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Memory.v
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Memory.v
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Module Type Memory.
Parameter adr : Set.
Parameter first : adr.
Parameter next : adr -> adr.
Parameter Mem : Type.
Parameter empty : Mem.
Parameter get : adr -> Mem -> nat.
Parameter set : adr -> nat -> Mem -> Mem.
Parameter free : adr -> Mem -> Mem.
Parameter isFreeFrom : adr -> Mem -> Prop.
Axiom isFreeFrom_free : forall (r : adr) (m : Mem) (n : nat), isFreeFrom r m -> free r (set r n m) = m.
Axiom isFreeFrom_set : forall (r : adr) (m : Mem) (n : nat), isFreeFrom r m -> isFreeFrom (next r) (set r n m).
Axiom get_set : forall (r : adr) (m : Mem) (n : nat), get r (set r n m) = n.
Axiom isFreeFrom_first : isFreeFrom first empty.
End Memory.
Inductive lta T n (r : T) : T -> Prop :=
| lea_self : lta T n r (n r)
| lea_next r' : lta T n r r' -> lta T n r (n r').
(* Extended memory model with additional axioms that are only used for
compiling variables. *)
Module Type MemoryExt.
Include Memory.
Axiom get_set' : forall (r : adr) (r' : adr) (m : Mem) (n : nat),
r <> r' -> get r (set r' n m) = get r m.
Infix "<" := (lta adr next).
Hint Constructors lta.
Axiom next_fresh : forall (r r' : adr), r < r' -> r <> r'.
End MemoryExt.