Merge pull request #152 from HEPLean/informal_defs

feat: Add informal_definition and informal_lemma

.github/workflows/docs.yml

@@ -1,18 +1,18 @@
-on: 
-  push: 
-    branches: 
+on:
+  push:
+    branches:
       - master
 
 name: Build and deploy documentation
 
 # borrowed from https://github.com/teorth/pfr/blob/master/.github/workflows/push.yml
-permissions: 
+permissions:
   contents: read
   pages: write
   id-token: write
 
-jobs: 
-  build_project: 
+jobs:
+  build_project:
     runs-on: ubuntu-latest
     name: Build project
     steps:
@@ -20,7 +20,7 @@ jobs:
         uses: actions/checkout@v4
         with:
           fetch-depth: 0
-      
+
       ##################
       # Remove this section if you don't want docs to be made
       - name: Install elan
@@ -53,13 +53,14 @@ jobs:
           key: MathlibDoc-${{ hashFiles('lake-manifest.json') }}
           restore-keys: |
             MathlibDoc-
-      
+
       - name: Build documentation
         run: lake -Kenv=dev build HepLean:docs
-      
-      - name: make TODO list 
-        run : lake exe find_TODOs mkFile 
 
+      - name: make TODO list
+        run : lake exe find_TODOs mkFile
+      - name: make list of informal proofs and lemmas
+        run : lake exe informal mkFile
       - name: Copy documentation to `docs/docs`
         run: |
           mv .lake/build/doc docs/docs
@@ -71,7 +72,7 @@ jobs:
           working-directory: docs
           ruby-version: "3.1" # Not needed with a .ruby-version file
           bundler-cache: true # runs 'bundle install' and caches installed gems automatically
-    
+
 
       - name: Bundle website
         working-directory: docs
@@ -85,6 +86,3 @@ jobs:
       - name: Deploy to GitHub Pages
         id: deployment
         uses: actions/deploy-pages@v1
-
-
-

HepLean.lean

@@ -61,6 +61,7 @@ import HepLean.FlavorPhysics.CKMMatrix.StandardParameterization.StandardParamete
 import HepLean.Mathematics.LinearMaps
 import HepLean.Mathematics.SO3.Basic
 import HepLean.Meta.AllFilePaths
+import HepLean.Meta.Informal
 import HepLean.Meta.TransverseTactics
 import HepLean.SpaceTime.Basic
 import HepLean.SpaceTime.CliffordAlgebra
@@ -82,6 +83,7 @@ import HepLean.SpaceTime.LorentzVector.LorentzAction
 import HepLean.SpaceTime.LorentzVector.NormOne
 import HepLean.SpaceTime.MinkowskiMetric
 import HepLean.SpaceTime.SL2C.Basic
+import HepLean.SpaceTime.WeylFermion.Basic
 import HepLean.StandardModel.Basic
 import HepLean.StandardModel.HiggsBoson.Basic
 import HepLean.StandardModel.HiggsBoson.GaugeAction

HepLean/Meta/Informal.lean

@@ -0,0 +1,157 @@
+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license.
+Authors: Joseph Tooby-Smith
+-/
+import Lean
+/-!
+
+## Informal definitions and lemmas
+
+-/
+open Lean Elab System
+
+/-! TODO: Derive a means to extract informal definitions and informal lemmas. -/
+
+/-! TODO: Can likely make this a bona-fide command. -/
+
+/-- The structure representating an informal definition. -/
+structure InformalDefinition where
+  /-- The name of the informal definition. This is autogenerated. -/
+  name : Name
+  /-- The mathematical description of the definition. -/
+  math : String
+  /-- The physics description of the definition. -/
+  physics : String
+  /-- References. -/
+  ref : String
+  /-- The names of top-level commands we expect this definition to depend on. -/
+  dependencies : List Name
+
+/-- The structure representating an informal proof. -/
+structure InformalLemma where
+  /-- The name of the informal lemma. This is autogenerated. -/
+  name : Name
+  /-- The mathematical description of the lemma. -/
+  math : String
+  /-- The physics description of the lemma. -/
+  physics : String
+  /-- A description of the proof. -/
+  proof : String
+  /-- References. -/
+  ref : String
+  /-- The names of top-level commands we expect this lemma to depend on. -/
+  dependencies : List Name
+
+namespace Informal
+
+/-- The Parser.Category we will use for assignments. -/
+declare_syntax_cat informalAssignment
+
+/-- The syntax describing an informal assignment of `ident` to a string. -/
+syntax (name := informalAssignment) ident ":≈" str : informalAssignment
+
+/-- The syntax describing an informal assignment of `ident` to a list. -/
+syntax (name := informalAssignmentDeps) ident ":≈" "[" sepBy(term, ",") "]" : informalAssignment
+
+/-- The syntax for the command informal_definition. -/
+syntax (name := informal_definition) "informal_definition " ident
+  " where " (colGt informalAssignment)* : command
+
+/-- The macro turning `informal_definition ... where ...` into a definition. -/
+macro "informal_definition " name:ident " where " assignments:informalAssignment* : command => do
+  let mut math_def? : Option (TSyntax `term) := none
+  let mut physics_def? : Option (TSyntax `term) := none
+  let mut ref_def? : Option (TSyntax `term) := none
+  let mut dep_def? : Option (TSyntax `term) := none
+  for assignment in assignments do
+    match assignment with
+    | `(informalAssignment| physics :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for physics"
+      physics_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignment| math :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for math"
+      math_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignment| ref :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for ref"
+      ref_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignmentDeps| deps :≈ [ $deps,* ]) =>
+      dep_def? := some (← `([ $deps,* ]))
+    | _ => Macro.throwError "invalid assignment syntax in informal_definition"
+  unless math_def?.isSome do
+    Macro.throwError "A 'math' assignments is required"
+  `(
+/-- An informal definition. -/
+def $name : InformalDefinition := {
+  name := $(Lean.quote name.getId),
+  physics := $(physics_def?.getD (← `("No physics description provided"))),
+  math := $(math_def?.getD (panic! "math not assigned")),
+  ref := $(ref_def?.getD (← `("No references provided"))),
+  dependencies := $(dep_def?.getD (← `([])))
+    })
+
+/-- The syntax for the command `informal_lemma`. -/
+syntax (name := informal_lemma) "informal_lemma " ident " where "
+  (colGt informalAssignment)* : command
+
+/-- The macro turning `informal_lemma ... where ...` into a definition. -/
+macro "informal_lemma " name:ident " where " assignments:informalAssignment* : command => do
+  let mut math_def? : Option (TSyntax `term) := none
+  let mut physics_def? : Option (TSyntax `term) := none
+  let mut proof_def? : Option (TSyntax `term) := none
+  let mut ref_def? : Option (TSyntax `term) := none
+  let mut dep_def? : Option (TSyntax `term) := none
+  for assignment in assignments do
+    match assignment with
+    | `(informalAssignment| physics :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for physics"
+      physics_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignment| math :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for math"
+      math_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignment| proof :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for proof"
+      proof_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignment| ref :≈ $val:str) =>
+      let some strVal := val.raw.isStrLit? | Macro.throwError "Expected string literal for ref"
+      ref_def? := some (← `($(Lean.quote strVal)))
+    | `(informalAssignmentDeps| deps :≈ [ $deps,* ]) =>
+      dep_def? := some (← `([ $deps,* ]))
+    | _ => Macro.throwError "invalid assignment syntax"
+  unless math_def?.isSome do
+    Macro.throwError "A 'math' assignments is required"
+  `(
+
+/-- An informal lemma. -/
+def $name : InformalLemma := {
+  name := $(Lean.quote name.getId),
+  physics := $(physics_def?.getD (← `("No physics description provided"))),
+  math := $(math_def?.getD (panic! "math not assigned")),
+  proof := $(proof_def?.getD (← `("No proof description provided"))),
+  ref := $(ref_def?.getD (← `("No references provided"))),
+  dependencies := $(dep_def?.getD (← `([])))
+    })
+
+/-- Is true if and only if a `ConstantInfo` corresponds to an `InformalLemma` or a
+  `InformalDefinition`. -/
+def isInformal (c : ConstantInfo) : Bool :=
+  match c with
+  | ConstantInfo.defnInfo c =>
+    if c.type.isAppOf ``InformalDefinition ∨ c.type.isAppOf ``InformalLemma then true else false
+  | _ => false
+
+/-- Is true if and only if a `ConstantInfo` corresponds to an `InformalLemma`. -/
+def isInformalLemma (c : ConstantInfo) : Bool :=
+  match c with
+  | ConstantInfo.defnInfo c =>
+    if c.type.isAppOf ``InformalLemma then true else false
+  | _ => false
+
+/-- Is true if and only if a `ConstantInfo` corresponds to an `InformalDefinition`. -/
+def isInformalDef (c : ConstantInfo) : Bool :=
+  match c with
+  | ConstantInfo.defnInfo c =>
+    if c.type.isAppOf ``InformalDefinition then true else false
+  | _ => false
+
+end Informal

HepLean/SpaceTime/WeylFermion/Basic.lean

@@ -0,0 +1,61 @@
+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joseph Tooby-Smith
+-/
+import HepLean.Meta.Informal
+/-!
+
+# Weyl fermions
+
+-/
+
+/-!
+
+## The definition of Weyl fermion vector spaces.
+
+-/
+
+informal_definition leftHandedWeylFermion where
+  math :≈ "The vector space ℂ^2 carrying the fundamental representation of SL(2,C)."
+  ref :≈ "https://particle.physics.ucdavis.edu/modernsusy/slides/slideimages/spinorfeynrules.pdf"
+
+informal_definition rightHandedWeylFermion where
+  math :≈ "The vector space ℂ^2 carrying the conjguate representation of SL(2,C)."
+  ref :≈ "https://particle.physics.ucdavis.edu/modernsusy/slides/slideimages/spinorfeynrules.pdf"
+
+informal_definition altLeftHandedWeylFermion where
+  math :≈ "The vector space ℂ^2 carrying the representation of SL(2,C) given by
+    M → (M⁻¹)ᵀ."
+  ref :≈ "https://particle.physics.ucdavis.edu/modernsusy/slides/slideimages/spinorfeynrules.pdf"
+
+informal_definition altRightHandedWeylFermion where
+  math :≈ "The vector space ℂ^2 carrying the representation of SL(2,C) given by
+    M → (M⁻¹)^†."
+  ref :≈ "https://particle.physics.ucdavis.edu/modernsusy/slides/slideimages/spinorfeynrules.pdf"
+
+/-!
+
+## Equivalences between Weyl fermion vector spaces.
+
+-/
+
+informal_definition leftHandedWeylFermionAltEquiv where
+  math :≈ "The linear equiv between leftHandedWeylFermion and altLeftHandedWeylFermion given
+    by multiplying an element of rightHandedWeylFermion by the matrix `εᵃ⁰ᵃ¹ = !![0, 1; -1, 0]]`."
+  deps :≈ [`leftHandedWeylFermion, `altLeftHandedWeylFermion]
+
+informal_lemma leftHandedWeylFermionAltEquiv_equivariant where
+  math :≈ "The linear equiv leftHandedWeylFermionAltEquiv is equivariant with respect to the
+    action of SL(2,C) on leftHandedWeylFermion and altLeftHandedWeylFermion."
+  deps :≈ [`leftHandedWeylFermionAltEquiv]
+
+informal_definition rightHandedWeylFermionAltEquiv where
+  math :≈ "The linear equiv between rightHandedWeylFermion and altRightHandedWeylFermion given
+    by multiplying an element of rightHandedWeylFermion by the matrix `εᵃ⁰ᵃ¹ = !![0, 1; -1, 0]]`"
+  deps :≈ [`rightHandedWeylFermion, `altRightHandedWeylFermion]
+
+informal_lemma rightHandedWeylFermionAltEquiv_equivariant where
+  math :≈ "The linear equiv rightHandedWeylFermionAltEquiv is equivariant with respect to the
+    action of SL(2,C) on rightHandedWeylFermion and altRightHandedWeylFermion."
+  deps :≈ [`rightHandedWeylFermionAltEquiv]

HepLean/StandardModel/HiggsBoson/Basic.lean

@@ -11,6 +11,7 @@ import Mathlib.Geometry.Manifold.VectorBundle.SmoothSection
 import Mathlib.Geometry.Manifold.Instances.Real
 import Mathlib.Analysis.InnerProductSpace.Basic
 import Mathlib.Geometry.Manifold.ContMDiff.Product
+import HepLean.Meta.Informal
 /-!
 
 # The Higgs field
@@ -173,6 +174,12 @@ def ofReal (a : ℝ) : HiggsField := (HiggsVec.ofReal a).toField
 /-- The higgs field which is all zero. -/
 def zero : HiggsField := ofReal 0
 
+informal_lemma zero_is_zero_section where
+  physics :≈ "The zero Higgs field is the zero section of the Higgs bundle."
+  math :≈ "The HiggsField `zero` defined by `ofReal 0`
+    is the constant zero-section of the bundle `HiggsBundle`."
+  deps :≈ [`StandardModel.HiggsField.zero]
+
 end HiggsField
 
 end

HepLean/StandardModel/HiggsBoson/GaugeAction.lean

@@ -190,6 +190,14 @@ theorem rotate_fst_real_snd_zero (φ : HiggsVec) :
   · simp only [Fin.mk_one, Fin.isValue, Pi.smul_apply, Function.comp_apply, cons_val_one, head_cons,
       tail_cons, smul_zero]
 
+informal_lemma stablity_group where
+  physics :≈ "The Higgs boson breaks electroweak symmetry down to the electromagnetic force."
+  math :≈ "The stablity group of the action of `rep` on `![0, Complex.ofReal ‖φ‖]`,
+    for non-zero `‖φ‖` is the `SU(3) x U(1)` subgroup of
+    `gaugeGroup := SU(3) x SU(2) x U(1)` with the embedding given by
+    `(g, e^{i θ}) ↦ (g, diag (e ^ {3 * i θ}, e ^ {- 3 * i θ}), e^{i θ})`."
+  deps :≈ [`StandardModel.HiggsVec, `StandardModel.HiggsVec.rep]
+
 end HiggsVec
 
 /-! TODO: Define the global gauge action on HiggsField. -/

HepLean/StandardModel/HiggsBoson/Potential.lean

@@ -5,6 +5,7 @@ Authors: Joseph Tooby-Smith
 -/
 import Mathlib.Algebra.QuadraticDiscriminant
 import HepLean.StandardModel.HiggsBoson.PointwiseInnerProd
+import HepLean.Meta.Informal
 /-!
 # The potential of the Higgs field
 
@@ -314,6 +315,12 @@ lemma isBounded_of_𝓵_pos (h : 0 < P.𝓵) : P.IsBounded := by
   have h2' := h2 φ x
   linarith
 
+informal_lemma isBounded_iff_of_𝓵_zero where
+  physics :≈ "When there is no quartic coupling, the potential is bounded iff the mass squared is
+    non-positive."
+  math :≈ "For `P : Potential` then P.IsBounded if and only if P.μ2 ≤ 0.
+    That is to say `- P.μ2 * ‖φ‖_H ^ 2 x` is bounded below if and only if `P.μ2 ≤ 0`."
+
 /-!
 
 ## Minimum and maximum

lakefile.toml

@@ -64,6 +64,10 @@ srcDir = "scripts"
 name = "free_simps"
 srcDir = "scripts/MetaPrograms"
 
+[[lean_exe]]
+name = "informal"
+srcDir = "scripts/MetaPrograms"
+
 # -- Optional inclusion of openAI_doc_check. Needs `llm` above.
 #[[lean_exe]]
 #name = "openAI_doc_check"

scripts/MetaPrograms/informal.lean

@@ -0,0 +1,188 @@
+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license.
+Authors: Joseph Tooby-Smith
+-/
+import Batteries.Lean.HashSet
+import Lean
+import Mathlib.Lean.Expr.Basic
+import Mathlib.Lean.CoreM
+import HepLean.Meta.Informal
+import ImportGraph.RequiredModules
+/-!
+
+# Extracting information about informal definitions and lemmas
+
+-/
+
+open Lean System Meta
+
+def getConst (imp : Import) : IO (Array (Import × ConstantInfo)) := do
+  let mFile ← findOLean imp.module
+  let (modData, _) ← readModuleData mFile
+  pure (modData.constants.map (fun c => (imp, c)))
+
+def getLineNumber (c : Name) : MetaM Nat := do
+  match ← findDeclarationRanges? c  with
+  | some decl => pure decl.range.pos.line
+  | none => panic! s!"{c} is a declaration without position"
+
+def getModule (c : Name) : MetaM Name := do
+  match Lean.Environment.getModuleFor? (← getEnv) c with
+  | some mod => pure mod
+  | none => panic! s!"{c} is a declaration without position"
+
+def depToString (d : Name) : MetaM String := do
+  let lineNo ← getLineNumber d
+  let mod ← getModule d
+  pure s!"    * {d}: ./{mod.toString.replace "." "/" ++ ".lean"}:{lineNo}"
+
+def depToWebString (d : Name) : MetaM String := do
+  let lineNo ← getLineNumber d
+  let mod ← getModule d
+  let webPath := "https://github.com/HEPLean/HepLean/blob/master/"++
+    (mod.toString.replace "." "/") ++ ".lean"
+  pure s!"    * [{d}]({webPath}#L{lineNo})"
+
+unsafe def informalLemmaToString (c : Import × ConstantInfo) : MetaM String := do
+  let lineNo ← getLineNumber c.2.name
+  let informalLemma ←
+    match c.2 with
+    | ConstantInfo.defnInfo c =>
+        Lean.Meta.evalExpr' InformalLemma ``InformalLemma c.value
+    | _ => panic! "This should not happen"
+  let dep ← informalLemma.dependencies.mapM fun d => depToString d
+  pure s!"
+Informal lemma: {informalLemma.name}
+- ./{c.1.module.toString.replace "." "/" ++ ".lean"}:{lineNo}
+- Math description: {informalLemma.math}
+- Physics description: {informalLemma.physics}
+- Proof description: {informalLemma.proof}
+- References: {informalLemma.ref}
+- Dependencies:\n{String.intercalate "\n" dep}"
+
+unsafe def informalLemmaToWebString (c : Import × ConstantInfo) : MetaM String := do
+  let lineNo ← getLineNumber c.2.name
+  let informalLemma ←
+    match c.2 with
+    | ConstantInfo.defnInfo c =>
+        Lean.Meta.evalExpr' InformalLemma ``InformalLemma c.value
+    | _ => panic! "This should not happen"
+  let dep ← informalLemma.dependencies.mapM fun d => depToWebString d
+  let webPath := "https://github.com/HEPLean/HepLean/blob/master/"++
+    (c.1.module.toString.replace "." "/") ++ ".lean"
+  pure s!"
+**Informal lemma**: [{informalLemma.name}]({webPath}#L{lineNo}) :=
+  *{informalLemma.math}*
+- Physics description: {informalLemma.physics}
+- Proof description: {informalLemma.proof}
+- References: {informalLemma.ref}
+- Dependencies:\n{String.intercalate "\n" dep}"
+
+unsafe def informalDefToString (c : Import × ConstantInfo) : MetaM String := do
+  let lineNo ← getLineNumber c.2.name
+  let informalDef ←
+    match c.2 with
+    | ConstantInfo.defnInfo c =>
+        Lean.Meta.evalExpr' InformalDefinition ``InformalDefinition c.value
+    | _ => panic! "This should not happen"
+  let dep ← informalDef.dependencies.mapM fun d => depToString d
+  pure s!"
+Informal def: {informalDef.name}
+- ./{c.1.module.toString.replace "." "/" ++ ".lean"}:{lineNo}
+- Math description: {informalDef.math}
+- Physics description: {informalDef.physics}
+- References: {informalDef.ref}
+- Dependencies:\n{String.intercalate "\n" dep}"
+
+unsafe def informalDefToWebString (c : Import × ConstantInfo) : MetaM String := do
+  let lineNo ← getLineNumber c.2.name
+  let informalDef ←
+    match c.2 with
+    | ConstantInfo.defnInfo c =>
+        Lean.Meta.evalExpr' InformalDefinition ``InformalDefinition c.value
+    | _ => panic! "This should not happen"
+  let dep ← informalDef.dependencies.mapM fun d => depToWebString d
+  let webPath := "https://github.com/HEPLean/HepLean/blob/master/"++
+    (c.1.module.toString.replace "." "/") ++ ".lean"
+  pure s!"
+**Informal def**: [{informalDef.name}]({webPath}#L{lineNo}) :=
+  *{informalDef.math}*
+- Physics description: {informalDef.physics}
+- References: {informalDef.ref}
+- Dependencies:\n{String.intercalate "\n" dep}"
+
+unsafe def informalToString (c : Import × ConstantInfo) : MetaM String := do
+  if Informal.isInformalLemma c.2 then
+    informalLemmaToString c
+  else if Informal.isInformalDef c.2 then
+    informalDefToString c
+  else
+    pure ""
+
+unsafe def informalToWebString (c : Import × ConstantInfo) : MetaM String := do
+  if Informal.isInformalLemma c.2 then
+    informalLemmaToWebString c
+  else if Informal.isInformalDef c.2 then
+    informalDefToWebString c
+  else
+    pure ""
+
+def informalFileHeader : String := s!"
+# Informal definitions and lemmas
+
+This file is automatically generated using `informal_lemma` and `informal_definition` commands
+appearing in the raw Lean code of HepLean.
+
+There is an implicit invitation to the reader to contribute to the formalization of
+ informal definitions and lemmas. You may also wish to contribute to HepLean by including
+ informal definitions and lemmas in the raw Lean code, especially if you do not have a
+ background in Lean.
+
+"
+
+unsafe def importToString (i : Import) : MetaM String := do
+  let constants ← getConst i
+  let constants := constants.filter (fun c => ¬ Lean.Name.isInternalDetail c.2.name)
+  let informalConst := constants.filter fun c => Informal.isInformal c.2
+  let informalConstLineNo ← informalConst.mapM fun c => getLineNumber c.2.name
+  let informalConstWithLineNo := informalConst.zip informalConstLineNo
+  let informalConstWithLineNoSort := informalConstWithLineNo.qsort (fun a b => a.2 < b.2)
+  let informalConst := informalConstWithLineNoSort.map (fun c => c.1)
+  let informalPrint ← (informalConst.mapM informalToString).run'
+  if informalPrint.isEmpty then
+    pure ""
+  else
+    pure ("\n\n" ++ i.module.toString ++ "\n" ++ String.intercalate "\n\n" informalPrint.toList)
+
+unsafe def importToWebString (i : Import) : MetaM String := do
+  let constants ← getConst i
+  let constants := constants.filter (fun c => ¬ Lean.Name.isInternalDetail c.2.name)
+  let informalConst := constants.filter fun c => Informal.isInformal c.2
+  let informalConstLineNo ← informalConst.mapM fun c => getLineNumber c.2.name
+  let informalConstWithLineNo := informalConst.zip informalConstLineNo
+  let informalConstWithLineNoSort := informalConstWithLineNo.qsort (fun a b => a.2 < b.2)
+  let informalConst := informalConstWithLineNoSort.map (fun c => c.1)
+  let informalPrint ← (informalConst.mapM informalToWebString).run'
+  if informalPrint.isEmpty then
+    pure ""
+  else
+    pure ("\n\n## " ++ i.module.toString ++ "\n" ++ String.intercalate "\n\n" informalPrint.toList)
+unsafe def main (args : List String) : IO Unit := do
+  initSearchPath (← findSysroot)
+  let mods : Name := `HepLean
+  let imp : Import := {module := mods}
+  let mFile ← findOLean imp.module
+  unless (← mFile.pathExists) do
+        throw <| IO.userError s!"object file '{mFile}' of module {imp.module} does not exist"
+  let (hepLeanMod, _) ← readModuleData mFile
+  let imports := hepLeanMod.imports.filter (fun c => c.module ≠ `Init)
+  let importString ← CoreM.withImportModules #[`HepLean] (imports.mapM importToString).run'
+  IO.println (String.intercalate "" importString.toList)
+  /- Writing out informal file. -/
+  let fileOut : System.FilePath := {toString := "./docs/Informal.md"}
+  if "mkFile" ∈ args then
+    let importWebString ← CoreM.withImportModules #[`HepLean] (imports.mapM importToWebString).run'
+    let out := String.intercalate "\n" importWebString.toList
+    IO.println (s!"Informal file made.")
+    IO.FS.writeFile fileOut (informalFileHeader ++ out)