
||||||
step0 (env1, e1) (env2, e2)
|
step1 (env1, e1) (env2, e2)
|
||||||
-> plug C e1 e1'
|
-> plug C e1 e1'
|
||||||
-> hasty M $0 e1' t
|
-> hasty M $0 e1' t
|
||||||
-> compatible M env1
|
-> compatible M env1
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue