74ffa1e413
This PR removes `Lean.Data.HashMap` and `HashSet`. These have been deprecated for 6 months, replaced by `Std.Data.HashMap` and `HashSet`.
76 lines
1.9 KiB
Text
76 lines
1.9 KiB
Text
import Std.Data.HashMap
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open Lean
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/--
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A circuit node declaration. These are not recursive but instead contain indices into an `Env`.
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-/
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inductive Decl where
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/--
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A node with a constant output value.
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-/
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| const (b : Bool)
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/--
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An input node to the circuit.
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-/
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| atom (idx : Nat)
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/--
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An AIG gate with configurable input nodes and polarity. `l` and `r` are the
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input node indices while `linv` and `rinv` say whether there is an inverter on
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the left or right input.
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-/
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| gate (l r : Nat) (linv rinv : Bool)
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deriving BEq, Hashable, DecidableEq
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/--
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A cache that is valid with respect to some `Array Decl`.
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-/
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abbrev Cache (_decls : Array Decl) := Std.HashMap Decl Nat
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/--
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Lookup a `decl` in a `cache`.
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If this returns `some i`, `Cache.find?_poperty` can be used to demonstrate: `decls[i] = decl`.
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-/
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@[irreducible]
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def Cache.find? (cache : Cache decls) (decl : Decl) : Option Nat :=
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match cache[decl]? with
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| some hit =>
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if h1:hit < decls.size then
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if decls[hit]'h1 = decl then
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some hit
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else
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none
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else
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none
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| none => none
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/--
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This states that all indices, found in a `Cache` that is valid with respect to some `decls`,
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are within bounds of `decls`.
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-/
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theorem Cache.find?_bounds {decls : Array Decl} {idx : Nat} (c : Cache decls) (decl : Decl)
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(h : c.find? decl = some idx) : idx < decls.size := by
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unfold find? at h
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split at h
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. split at h
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. split at h
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. injection h
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omega
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. contradiction
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. contradiction
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. contradiction
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/--
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This states that if `Cache.find? decl` returns `some i`, `decls[i] = decl`, holds.
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-/
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theorem Cache.find?_property {decls : Array Decl} {idx : Nat} (c : Cache decls) (decl : Decl)
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(h : c.find? decl = some idx) : decls[idx]'(Cache.find?_bounds c decl h) = decl := by
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unfold find? at h
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split at h
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. split at h
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. split at h
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. injection h
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subst idx; assumption
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. contradiction
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. contradiction
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. contradiction
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