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  1. Jon Awbrey @[email protected] ·

    Propositions As Types Analogy • 1
    • inquiryintoinquiry.com/2013/01

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    Proof Hint ∶ Proof ∶ Proposition
    ∷
    Untyped Term ∶ Typed Term ∶ Type

    or

    Proof Hint ∶ Untyped Term
    ∷
    Proof ∶ Typed Term
    ∷
    Proposition ∶ Type

    See my working notes on the Propositions As Types Analogy —
    • oeis.org/wiki/Propositions_As_

    #Mathematics #CategoryTheory #ProofTheory #TypeTheory
    #Logic #Analogy #Isomorphism #PropositionalCalculus
    #CombinatorCalculus #CombinatoryLogic #LambdaCalculus
    #Peirce #LogicalGraphs #GraphTheory #RelationTheory

    #relationtheory #graphtheory #logicalgraphs #peirce #lambdacalculus #combinatorylogic
  2. Jon Awbrey @[email protected] ·

    Propositions As Types Analogy • 1
    • inquiryintoinquiry.com/2013/01

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    Proof Hint ∶ Proof ∶ Proposition
    ∷
    Untyped Term ∶ Typed Term ∶ Type

    or

    Proof Hint ∶ Untyped Term
    ∷
    Proof ∶ Typed Term
    ∷
    Proposition ∶ Type

    See my working notes on the Propositions As Types Analogy —
    • oeis.org/wiki/Propositions_As_

    #Mathematics #CategoryTheory #ProofTheory #TypeTheory
    #Logic #Analogy #Isomorphism #PropositionalCalculus
    #CombinatorCalculus #CombinatoryLogic #LambdaCalculus
    #Peirce #LogicalGraphs #GraphTheory #RelationTheory

    #relationtheory #graphtheory #logicalgraphs #peirce #lambdacalculus #combinatorylogic
  3. Jon Awbrey @[email protected] ·

    Propositions As Types Analogy • 1
    • inquiryintoinquiry.com/2013/01

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    Proof Hint ∶ Proof ∶ Proposition
    ∷
    Untyped Term ∶ Typed Term ∶ Type

    or

    Proof Hint ∶ Untyped Term
    ∷
    Proof ∶ Typed Term
    ∷
    Proposition ∶ Type

    See my working notes on the Propositions As Types Analogy —
    • oeis.org/wiki/Propositions_As_

    #Mathematics #CategoryTheory #ProofTheory #TypeTheory
    #Logic #Analogy #Isomorphism #PropositionalCalculus
    #CombinatorCalculus #CombinatoryLogic #LambdaCalculus
    #Peirce #LogicalGraphs #GraphTheory #RelationTheory

    #relationtheory #graphtheory #logicalgraphs #peirce #lambdacalculus #combinatorylogic
  4. Jon Awbrey @[email protected] ·

    Propositions As Types Analogy • 1
    • inquiryintoinquiry.com/2013/01

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    Proof Hint ∶ Proof ∶ Proposition
    ∷
    Untyped Term ∶ Typed Term ∶ Type

    or

    Proof Hint ∶ Untyped Term
    ∷
    Proof ∶ Typed Term
    ∷
    Proposition ∶ Type

    See my working notes on the Propositions As Types Analogy —
    • oeis.org/wiki/Propositions_As_

    #Mathematics #CategoryTheory #ProofTheory #TypeTheory
    #Logic #Analogy #Isomorphism #PropositionalCalculus
    #CombinatorCalculus #CombinatoryLogic #LambdaCalculus
    #Peirce #LogicalGraphs #GraphTheory #RelationTheory

    #mathematics #categorytheory #prooftheory #typetheory #logic #analogy
  5. Jon Awbrey @[email protected] ·

    Propositions As Types Analogy • 1
    • inquiryintoinquiry.com/2013/01

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    Proof Hint ∶ Proof ∶ Proposition
    ∷
    Untyped Term ∶ Typed Term ∶ Type

    or

    Proof Hint ∶ Untyped Term
    ∷
    Proof ∶ Typed Term
    ∷
    Proposition ∶ Type

    See my working notes on the Propositions As Types Analogy —
    • oeis.org/wiki/Propositions_As_

    #Mathematics #CategoryTheory #ProofTheory #TypeTheory
    #Logic #Analogy #Isomorphism #PropositionalCalculus
    #CombinatorCalculus #CombinatoryLogic #LambdaCalculus
    #Peirce #LogicalGraphs #GraphTheory #RelationTheory

    #relationtheory #graphtheory #logicalgraphs #peirce #lambdacalculus #combinatorylogic
  6. Inquiry Into Inquiry @[email protected] ·

    Propositions As Types Analogy • 1

    Re: R.J. Lipton • Mathematical Tricks

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy.

    And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    See my working notes on the Propositions As Types Analogy for more information.

    #Animata #CSPeirce #CombinatorCalculus #CombinatoryLogic #CurryHowardIsomorphism #GraphTheory #LambdaCalculus #Logic #LogicalGraphs #Mathematics #ProofTheory #PropositionsAsTypesAnalogy #TypeTheory

    #animata #cspeirce #combinatorcalculus #combinatorylogic #curryhowardisomorphism #graphtheory