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Wolfram Language
LeanLink
Tutorials
Checking Mathlib with TypeTheory
Exploring Mathlib with LeanLink
An Import Graph for Mathlib
Getting Started with LeanLink
Guides
Lean 4 from the Wolfram Language
Symbols
ImportDOT
LeanApp
LeanBuild
LeanBVar
LeanCallGraph
LeanCompile
LeanConstantInfo
LeanConstant
LeanConst
LeanEnvironment
LeanEvaluate
LeanExport
LeanExportString
LeanExprGraph
LeanExpr
LeanForall
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LeanFVar
LeanGoal
LeanImport
LeanImportString
LeanLam
LeanLet
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LeanLevelMax
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LeanLevelParam
LeanLevelSucc
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LeanListConstants
LeanListTheorems
LeanLitNat
LeanLitStr
LeanLoadEnvironment
LeanMVar
LeanNoValue
LeanProj
LeanSort
LeanState
LeanTactic
LeanTerm
LeanToFunction
LeanToTypeTheory
LeanTruncated
LeanValue
ProofToLean
TypeTheoryToLean
Lean 4 from the Wolfram Language
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f
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`
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embeds the
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4
theorem prover in the Wolfram Language through a native
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y
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k
shim.
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and
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load constants from a compiled module (Mathlib included) or a source string into a
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v
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m
e
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t
of
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values; each term carries its type and proof as symbolic expression trees built from the CIC heads (
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,
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A
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,
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.
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and
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run interactive tactic proofs,
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transpiles a Wolfram
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into checkable Lean,
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and
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exchange proofs with the Wolfram Language proof engine TypeTheory, and
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m
p
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lowers a Lean definition to a
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c
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i
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C
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p
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function.
Importing and exporting
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t
import constants from a compiled Lean module, returning a
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compile a Lean 4 source string into a
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; with
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it can import a built project
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build a Lake project's modules with its pinned toolchain
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evaluate a Lean expression with
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and return its value
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convert a
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back to Lean 4 source
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write a
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to a
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file
Environments and terms
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a collection of named Lean constants; supports
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one Lean constant, with
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properties
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the raw
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record returned by the native shim
Querying a loaded environment
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the type of a constant as a symbolic expression tree
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the proof or definition body of a constant
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full constant info as a
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every constant in a module as an
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load a Lean environment handle for repeated queries
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release a loaded environment handle
Expression heads (CIC)
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a reference to a declared constant at given universe levels
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p
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function application
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/ dependent function (arrow) type
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a free variable (local hypothesis or parameter)
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a metavariable (unresolved placeholder)
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a universe (
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a natural-number literal
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a string literal
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a structure-field projection
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marks a constant with no body (axiom, opaque)
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marks an expression cut off at the depth limit
Universe levels
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level 0, the universe of
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the successor of a level
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the maximum of two levels
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the impredicative max (collapses to 0)
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a named universe parameter (
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)
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a universe metavariable
Interactive proofs
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open a theorem as a proof goal; holds
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a tactic, applied as
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a single goal, with
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Transpiling Wolfram proofs
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transpile a Wolfram
P
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b
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into a checkable
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The TypeTheory proof engine
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T
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import Lean constants into the Wolfram Language proof engine
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T
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, whose own kernel checks them again
T
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T
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T
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a
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write a TypeTheory proof as Lean source, for Lean's kernel to check
Compiling Lean to native code
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T
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F
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c
t
i
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n
convert a
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into a
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with
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arguments
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C
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p
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compile a
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(or whole environment) via
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C
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Out-of-process project queries
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expression graph for a constant, computed by a Lean subprocess
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l
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call / dependency graph for a constant, via subprocess
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list a project's theorems via subprocess
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import a DOT digraph file as a styled
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